changeset 71:7e9d1cfcc562

NaCl: added ed25519 public key message signing implementation
author Ivo Smits <Ivo@UCIS.nl>
date Fri, 01 Nov 2013 00:07:36 +0100
parents c22be6c412de
children b7d981ccd434
files NaCl/crypto_hash/sha512.cs NaCl/crypto_sign/ed25519.cs NaCl/crypto_sign/edwards25519sha512batch.cs UCIS.Core.csproj
diffstat 4 files changed, 2738 insertions(+), 2 deletions(-) [+]
line wrap: on
line diff
--- a/NaCl/crypto_hash/sha512.cs	Wed Oct 30 15:32:58 2013 +0100
+++ b/NaCl/crypto_hash/sha512.cs	Fri Nov 01 00:07:36 2013 +0100
@@ -15,6 +15,11 @@
   0x5b,0xe0,0xcd,0x19,0x13,0x7e,0x21,0x79
 };*/
 
+		public static unsafe void crypto_hash(Byte[] outv, Byte[] inv, int inlen) {
+			if (outv.Length < 64) throw new ArgumentException("outv.Length < 64");
+			if (inv.Length < inlen) throw new ArgumentException("inv.Length < inlen");
+			fixed (Byte* outp = outv, inp = inv) crypto_hash(outp, inp, (UInt64)inlen);
+		}
 		public static unsafe void crypto_hash(Byte* outp, Byte* inp, UInt64 inlen) {
 //			Byte[] h = new Byte[64];
 			Byte[] padded = new Byte[256];
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/NaCl/crypto_sign/ed25519.cs	Fri Nov 01 00:07:36 2013 +0100
@@ -0,0 +1,2732 @@
+using System;
+using System.Text;
+
+namespace UCIS.NaCl.crypto_sign {
+	public static class ed25519 {
+		public const int SECRETKEYBYTES = 64;
+		public const int PUBLICKEYBYTES = 32;
+		public const int SEEDBYTES = 32;
+		public const int BYTES = 64;
+
+		unsafe struct fe {
+			fixed Int32 v[10];
+			public int this[int index] {
+				get { fixed (Int32* vp = v) return vp[index]; }
+				set { fixed (Int32* vp = v) vp[index] = value; }
+			}
+			public override string ToString() {
+				return String.Format("{0}, {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}", this[0], this[1], this[2], this[3], this[4], this[5], this[6], this[7], this[8], this[9]);
+			}
+		}
+		struct ge_precomp {
+			public fe yplusx;
+			public fe yminusx;
+			public fe xy2d;
+			public ge_precomp(Int32[] data, int offset)
+				: this() {
+				yplusx = fe_unpack(offset + 0 * 10, data);
+				yminusx = fe_unpack(offset + 1 * 10, data);
+				xy2d = fe_unpack(offset + 2 * 10, data);
+			}
+		}
+		struct ge_p1p1 {
+			public fe X;
+			public fe Y;
+			public fe Z;
+			public fe T;
+		}
+		struct ge_p2 {
+			public fe X;
+			public fe Y;
+			public fe Z;
+		}
+		struct ge_p3 {
+			public fe X;
+			public fe Y;
+			public fe Z;
+			public fe T;
+		}
+
+		static fe fe_unpack(int offset, Int32[] data) {
+			fe ret = new fe();
+			for (int i = 0; i < 10; i++) ret[i] = data[offset + i];
+			return ret;
+		}
+		static ge_precomp[] base_unpack(int n, int offset, Int32[] data) {
+			ge_precomp[] ret = new ge_precomp[n];
+			for (int i = 0; i < n; i++) ret[i] = new ge_precomp(data, offset + i * 3 * 10);
+			return ret;
+		}
+		static ge_precomp[][] base_unpack_a(int a, int b, Int32[] data) {
+			ge_precomp[][] ret = new ge_precomp[a][];
+			for (int i = 0; i < a; i++) ret[i] = base_unpack(b, i * b * 3 * 10, data);
+			return ret;
+		}
+		static ge_precomp[][] basev = base_unpack_a(32, 8,
+			new Int32[32 * 8 * 3 * 10] {
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+-9660625,12374379,-27006999,-7026148,-7724114,-12314514,11879682,5400171,519526,-1235876,
+22258397,-16332233,-7869817,14613016,-22520255,-2950923,-20353881,7315967,16648397,7605640,
+-8081308,-8464597,-8223311,9719710,19259459,-15348212,23994942,-5281555,-9468848,4763278,
+-21699244,9220969,-15730624,1084137,-25476107,-2852390,31088447,-7764523,-11356529,728112,
+26047220,-11751471,-6900323,-16521798,24092068,9158119,-4273545,-12555558,-29365436,-5498272,
+17510331,-322857,5854289,8403524,17133918,-3112612,-28111007,12327945,10750447,10014012,
+-10312768,3936952,9156313,-8897683,16498692,-994647,-27481051,-666732,3424691,7540221,
+30322361,-6964110,11361005,-4143317,7433304,4989748,-7071422,-16317219,-9244265,15258046,
+13054562,-2779497,19155474,469045,-12482797,4566042,5631406,2711395,1062915,-5136345,
+-19240248,-11254599,-29509029,-7499965,-5835763,13005411,-6066489,12194497,32960380,1459310,
+19852034,7027924,23669353,10020366,8586503,-6657907,394197,-6101885,18638003,-11174937,
+31395534,15098109,26581030,8030562,-16527914,-5007134,9012486,-7584354,-6643087,-5442636,
+-9192165,-2347377,-1997099,4529534,25766844,607986,-13222,9677543,-32294889,-6456008,
+-2444496,-149937,29348902,8186665,1873760,12489863,-30934579,-7839692,-7852844,-8138429,
+-15236356,-15433509,7766470,746860,26346930,-10221762,-27333451,10754588,-9431476,5203576,
+31834314,14135496,-770007,5159118,20917671,-16768096,-7467973,-7337524,31809243,7347066,
+-9606723,-11874240,20414459,13033986,13716524,-11691881,19797970,-12211255,15192876,-2087490,
+-12663563,-2181719,1168162,-3804809,26747877,-14138091,10609330,12694420,33473243,-13382104,
+33184999,11180355,15832085,-11385430,-1633671,225884,15089336,-11023903,-6135662,14480053,
+31308717,-5619998,31030840,-1897099,15674547,-6582883,5496208,13685227,27595050,8737275,
+-20318852,-15150239,10933843,-16178022,8335352,-7546022,-31008351,-12610604,26498114,66511,
+22644454,-8761729,-16671776,4884562,-3105614,-13559366,30540766,-4286747,-13327787,-7515095,
+-28017847,9834845,18617207,-2681312,-3401956,-13307506,8205540,13585437,-17127465,15115439,
+23711543,-672915,31206561,-8362711,6164647,-9709987,-33535882,-1426096,8236921,16492939,
+-23910559,-13515526,-26299483,-4503841,25005590,-7687270,19574902,10071562,6708380,-6222424,
+2101391,-4930054,19702731,2367575,-15427167,1047675,5301017,9328700,29955601,-11678310,
+3096359,9271816,-21620864,-15521844,-14847996,-7592937,-25892142,-12635595,-9917575,6216608,
+-32615849,338663,-25195611,2510422,-29213566,-13820213,24822830,-6146567,-26767480,7525079,
+-23066649,-13985623,16133487,-7896178,-3389565,778788,-910336,-2782495,-19386633,11994101,
+21691500,-13624626,-641331,-14367021,3285881,-3483596,-25064666,9718258,-7477437,13381418,
+18445390,-4202236,14979846,11622458,-1727110,-3582980,23111648,-6375247,28535282,15779576,
+30098053,3089662,-9234387,16662135,-21306940,11308411,-14068454,12021730,9955285,-16303356,
+9734894,-14576830,-7473633,-9138735,2060392,11313496,-18426029,9924399,20194861,13380996,
+-26378102,-7965207,-22167821,15789297,-18055342,-6168792,-1984914,15707771,26342023,10146099,
+-26016874,-219943,21339191,-41388,19745256,-2878700,-29637280,2227040,21612326,-545728,
+-13077387,1184228,23562814,-5970442,-20351244,-6348714,25764461,12243797,-20856566,11649658,
+-10031494,11262626,27384172,2271902,26947504,-15997771,39944,6114064,33514190,2333242,
+-21433588,-12421821,8119782,7219913,-21830522,-9016134,-6679750,-12670638,24350578,-13450001,
+-4116307,-11271533,-23886186,4843615,-30088339,690623,-31536088,-10406836,8317860,12352766,
+18200138,-14475911,-33087759,-2696619,-23702521,-9102511,-23552096,-2287550,20712163,6719373,
+26656208,6075253,-7858556,1886072,-28344043,4262326,11117530,-3763210,26224235,-3297458,
+-17168938,-14854097,-3395676,-16369877,-19954045,14050420,21728352,9493610,18620611,-16428628,
+-13323321,13325349,11432106,5964811,18609221,6062965,-5269471,-9725556,-30701573,-16479657,
+-23860538,-11233159,26961357,1640861,-32413112,-16737940,12248509,-5240639,13735342,1934062,
+25089769,6742589,17081145,-13406266,21909293,-16067981,-15136294,-3765346,-21277997,5473616,
+31883677,-7961101,1083432,-11572403,22828471,13290673,-7125085,12469656,29111212,-5451014,
+24244947,-15050407,-26262976,2791540,-14997599,16666678,24367466,6388839,-10295587,452383,
+-25640782,-3417841,5217916,16224624,19987036,-4082269,-24236251,-5915248,15766062,8407814,
+-20406999,13990231,15495425,16395525,5377168,15166495,-8917023,-4388953,-8067909,2276718,
+30157918,12924066,-17712050,9245753,19895028,3368142,-23827587,5096219,22740376,-7303417,
+2041139,-14256350,7783687,13876377,-25946985,-13352459,24051124,13742383,-15637599,13295222,
+33338237,-8505733,12532113,7977527,9106186,-1715251,-17720195,-4612972,-4451357,-14669444,
+-20045281,5454097,-14346548,6447146,28862071,1883651,-2469266,-4141880,7770569,9620597,
+23208068,7979712,33071466,8149229,1758231,-10834995,30945528,-1694323,-33502340,-14767970,
+1439958,-16270480,-1079989,-793782,4625402,10647766,-5043801,1220118,30494170,-11440799,
+-5037580,-13028295,-2970559,-3061767,15640974,-6701666,-26739026,926050,-1684339,-13333647,
+13908495,-3549272,30919928,-6273825,-21521863,7989039,9021034,9078865,3353509,4033511,
+-29663431,-15113610,32259991,-344482,24295849,-12912123,23161163,8839127,27485041,7356032,
+9661027,705443,11980065,-5370154,-1628543,14661173,-6346142,2625015,28431036,-16771834,
+-23839233,-8311415,-25945511,7480958,-17681669,-8354183,-22545972,14150565,15970762,4099461,
+29262576,16756590,26350592,-8793563,8529671,-11208050,13617293,-9937143,11465739,8317062,
+-25493081,-6962928,32500200,-9419051,-23038724,-2302222,14898637,3848455,20969334,-5157516,
+-20384450,-14347713,-18336405,13884722,-33039454,2842114,-21610826,-3649888,11177095,14989547,
+-24496721,-11716016,16959896,2278463,12066309,10137771,13515641,2581286,-28487508,9930240,
+-17751622,-2097826,16544300,-13009300,-15914807,-14949081,18345767,-13403753,16291481,-5314038,
+-33229194,2553288,32678213,9875984,8534129,6889387,-9676774,6957617,4368891,9788741,
+16660756,7281060,-10830758,12911820,20108584,-8101676,-21722536,-8613148,16250552,-11111103,
+-19765507,2390526,-16551031,14161980,1905286,6414907,4689584,10604807,-30190403,4782747,
+-1354539,14736941,-7367442,-13292886,7710542,-14155590,-9981571,4383045,22546403,437323,
+31665577,-12180464,-16186830,1491339,-18368625,3294682,27343084,2786261,-30633590,-14097016,
+-14467279,-683715,-33374107,7448552,19294360,14334329,-19690631,2355319,-19284671,-6114373,
+15121312,-15796162,6377020,-6031361,-10798111,-12957845,18952177,15496498,-29380133,11754228,
+-2637277,-13483075,8488727,-14303896,12728761,-1622493,7141596,11724556,22761615,-10134141,
+16918416,11729663,-18083579,3022987,-31015732,-13339659,-28741185,-12227393,32851222,11717399,
+11166634,7338049,-6722523,4531520,-29468672,-7302055,31474879,3483633,-1193175,-4030831,
+-185635,9921305,31456609,-13536438,-12013818,13348923,33142652,6546660,-19985279,-3948376,
+-32460596,11266712,-11197107,-7899103,31703694,3855903,-8537131,-12833048,-30772034,-15486313,
+-18006477,12709068,3991746,-6479188,-21491523,-10550425,-31135347,-16049879,10928917,3011958,
+-6957757,-15594337,31696059,334240,29576716,14796075,-30831056,-12805180,18008031,10258577,
+-22448644,15655569,7018479,-4410003,-30314266,-1201591,-1853465,1367120,25127874,6671743,
+29701166,-14373934,-10878120,9279288,-17568,13127210,21382910,11042292,25838796,4642684,
+-20430234,14955537,-24126347,8124619,-5369288,-5990470,30468147,-13900640,18423289,4177476,
+#endregion
+		});
+
+		static void fe_0(out fe h) {
+			h = new fe();
+			h[0] = 0;
+			h[1] = 0;
+			h[2] = 0;
+			h[3] = 0;
+			h[4] = 0;
+			h[5] = 0;
+			h[6] = 0;
+			h[7] = 0;
+			h[8] = 0;
+			h[9] = 0;
+		}
+		static void fe_1(out fe h) {
+			h = new fe();
+			h[0] = 1;
+			h[1] = 0;
+			h[2] = 0;
+			h[3] = 0;
+			h[4] = 0;
+			h[5] = 0;
+			h[6] = 0;
+			h[7] = 0;
+			h[8] = 0;
+			h[9] = 0;
+		}
+		static void ge_p3_0(out ge_p3 h) {
+			fe_0(out h.X);
+			fe_1(out h.Y);
+			fe_1(out h.Z);
+			fe_0(out h.T);
+		}
+		static Byte negative(SByte b) {
+			UInt64 x = (UInt64)(Int64)b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
+			x >>= 63; /* 1: yes; 0: no */
+			return (Byte)x;
+		}
+		static void ge_precomp_0(out ge_precomp h) {
+			fe_1(out h.yplusx);
+			fe_1(out h.yminusx);
+			fe_0(out h.xy2d);
+		}
+		static void fe_cmov(ref fe f, ref fe g, Int32 b) {
+			Int32 f0 = f[0];
+			Int32 f1 = f[1];
+			Int32 f2 = f[2];
+			Int32 f3 = f[3];
+			Int32 f4 = f[4];
+			Int32 f5 = f[5];
+			Int32 f6 = f[6];
+			Int32 f7 = f[7];
+			Int32 f8 = f[8];
+			Int32 f9 = f[9];
+			Int32 g0 = g[0];
+			Int32 g1 = g[1];
+			Int32 g2 = g[2];
+			Int32 g3 = g[3];
+			Int32 g4 = g[4];
+			Int32 g5 = g[5];
+			Int32 g6 = g[6];
+			Int32 g7 = g[7];
+			Int32 g8 = g[8];
+			Int32 g9 = g[9];
+			Int32 x0 = f0 ^ g0;
+			Int32 x1 = f1 ^ g1;
+			Int32 x2 = f2 ^ g2;
+			Int32 x3 = f3 ^ g3;
+			Int32 x4 = f4 ^ g4;
+			Int32 x5 = f5 ^ g5;
+			Int32 x6 = f6 ^ g6;
+			Int32 x7 = f7 ^ g7;
+			Int32 x8 = f8 ^ g8;
+			Int32 x9 = f9 ^ g9;
+			b = -b;
+			x0 &= b;
+			x1 &= b;
+			x2 &= b;
+			x3 &= b;
+			x4 &= b;
+			x5 &= b;
+			x6 &= b;
+			x7 &= b;
+			x8 &= b;
+			x9 &= b;
+			f[0] = f0 ^ x0;
+			f[1] = f1 ^ x1;
+			f[2] = f2 ^ x2;
+			f[3] = f3 ^ x3;
+			f[4] = f4 ^ x4;
+			f[5] = f5 ^ x5;
+			f[6] = f6 ^ x6;
+			f[7] = f7 ^ x7;
+			f[8] = f8 ^ x8;
+			f[9] = f9 ^ x9;
+		}
+		static void cmov(ref ge_precomp t, ref ge_precomp u, Byte b) {
+			fe_cmov(ref t.yplusx, ref u.yplusx, b);
+			fe_cmov(ref t.yminusx, ref u.yminusx, b);
+			fe_cmov(ref t.xy2d, ref u.xy2d, b);
+		}
+		static Byte equal(Byte b, SByte c) {
+			Byte ub = (Byte)b;
+			Byte uc = (Byte)c;
+			Byte x = (Byte)(ub ^ uc); /* 0: yes; 1..255: no */
+			UInt32 y = x; /* 0: yes; 1..255: no */
+			y -= 1; /* 4294967295: yes; 0..254: no */
+			y >>= 31; /* 1: yes; 0: no */
+			return (Byte)y;
+		}
+		static void fe_copy(out fe h, ref fe f) {
+			Int32 f0 = f[0];
+			Int32 f1 = f[1];
+			Int32 f2 = f[2];
+			Int32 f3 = f[3];
+			Int32 f4 = f[4];
+			Int32 f5 = f[5];
+			Int32 f6 = f[6];
+			Int32 f7 = f[7];
+			Int32 f8 = f[8];
+			Int32 f9 = f[9];
+			h = new fe();
+			h[0] = f0;
+			h[1] = f1;
+			h[2] = f2;
+			h[3] = f3;
+			h[4] = f4;
+			h[5] = f5;
+			h[6] = f6;
+			h[7] = f7;
+			h[8] = f8;
+			h[9] = f9;
+		}
+		static void fe_neg(out fe h, ref fe f) {
+			Int32 f0 = f[0];
+			Int32 f1 = f[1];
+			Int32 f2 = f[2];
+			Int32 f3 = f[3];
+			Int32 f4 = f[4];
+			Int32 f5 = f[5];
+			Int32 f6 = f[6];
+			Int32 f7 = f[7];
+			Int32 f8 = f[8];
+			Int32 f9 = f[9];
+			Int32 h0 = -f0;
+			Int32 h1 = -f1;
+			Int32 h2 = -f2;
+			Int32 h3 = -f3;
+			Int32 h4 = -f4;
+			Int32 h5 = -f5;
+			Int32 h6 = -f6;
+			Int32 h7 = -f7;
+			Int32 h8 = -f8;
+			Int32 h9 = -f9;
+			h = new fe();
+			h[0] = h0;
+			h[1] = h1;
+			h[2] = h2;
+			h[3] = h3;
+			h[4] = h4;
+			h[5] = h5;
+			h[6] = h6;
+			h[7] = h7;
+			h[8] = h8;
+			h[9] = h9;
+		}
+		static void select(out ge_precomp t, int pos, SByte b) {
+			ge_precomp minust;
+			Byte bnegative = negative(b);
+			Byte babs = (Byte)(b - (((-bnegative) & b) << 1));
+			ge_precomp_0(out t);
+			cmov(ref t, ref basev[pos][0], equal(babs, 1));
+			cmov(ref t, ref basev[pos][1], equal(babs, 2));
+			cmov(ref t, ref basev[pos][2], equal(babs, 3));
+			cmov(ref t, ref basev[pos][3], equal(babs, 4));
+			cmov(ref t, ref basev[pos][4], equal(babs, 5));
+			cmov(ref t, ref basev[pos][5], equal(babs, 6));
+			cmov(ref t, ref basev[pos][6], equal(babs, 7));
+			cmov(ref t, ref basev[pos][7], equal(babs, 8));
+			fe_copy(out minust.yplusx, ref t.yminusx);
+			fe_copy(out minust.yminusx, ref t.yplusx);
+			fe_neg(out minust.xy2d, ref t.xy2d);
+			cmov(ref t, ref minust, bnegative);
+		}
+		static void fe_add(out fe h, ref fe f, ref fe g) {
+			Int32 f0 = f[0];
+			Int32 f1 = f[1];
+			Int32 f2 = f[2];
+			Int32 f3 = f[3];
+			Int32 f4 = f[4];
+			Int32 f5 = f[5];
+			Int32 f6 = f[6];
+			Int32 f7 = f[7];
+			Int32 f8 = f[8];
+			Int32 f9 = f[9];
+			Int32 g0 = g[0];
+			Int32 g1 = g[1];
+			Int32 g2 = g[2];
+			Int32 g3 = g[3];
+			Int32 g4 = g[4];
+			Int32 g5 = g[5];
+			Int32 g6 = g[6];
+			Int32 g7 = g[7];
+			Int32 g8 = g[8];
+			Int32 g9 = g[9];
+			Int32 h0 = f0 + g0;
+			Int32 h1 = f1 + g1;
+			Int32 h2 = f2 + g2;
+			Int32 h3 = f3 + g3;
+			Int32 h4 = f4 + g4;
+			Int32 h5 = f5 + g5;
+			Int32 h6 = f6 + g6;
+			Int32 h7 = f7 + g7;
+			Int32 h8 = f8 + g8;
+			Int32 h9 = f9 + g9;
+			h = new fe();
+			h[0] = h0;
+			h[1] = h1;
+			h[2] = h2;
+			h[3] = h3;
+			h[4] = h4;
+			h[5] = h5;
+			h[6] = h6;
+			h[7] = h7;
+			h[8] = h8;
+			h[9] = h9;
+		}
+		static void fe_sub(out fe h, ref fe f, ref fe g) {
+			Int32 f0 = f[0];
+			Int32 f1 = f[1];
+			Int32 f2 = f[2];
+			Int32 f3 = f[3];
+			Int32 f4 = f[4];
+			Int32 f5 = f[5];
+			Int32 f6 = f[6];
+			Int32 f7 = f[7];
+			Int32 f8 = f[8];
+			Int32 f9 = f[9];
+			Int32 g0 = g[0];
+			Int32 g1 = g[1];
+			Int32 g2 = g[2];
+			Int32 g3 = g[3];
+			Int32 g4 = g[4];
+			Int32 g5 = g[5];
+			Int32 g6 = g[6];
+			Int32 g7 = g[7];
+			Int32 g8 = g[8];
+			Int32 g9 = g[9];
+			Int32 h0 = f0 - g0;
+			Int32 h1 = f1 - g1;
+			Int32 h2 = f2 - g2;
+			Int32 h3 = f3 - g3;
+			Int32 h4 = f4 - g4;
+			Int32 h5 = f5 - g5;
+			Int32 h6 = f6 - g6;
+			Int32 h7 = f7 - g7;
+			Int32 h8 = f8 - g8;
+			Int32 h9 = f9 - g9;
+			h = new fe();
+			h[0] = h0;
+			h[1] = h1;
+			h[2] = h2;
+			h[3] = h3;
+			h[4] = h4;
+			h[5] = h5;
+			h[6] = h6;
+			h[7] = h7;
+			h[8] = h8;
+			h[9] = h9;
+		}
+		static void fe_mul(out fe h, ref fe f, ref fe g) {
+			Int32 f0 = f[0];
+			Int32 f1 = f[1];
+			Int32 f2 = f[2];
+			Int32 f3 = f[3];
+			Int32 f4 = f[4];
+			Int32 f5 = f[5];
+			Int32 f6 = f[6];
+			Int32 f7 = f[7];
+			Int32 f8 = f[8];
+			Int32 f9 = f[9];
+			Int32 g0 = g[0];
+			Int32 g1 = g[1];
+			Int32 g2 = g[2];
+			Int32 g3 = g[3];
+			Int32 g4 = g[4];
+			Int32 g5 = g[5];
+			Int32 g6 = g[6];
+			Int32 g7 = g[7];
+			Int32 g8 = g[8];
+			Int32 g9 = g[9];
+			Int32 g1_19 = 19 * g1; /* 1.959375*2^29 */
+			Int32 g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
+			Int32 g3_19 = 19 * g3;
+			Int32 g4_19 = 19 * g4;
+			Int32 g5_19 = 19 * g5;
+			Int32 g6_19 = 19 * g6;
+			Int32 g7_19 = 19 * g7;
+			Int32 g8_19 = 19 * g8;
+			Int32 g9_19 = 19 * g9;
+			Int32 f1_2 = 2 * f1;
+			Int32 f3_2 = 2 * f3;
+			Int32 f5_2 = 2 * f5;
+			Int32 f7_2 = 2 * f7;
+			Int32 f9_2 = 2 * f9;
+			Int64 f0g0 = f0 * (Int64)g0;
+			Int64 f0g1 = f0 * (Int64)g1;
+			Int64 f0g2 = f0 * (Int64)g2;
+			Int64 f0g3 = f0 * (Int64)g3;
+			Int64 f0g4 = f0 * (Int64)g4;
+			Int64 f0g5 = f0 * (Int64)g5;
+			Int64 f0g6 = f0 * (Int64)g6;
+			Int64 f0g7 = f0 * (Int64)g7;
+			Int64 f0g8 = f0 * (Int64)g8;
+			Int64 f0g9 = f0 * (Int64)g9;
+			Int64 f1g0 = f1 * (Int64)g0;
+			Int64 f1g1_2 = f1_2 * (Int64)g1;
+			Int64 f1g2 = f1 * (Int64)g2;
+			Int64 f1g3_2 = f1_2 * (Int64)g3;
+			Int64 f1g4 = f1 * (Int64)g4;
+			Int64 f1g5_2 = f1_2 * (Int64)g5;
+			Int64 f1g6 = f1 * (Int64)g6;
+			Int64 f1g7_2 = f1_2 * (Int64)g7;
+			Int64 f1g8 = f1 * (Int64)g8;
+			Int64 f1g9_38 = f1_2 * (Int64)g9_19;
+			Int64 f2g0 = f2 * (Int64)g0;
+			Int64 f2g1 = f2 * (Int64)g1;
+			Int64 f2g2 = f2 * (Int64)g2;
+			Int64 f2g3 = f2 * (Int64)g3;
+			Int64 f2g4 = f2 * (Int64)g4;
+			Int64 f2g5 = f2 * (Int64)g5;
+			Int64 f2g6 = f2 * (Int64)g6;
+			Int64 f2g7 = f2 * (Int64)g7;
+			Int64 f2g8_19 = f2 * (Int64)g8_19;
+			Int64 f2g9_19 = f2 * (Int64)g9_19;
+			Int64 f3g0 = f3 * (Int64)g0;
+			Int64 f3g1_2 = f3_2 * (Int64)g1;
+			Int64 f3g2 = f3 * (Int64)g2;
+			Int64 f3g3_2 = f3_2 * (Int64)g3;
+			Int64 f3g4 = f3 * (Int64)g4;
+			Int64 f3g5_2 = f3_2 * (Int64)g5;
+			Int64 f3g6 = f3 * (Int64)g6;
+			Int64 f3g7_38 = f3_2 * (Int64)g7_19;
+			Int64 f3g8_19 = f3 * (Int64)g8_19;
+			Int64 f3g9_38 = f3_2 * (Int64)g9_19;
+			Int64 f4g0 = f4 * (Int64)g0;
+			Int64 f4g1 = f4 * (Int64)g1;
+			Int64 f4g2 = f4 * (Int64)g2;
+			Int64 f4g3 = f4 * (Int64)g3;
+			Int64 f4g4 = f4 * (Int64)g4;
+			Int64 f4g5 = f4 * (Int64)g5;
+			Int64 f4g6_19 = f4 * (Int64)g6_19;
+			Int64 f4g7_19 = f4 * (Int64)g7_19;
+			Int64 f4g8_19 = f4 * (Int64)g8_19;
+			Int64 f4g9_19 = f4 * (Int64)g9_19;
+			Int64 f5g0 = f5 * (Int64)g0;
+			Int64 f5g1_2 = f5_2 * (Int64)g1;
+			Int64 f5g2 = f5 * (Int64)g2;
+			Int64 f5g3_2 = f5_2 * (Int64)g3;
+			Int64 f5g4 = f5 * (Int64)g4;
+			Int64 f5g5_38 = f5_2 * (Int64)g5_19;
+			Int64 f5g6_19 = f5 * (Int64)g6_19;
+			Int64 f5g7_38 = f5_2 * (Int64)g7_19;
+			Int64 f5g8_19 = f5 * (Int64)g8_19;
+			Int64 f5g9_38 = f5_2 * (Int64)g9_19;
+			Int64 f6g0 = f6 * (Int64)g0;
+			Int64 f6g1 = f6 * (Int64)g1;
+			Int64 f6g2 = f6 * (Int64)g2;
+			Int64 f6g3 = f6 * (Int64)g3;
+			Int64 f6g4_19 = f6 * (Int64)g4_19;
+			Int64 f6g5_19 = f6 * (Int64)g5_19;
+			Int64 f6g6_19 = f6 * (Int64)g6_19;
+			Int64 f6g7_19 = f6 * (Int64)g7_19;
+			Int64 f6g8_19 = f6 * (Int64)g8_19;
+			Int64 f6g9_19 = f6 * (Int64)g9_19;
+			Int64 f7g0 = f7 * (Int64)g0;
+			Int64 f7g1_2 = f7_2 * (Int64)g1;
+			Int64 f7g2 = f7 * (Int64)g2;
+			Int64 f7g3_38 = f7_2 * (Int64)g3_19;
+			Int64 f7g4_19 = f7 * (Int64)g4_19;
+			Int64 f7g5_38 = f7_2 * (Int64)g5_19;
+			Int64 f7g6_19 = f7 * (Int64)g6_19;
+			Int64 f7g7_38 = f7_2 * (Int64)g7_19;
+			Int64 f7g8_19 = f7 * (Int64)g8_19;
+			Int64 f7g9_38 = f7_2 * (Int64)g9_19;
+			Int64 f8g0 = f8 * (Int64)g0;
+			Int64 f8g1 = f8 * (Int64)g1;
+			Int64 f8g2_19 = f8 * (Int64)g2_19;
+			Int64 f8g3_19 = f8 * (Int64)g3_19;
+			Int64 f8g4_19 = f8 * (Int64)g4_19;
+			Int64 f8g5_19 = f8 * (Int64)g5_19;
+			Int64 f8g6_19 = f8 * (Int64)g6_19;
+			Int64 f8g7_19 = f8 * (Int64)g7_19;
+			Int64 f8g8_19 = f8 * (Int64)g8_19;
+			Int64 f8g9_19 = f8 * (Int64)g9_19;
+			Int64 f9g0 = f9 * (Int64)g0;
+			Int64 f9g1_38 = f9_2 * (Int64)g1_19;
+			Int64 f9g2_19 = f9 * (Int64)g2_19;
+			Int64 f9g3_38 = f9_2 * (Int64)g3_19;
+			Int64 f9g4_19 = f9 * (Int64)g4_19;
+			Int64 f9g5_38 = f9_2 * (Int64)g5_19;
+			Int64 f9g6_19 = f9 * (Int64)g6_19;
+			Int64 f9g7_38 = f9_2 * (Int64)g7_19;
+			Int64 f9g8_19 = f9 * (Int64)g8_19;
+			Int64 f9g9_38 = f9_2 * (Int64)g9_19;
+			Int64 h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
+			Int64 h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
+			Int64 h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
+			Int64 h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
+			Int64 h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
+			Int64 h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
+			Int64 h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38;
+			Int64 h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19;
+			Int64 h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38;
+			Int64 h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0;
+			Int64 carry0;
+			Int64 carry1;
+			Int64 carry2;
+			Int64 carry3;
+			Int64 carry4;
+			Int64 carry5;
+			Int64 carry6;
+			Int64 carry7;
+			Int64 carry8;
+			Int64 carry9;
+			carry0 = (h0 + (Int64)(1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+			carry4 = (h4 + (Int64)(1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+			carry1 = (h1 + (Int64)(1 << 24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+			carry5 = (h5 + (Int64)(1 << 24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+			carry2 = (h2 + (Int64)(1 << 25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+			carry6 = (h6 + (Int64)(1 << 25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+			carry3 = (h3 + (Int64)(1 << 24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+			carry7 = (h7 + (Int64)(1 << 24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+			carry4 = (h4 + (Int64)(1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+			carry8 = (h8 + (Int64)(1 << 25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+			carry9 = (h9 + (Int64)(1 << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+			carry0 = (h0 + (Int64)(1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+			h = new fe();
+			h[0] = (Int32)h0;
+			h[1] = (Int32)h1;
+			h[2] = (Int32)h2;
+			h[3] = (Int32)h3;
+			h[4] = (Int32)h4;
+			h[5] = (Int32)h5;
+			h[6] = (Int32)h6;
+			h[7] = (Int32)h7;
+			h[8] = (Int32)h8;
+			h[9] = (Int32)h9;
+		}
+		static void ge_madd(out ge_p1p1 r, ref ge_p3 p, ref ge_precomp q) {
+			fe t0;
+			fe_add(out r.X, ref p.Y, ref p.X);
+			fe_sub(out r.Y, ref p.Y, ref p.X);
+			fe_mul(out r.Z, ref r.X, ref q.yplusx);
+			fe_mul(out r.Y, ref r.Y, ref q.yminusx);
+			fe_mul(out r.T, ref q.xy2d, ref p.T);
+			fe_add(out t0, ref p.Z, ref p.Z);
+			fe_sub(out r.X, ref r.Z, ref r.Y);
+			fe_add(out r.Y, ref r.Z, ref r.Y);
+			fe_add(out r.Z, ref t0, ref r.T);
+			fe_sub(out r.T, ref t0, ref r.T);
+		}
+		static void ge_p1p1_to_p3(out ge_p3 r, ref ge_p1p1 p) {
+			fe_mul(out r.X, ref p.X, ref p.T);
+			fe_mul(out r.Y, ref p.Y, ref p.Z);
+			fe_mul(out r.Z, ref p.Z, ref p.T);
+			fe_mul(out r.T, ref p.X, ref p.Y);
+		}
+		static void ge_p3_to_p2(out ge_p2 r, ref ge_p3 p) {
+			fe_copy(out r.X, ref p.X);
+			fe_copy(out r.Y, ref p.Y);
+			fe_copy(out r.Z, ref p.Z);
+		}
+		static void fe_sq(out fe h, ref fe f) {
+			Int32 f0 = f[0];
+			Int32 f1 = f[1];
+			Int32 f2 = f[2];
+			Int32 f3 = f[3];
+			Int32 f4 = f[4];
+			Int32 f5 = f[5];
+			Int32 f6 = f[6];
+			Int32 f7 = f[7];
+			Int32 f8 = f[8];
+			Int32 f9 = f[9];
+			Int32 f0_2 = 2 * f0;
+			Int32 f1_2 = 2 * f1;
+			Int32 f2_2 = 2 * f2;
+			Int32 f3_2 = 2 * f3;
+			Int32 f4_2 = 2 * f4;
+			Int32 f5_2 = 2 * f5;
+			Int32 f6_2 = 2 * f6;
+			Int32 f7_2 = 2 * f7;
+			Int32 f5_38 = 38 * f5; /* 1.959375*2^30 */
+			Int32 f6_19 = 19 * f6; /* 1.959375*2^30 */
+			Int32 f7_38 = 38 * f7; /* 1.959375*2^30 */
+			Int32 f8_19 = 19 * f8; /* 1.959375*2^30 */
+			Int32 f9_38 = 38 * f9; /* 1.959375*2^30 */
+			Int64 f0f0 = f0 * (Int64)f0;
+			Int64 f0f1_2 = f0_2 * (Int64)f1;
+			Int64 f0f2_2 = f0_2 * (Int64)f2;
+			Int64 f0f3_2 = f0_2 * (Int64)f3;
+			Int64 f0f4_2 = f0_2 * (Int64)f4;
+			Int64 f0f5_2 = f0_2 * (Int64)f5;
+			Int64 f0f6_2 = f0_2 * (Int64)f6;
+			Int64 f0f7_2 = f0_2 * (Int64)f7;
+			Int64 f0f8_2 = f0_2 * (Int64)f8;
+			Int64 f0f9_2 = f0_2 * (Int64)f9;
+			Int64 f1f1_2 = f1_2 * (Int64)f1;
+			Int64 f1f2_2 = f1_2 * (Int64)f2;
+			Int64 f1f3_4 = f1_2 * (Int64)f3_2;
+			Int64 f1f4_2 = f1_2 * (Int64)f4;
+			Int64 f1f5_4 = f1_2 * (Int64)f5_2;
+			Int64 f1f6_2 = f1_2 * (Int64)f6;
+			Int64 f1f7_4 = f1_2 * (Int64)f7_2;
+			Int64 f1f8_2 = f1_2 * (Int64)f8;
+			Int64 f1f9_76 = f1_2 * (Int64)f9_38;
+			Int64 f2f2 = f2 * (Int64)f2;
+			Int64 f2f3_2 = f2_2 * (Int64)f3;
+			Int64 f2f4_2 = f2_2 * (Int64)f4;
+			Int64 f2f5_2 = f2_2 * (Int64)f5;
+			Int64 f2f6_2 = f2_2 * (Int64)f6;
+			Int64 f2f7_2 = f2_2 * (Int64)f7;
+			Int64 f2f8_38 = f2_2 * (Int64)f8_19;
+			Int64 f2f9_38 = f2 * (Int64)f9_38;
+			Int64 f3f3_2 = f3_2 * (Int64)f3;
+			Int64 f3f4_2 = f3_2 * (Int64)f4;
+			Int64 f3f5_4 = f3_2 * (Int64)f5_2;
+			Int64 f3f6_2 = f3_2 * (Int64)f6;
+			Int64 f3f7_76 = f3_2 * (Int64)f7_38;
+			Int64 f3f8_38 = f3_2 * (Int64)f8_19;
+			Int64 f3f9_76 = f3_2 * (Int64)f9_38;
+			Int64 f4f4 = f4 * (Int64)f4;
+			Int64 f4f5_2 = f4_2 * (Int64)f5;
+			Int64 f4f6_38 = f4_2 * (Int64)f6_19;
+			Int64 f4f7_38 = f4 * (Int64)f7_38;
+			Int64 f4f8_38 = f4_2 * (Int64)f8_19;
+			Int64 f4f9_38 = f4 * (Int64)f9_38;
+			Int64 f5f5_38 = f5 * (Int64)f5_38;
+			Int64 f5f6_38 = f5_2 * (Int64)f6_19;
+			Int64 f5f7_76 = f5_2 * (Int64)f7_38;
+			Int64 f5f8_38 = f5_2 * (Int64)f8_19;
+			Int64 f5f9_76 = f5_2 * (Int64)f9_38;
+			Int64 f6f6_19 = f6 * (Int64)f6_19;
+			Int64 f6f7_38 = f6 * (Int64)f7_38;
+			Int64 f6f8_38 = f6_2 * (Int64)f8_19;
+			Int64 f6f9_38 = f6 * (Int64)f9_38;
+			Int64 f7f7_38 = f7 * (Int64)f7_38;
+			Int64 f7f8_38 = f7_2 * (Int64)f8_19;
+			Int64 f7f9_76 = f7_2 * (Int64)f9_38;
+			Int64 f8f8_19 = f8 * (Int64)f8_19;
+			Int64 f8f9_38 = f8 * (Int64)f9_38;
+			Int64 f9f9_38 = f9 * (Int64)f9_38;
+			Int64 h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
+			Int64 h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
+			Int64 h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
+			Int64 h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
+			Int64 h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
+			Int64 h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
+			Int64 h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
+			Int64 h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
+			Int64 h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
+			Int64 h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
+			Int64 carry0;
+			Int64 carry1;
+			Int64 carry2;
+			Int64 carry3;
+			Int64 carry4;
+			Int64 carry5;
+			Int64 carry6;
+			Int64 carry7;
+			Int64 carry8;
+			Int64 carry9;
+
+			carry0 = (h0 + (Int64)(1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+			carry4 = (h4 + (Int64)(1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+
+			carry1 = (h1 + (Int64)(1 << 24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+			carry5 = (h5 + (Int64)(1 << 24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+
+			carry2 = (h2 + (Int64)(1 << 25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+			carry6 = (h6 + (Int64)(1 << 25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+
+			carry3 = (h3 + (Int64)(1 << 24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+			carry7 = (h7 + (Int64)(1 << 24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+			carry4 = (h4 + (Int64)(1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+			carry8 = (h8 + (Int64)(1 << 25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+			carry9 = (h9 + (Int64)(1 << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+
+			carry0 = (h0 + (Int64)(1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+
+			h = new fe();
+			h[0] = (Int32)h0;
+			h[1] = (Int32)h1;
+			h[2] = (Int32)h2;
+			h[3] = (Int32)h3;
+			h[4] = (Int32)h4;
+			h[5] = (Int32)h5;
+			h[6] = (Int32)h6;
+			h[7] = (Int32)h7;
+			h[8] = (Int32)h8;
+			h[9] = (Int32)h9;
+		}
+		static void fe_sq2(out fe h, ref fe f) {
+			Int32 f0 = f[0];
+			Int32 f1 = f[1];
+			Int32 f2 = f[2];
+			Int32 f3 = f[3];
+			Int32 f4 = f[4];
+			Int32 f5 = f[5];
+			Int32 f6 = f[6];
+			Int32 f7 = f[7];
+			Int32 f8 = f[8];
+			Int32 f9 = f[9];
+			Int32 f0_2 = 2 * f0;
+			Int32 f1_2 = 2 * f1;
+			Int32 f2_2 = 2 * f2;
+			Int32 f3_2 = 2 * f3;
+			Int32 f4_2 = 2 * f4;
+			Int32 f5_2 = 2 * f5;
+			Int32 f6_2 = 2 * f6;
+			Int32 f7_2 = 2 * f7;
+			Int32 f5_38 = 38 * f5; /* 1.959375*2^30 */
+			Int32 f6_19 = 19 * f6; /* 1.959375*2^30 */
+			Int32 f7_38 = 38 * f7; /* 1.959375*2^30 */
+			Int32 f8_19 = 19 * f8; /* 1.959375*2^30 */
+			Int32 f9_38 = 38 * f9; /* 1.959375*2^30 */
+			Int64 f0f0 = f0 * (Int64)f0;
+			Int64 f0f1_2 = f0_2 * (Int64)f1;
+			Int64 f0f2_2 = f0_2 * (Int64)f2;
+			Int64 f0f3_2 = f0_2 * (Int64)f3;
+			Int64 f0f4_2 = f0_2 * (Int64)f4;
+			Int64 f0f5_2 = f0_2 * (Int64)f5;
+			Int64 f0f6_2 = f0_2 * (Int64)f6;
+			Int64 f0f7_2 = f0_2 * (Int64)f7;
+			Int64 f0f8_2 = f0_2 * (Int64)f8;
+			Int64 f0f9_2 = f0_2 * (Int64)f9;
+			Int64 f1f1_2 = f1_2 * (Int64)f1;
+			Int64 f1f2_2 = f1_2 * (Int64)f2;
+			Int64 f1f3_4 = f1_2 * (Int64)f3_2;
+			Int64 f1f4_2 = f1_2 * (Int64)f4;
+			Int64 f1f5_4 = f1_2 * (Int64)f5_2;
+			Int64 f1f6_2 = f1_2 * (Int64)f6;
+			Int64 f1f7_4 = f1_2 * (Int64)f7_2;
+			Int64 f1f8_2 = f1_2 * (Int64)f8;
+			Int64 f1f9_76 = f1_2 * (Int64)f9_38;
+			Int64 f2f2 = f2 * (Int64)f2;
+			Int64 f2f3_2 = f2_2 * (Int64)f3;
+			Int64 f2f4_2 = f2_2 * (Int64)f4;
+			Int64 f2f5_2 = f2_2 * (Int64)f5;
+			Int64 f2f6_2 = f2_2 * (Int64)f6;
+			Int64 f2f7_2 = f2_2 * (Int64)f7;
+			Int64 f2f8_38 = f2_2 * (Int64)f8_19;
+			Int64 f2f9_38 = f2 * (Int64)f9_38;
+			Int64 f3f3_2 = f3_2 * (Int64)f3;
+			Int64 f3f4_2 = f3_2 * (Int64)f4;
+			Int64 f3f5_4 = f3_2 * (Int64)f5_2;
+			Int64 f3f6_2 = f3_2 * (Int64)f6;
+			Int64 f3f7_76 = f3_2 * (Int64)f7_38;
+			Int64 f3f8_38 = f3_2 * (Int64)f8_19;
+			Int64 f3f9_76 = f3_2 * (Int64)f9_38;
+			Int64 f4f4 = f4 * (Int64)f4;
+			Int64 f4f5_2 = f4_2 * (Int64)f5;
+			Int64 f4f6_38 = f4_2 * (Int64)f6_19;
+			Int64 f4f7_38 = f4 * (Int64)f7_38;
+			Int64 f4f8_38 = f4_2 * (Int64)f8_19;
+			Int64 f4f9_38 = f4 * (Int64)f9_38;
+			Int64 f5f5_38 = f5 * (Int64)f5_38;
+			Int64 f5f6_38 = f5_2 * (Int64)f6_19;
+			Int64 f5f7_76 = f5_2 * (Int64)f7_38;
+			Int64 f5f8_38 = f5_2 * (Int64)f8_19;
+			Int64 f5f9_76 = f5_2 * (Int64)f9_38;
+			Int64 f6f6_19 = f6 * (Int64)f6_19;
+			Int64 f6f7_38 = f6 * (Int64)f7_38;
+			Int64 f6f8_38 = f6_2 * (Int64)f8_19;
+			Int64 f6f9_38 = f6 * (Int64)f9_38;
+			Int64 f7f7_38 = f7 * (Int64)f7_38;
+			Int64 f7f8_38 = f7_2 * (Int64)f8_19;
+			Int64 f7f9_76 = f7_2 * (Int64)f9_38;
+			Int64 f8f8_19 = f8 * (Int64)f8_19;
+			Int64 f8f9_38 = f8 * (Int64)f9_38;
+			Int64 f9f9_38 = f9 * (Int64)f9_38;
+			Int64 h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
+			Int64 h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
+			Int64 h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
+			Int64 h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
+			Int64 h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
+			Int64 h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
+			Int64 h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
+			Int64 h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
+			Int64 h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
+			Int64 h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
+			Int64 carry0;
+			Int64 carry1;
+			Int64 carry2;
+			Int64 carry3;
+			Int64 carry4;
+			Int64 carry5;
+			Int64 carry6;
+			Int64 carry7;
+			Int64 carry8;
+			Int64 carry9;
+
+			h0 += h0;
+			h1 += h1;
+			h2 += h2;
+			h3 += h3;
+			h4 += h4;
+			h5 += h5;
+			h6 += h6;
+			h7 += h7;
+			h8 += h8;
+			h9 += h9;
+
+			carry0 = (h0 + (Int64)(1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+			carry4 = (h4 + (Int64)(1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+
+			carry1 = (h1 + (Int64)(1 << 24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+			carry5 = (h5 + (Int64)(1 << 24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+
+			carry2 = (h2 + (Int64)(1 << 25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+			carry6 = (h6 + (Int64)(1 << 25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+
+			carry3 = (h3 + (Int64)(1 << 24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+			carry7 = (h7 + (Int64)(1 << 24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+			carry4 = (h4 + (Int64)(1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+			carry8 = (h8 + (Int64)(1 << 25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+			carry9 = (h9 + (Int64)(1 << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+
+			carry0 = (h0 + (Int64)(1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+
+			h = new fe();
+			h[0] = (Int32)h0;
+			h[1] = (Int32)h1;
+			h[2] = (Int32)h2;
+			h[3] = (Int32)h3;
+			h[4] = (Int32)h4;
+			h[5] = (Int32)h5;
+			h[6] = (Int32)h6;
+			h[7] = (Int32)h7;
+			h[8] = (Int32)h8;
+			h[9] = (Int32)h9;
+		}
+		static void ge_p2_dbl(out ge_p1p1 r, ref ge_p2 p) {
+			fe t0;
+			fe_sq(out r.X, ref p.X);
+			fe_sq(out r.Z, ref p.Y);
+			fe_sq2(out r.T, ref p.Z);
+			fe_add(out r.Y, ref p.X, ref p.Y);
+			fe_sq(out t0, ref r.Y);
+			fe_add(out r.Y, ref r.Z, ref r.X);
+			fe_sub(out r.Z, ref r.Z, ref r.X);
+			fe_sub(out r.X, ref t0, ref r.Y);
+			fe_sub(out r.T, ref r.T, ref r.Z);
+		}
+		static void ge_p3_dbl(out ge_p1p1 r, ref ge_p3 p) {
+			ge_p2 q;
+			ge_p3_to_p2(out q, ref p);
+			ge_p2_dbl(out r, ref q);
+		}
+		static void ge_p1p1_to_p2(out ge_p2 r, ref ge_p1p1 p) {
+			fe_mul(out r.X, ref p.X, ref p.T);
+			fe_mul(out r.Y, ref p.Y, ref p.Z);
+			fe_mul(out r.Z, ref p.Z, ref p.T);
+		}
+		static unsafe void ge_scalarmult_base(out ge_p3 h, Byte* a) {
+			SByte[] e = new SByte[64];
+
+			for (int i = 0; i < 32; ++i) {
+				e[2 * i + 0] = (sbyte)((a[i] >> 0) & 15);
+				e[2 * i + 1] = (sbyte)((a[i] >> 4) & 15);
+			}
+
+			SByte carry = 0;
+			for (int i = 0; i < 63; ++i) {
+				e[i] += carry;
+				carry = (sbyte)(e[i] + 8);
+				carry >>= 4;
+				e[i] -= (sbyte)(carry << 4);
+			}
+			e[63] += carry;
+
+			ge_p3_0(out h);
+			ge_precomp t;
+			ge_p1p1 r;
+			for (int i = 1; i < 64; i += 2) {
+				select(out t, i / 2, e[i]);
+				ge_madd(out r, ref h, ref t); ge_p1p1_to_p3(out h, ref r);
+			}
+
+			ge_p2 s;
+			ge_p3_dbl(out r, ref h); ge_p1p1_to_p2(out s, ref r);
+			ge_p2_dbl(out r, ref s); ge_p1p1_to_p2(out s, ref r);
+			ge_p2_dbl(out r, ref s); ge_p1p1_to_p2(out s, ref r);
+			ge_p2_dbl(out r, ref s); ge_p1p1_to_p3(out h, ref r);
+
+			for (int i = 0; i < 64; i += 2) {
+				select(out t, i / 2, e[i]);
+				ge_madd(out r, ref h, ref t); ge_p1p1_to_p3(out h, ref r);
+			}
+		}
+		static void fe_invert(out fe outv, ref fe z) {
+			fe t0;
+			fe t1;
+			fe t2;
+			fe t3;
+			fe_sq(out t0, ref z); for (int i = 1; i < 1; ++i) fe_sq(out t0, ref t0);
+			fe_sq(out t1, ref t0); for (int i = 1; i < 2; ++i) fe_sq(out t1, ref t1);
+			fe_mul(out t1, ref z, ref t1);
+			fe_mul(out t0, ref t0, ref t1);
+			fe_sq(out t2, ref t0); for (int i = 1; i < 1; ++i) fe_sq(out t2, ref t2);
+			fe_mul(out t1, ref t1, ref t2);
+			fe_sq(out t2, ref t1); for (int i = 1; i < 5; ++i) fe_sq(out t2, ref t2);
+			fe_mul(out t1, ref t2, ref t1);
+			fe_sq(out t2, ref t1); for (int i = 1; i < 10; ++i) fe_sq(out t2, ref t2);
+			fe_mul(out t2, ref t2, ref t1);
+			fe_sq(out t3, ref t2); for (int i = 1; i < 20; ++i) fe_sq(out t3, ref t3);
+			fe_mul(out t2, ref t3, ref t2);
+			fe_sq(out t2, ref t2); for (int i = 1; i < 10; ++i) fe_sq(out t2, ref t2);
+			fe_mul(out t1, ref t2, ref t1);
+			fe_sq(out t2, ref t1); for (int i = 1; i < 50; ++i) fe_sq(out t2, ref t2);
+			fe_mul(out t2, ref t2, ref t1);
+			fe_sq(out t3, ref t2); for (int i = 1; i < 100; ++i) fe_sq(out t3, ref t3);
+			fe_mul(out t2, ref t3, ref t2);
+			fe_sq(out t2, ref t2); for (int i = 1; i < 50; ++i) fe_sq(out t2, ref t2);
+			fe_mul(out t1, ref t2, ref t1);
+			fe_sq(out t1, ref t1); for (int i = 1; i < 5; ++i) fe_sq(out t1, ref t1);
+			fe_mul(out outv, ref t1, ref t0);
+		}
+		static unsafe void fe_tobytes(Byte* s, ref fe h) {
+			Int32 h0 = h[0];
+			Int32 h1 = h[1];
+			Int32 h2 = h[2];
+			Int32 h3 = h[3];
+			Int32 h4 = h[4];
+			Int32 h5 = h[5];
+			Int32 h6 = h[6];
+			Int32 h7 = h[7];
+			Int32 h8 = h[8];
+			Int32 h9 = h[9];
+			Int32 q;
+			Int32 carry0;
+			Int32 carry1;
+			Int32 carry2;
+			Int32 carry3;
+			Int32 carry4;
+			Int32 carry5;
+			Int32 carry6;
+			Int32 carry7;
+			Int32 carry8;
+			Int32 carry9;
+
+			q = (19 * h9 + (((Int32)1) << 24)) >> 25;
+			q = (h0 + q) >> 26;
+			q = (h1 + q) >> 25;
+			q = (h2 + q) >> 26;
+			q = (h3 + q) >> 25;
+			q = (h4 + q) >> 26;
+			q = (h5 + q) >> 25;
+			q = (h6 + q) >> 26;
+			q = (h7 + q) >> 25;
+			q = (h8 + q) >> 26;
+			q = (h9 + q) >> 25;
+
+			h0 += 19 * q;
+
+			carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
+			carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
+			carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
+			carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
+			carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
+			carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
+			carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
+			carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
+			carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
+			carry9 = h9 >> 25; h9 -= carry9 << 25;
+			/* h10 = carry9 */
+
+			s[0] = (Byte)(h0 >> 0);
+			s[1] = (Byte)(h0 >> 8);
+			s[2] = (Byte)(h0 >> 16);
+			s[3] = (Byte)((h0 >> 24) | (h1 << 2));
+			s[4] = (Byte)(h1 >> 6);
+			s[5] = (Byte)(h1 >> 14);
+			s[6] = (Byte)((h1 >> 22) | (h2 << 3));
+			s[7] = (Byte)(h2 >> 5);
+			s[8] = (Byte)(h2 >> 13);
+			s[9] = (Byte)((h2 >> 21) | (h3 << 5));
+			s[10] = (Byte)(h3 >> 3);
+			s[11] = (Byte)(h3 >> 11);
+			s[12] = (Byte)((h3 >> 19) | (h4 << 6));
+			s[13] = (Byte)(h4 >> 2);
+			s[14] = (Byte)(h4 >> 10);
+			s[15] = (Byte)(h4 >> 18);
+			s[16] = (Byte)(h5 >> 0);
+			s[17] = (Byte)(h5 >> 8);
+			s[18] = (Byte)(h5 >> 16);
+			s[19] = (Byte)((h5 >> 24) | (h6 << 1));
+			s[20] = (Byte)(h6 >> 7);
+			s[21] = (Byte)(h6 >> 15);
+			s[22] = (Byte)((h6 >> 23) | (h7 << 3));
+			s[23] = (Byte)(h7 >> 5);
+			s[24] = (Byte)(h7 >> 13);
+			s[25] = (Byte)((h7 >> 21) | (h8 << 4));
+			s[26] = (Byte)(h8 >> 4);
+			s[27] = (Byte)(h8 >> 12);
+			s[28] = (Byte)((h8 >> 20) | (h9 << 6));
+			s[29] = (Byte)(h9 >> 2);
+			s[30] = (Byte)(h9 >> 10);
+			s[31] = (Byte)(h9 >> 18);
+		}
+		static unsafe int fe_isnegative(ref fe f) {
+			Byte* s = stackalloc Byte[32];
+			fe_tobytes(s, ref f);
+			return s[0] & 1;
+		}
+		static unsafe void ge_p3_tobytes(Byte* s, ref ge_p3 h) {
+			fe recip;
+			fe x;
+			fe y;
+			fe_invert(out recip, ref h.Z);
+			fe_mul(out x, ref h.X, ref recip);
+			fe_mul(out y, ref h.Y, ref recip);
+			fe_tobytes(s, ref y);
+			s[31] ^= (Byte)(fe_isnegative(ref x) << 7);
+		}
+
+		public static unsafe void crypto_sign_seed_keypair(out Byte[] pk, out Byte[] sk, Byte[] seed) {
+			if (seed.Length < SEEDBYTES) throw new ArgumentException("seed.Length < SEEDBYTES");
+			sk = new Byte[SECRETKEYBYTES];
+			crypto_hash.sha512.crypto_hash(sk, seed, 32);
+			sk[0] &= 248;
+			sk[31] &= 63;
+			sk[31] |= 64;
+
+			ge_p3 A;
+			fixed (Byte* skp = sk) ge_scalarmult_base(out A, skp);
+			pk = new Byte[PUBLICKEYBYTES];
+			fixed (Byte* pkp = pk) ge_p3_tobytes(pkp, ref A);
+
+			for (int i = 0; i < 32; ++i) sk[i] = seed[i];
+			for (int i = 0; i < 32; ++i) sk[32 + i] = pk[i];
+		}
+
+		public static void crypto_sign_keypair(out Byte[] pk, out Byte[] sk) {
+			Byte[] seed = randombytes.generate(32);
+			crypto_sign_seed_keypair(out pk, out sk, seed);
+		}
+
+		public static unsafe void crypto_sign_getpublickey(out Byte[] pk, Byte[] sk) {
+			pk = UCIS.Util.ArrayUtil.Slice(sk, 32, 32);
+		}
+
+		static unsafe Int64 load_3(Byte* inv) {
+			UInt64 result;
+			result = (UInt64)inv[0];
+			result |= ((UInt64)inv[1]) << 8;
+			result |= ((UInt64)inv[2]) << 16;
+			return (Int64)result;
+		}
+		static unsafe Int64 load_4(Byte* inv) {
+			UInt64 result;
+			result = (UInt64)inv[0];
+			result |= ((UInt64)inv[1]) << 8;
+			result |= ((UInt64)inv[2]) << 16;
+			result |= ((UInt64)inv[3]) << 24;
+			return (Int64)result;
+		}
+		static unsafe void sc_reduce(Byte* s) {
+			Int64 s0 = 2097151 & load_3(s);
+			Int64 s1 = 2097151 & (load_4(s + 2) >> 5);
+			Int64 s2 = 2097151 & (load_3(s + 5) >> 2);
+			Int64 s3 = 2097151 & (load_4(s + 7) >> 7);
+			Int64 s4 = 2097151 & (load_4(s + 10) >> 4);
+			Int64 s5 = 2097151 & (load_3(s + 13) >> 1);
+			Int64 s6 = 2097151 & (load_4(s + 15) >> 6);
+			Int64 s7 = 2097151 & (load_3(s + 18) >> 3);
+			Int64 s8 = 2097151 & load_3(s + 21);
+			Int64 s9 = 2097151 & (load_4(s + 23) >> 5);
+			Int64 s10 = 2097151 & (load_3(s + 26) >> 2);
+			Int64 s11 = 2097151 & (load_4(s + 28) >> 7);
+			Int64 s12 = 2097151 & (load_4(s + 31) >> 4);
+			Int64 s13 = 2097151 & (load_3(s + 34) >> 1);
+			Int64 s14 = 2097151 & (load_4(s + 36) >> 6);
+			Int64 s15 = 2097151 & (load_3(s + 39) >> 3);
+			Int64 s16 = 2097151 & load_3(s + 42);
+			Int64 s17 = 2097151 & (load_4(s + 44) >> 5);
+			Int64 s18 = 2097151 & (load_3(s + 47) >> 2);
+			Int64 s19 = 2097151 & (load_4(s + 49) >> 7);
+			Int64 s20 = 2097151 & (load_4(s + 52) >> 4);
+			Int64 s21 = 2097151 & (load_3(s + 55) >> 1);
+			Int64 s22 = 2097151 & (load_4(s + 57) >> 6);
+			Int64 s23 = (load_4(s + 60) >> 3);
+			Int64 carry0;
+			Int64 carry1;
+			Int64 carry2;
+			Int64 carry3;
+			Int64 carry4;
+			Int64 carry5;
+			Int64 carry6;
+			Int64 carry7;
+			Int64 carry8;
+			Int64 carry9;
+			Int64 carry10;
+			Int64 carry11;
+			Int64 carry12;
+			Int64 carry13;
+			Int64 carry14;
+			Int64 carry15;
+			Int64 carry16;
+
+			s11 += s23 * 666643;
+			s12 += s23 * 470296;
+			s13 += s23 * 654183;
+			s14 -= s23 * 997805;
+			s15 += s23 * 136657;
+			s16 -= s23 * 683901;
+
+
+			s10 += s22 * 666643;
+			s11 += s22 * 470296;
+			s12 += s22 * 654183;
+			s13 -= s22 * 997805;
+			s14 += s22 * 136657;
+			s15 -= s22 * 683901;
+
+
+			s9 += s21 * 666643;
+			s10 += s21 * 470296;
+			s11 += s21 * 654183;
+			s12 -= s21 * 997805;
+			s13 += s21 * 136657;
+			s14 -= s21 * 683901;
+
+
+			s8 += s20 * 666643;
+			s9 += s20 * 470296;
+			s10 += s20 * 654183;
+			s11 -= s20 * 997805;
+			s12 += s20 * 136657;
+			s13 -= s20 * 683901;
+
+
+			s7 += s19 * 666643;
+			s8 += s19 * 470296;
+			s9 += s19 * 654183;
+			s10 -= s19 * 997805;
+			s11 += s19 * 136657;
+			s12 -= s19 * 683901;
+
+			s6 += s18 * 666643;
+			s7 += s18 * 470296;
+			s8 += s18 * 654183;
+			s9 -= s18 * 997805;
+			s10 += s18 * 136657;
+			s11 -= s18 * 683901;
+
+			carry6 = (s6 + (1 << 20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+			carry8 = (s8 + (1 << 20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+			carry10 = (s10 + (1 << 20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+			carry12 = (s12 + (1 << 20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
+			carry14 = (s14 + (1 << 20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
+			carry16 = (s16 + (1 << 20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
+
+			carry7 = (s7 + (1 << 20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+			carry9 = (s9 + (1 << 20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+			carry11 = (s11 + (1 << 20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+			carry13 = (s13 + (1 << 20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
+			carry15 = (s15 + (1 << 20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
+
+			s5 += s17 * 666643;
+			s6 += s17 * 470296;
+			s7 += s17 * 654183;
+			s8 -= s17 * 997805;
+			s9 += s17 * 136657;
+			s10 -= s17 * 683901;
+
+			s4 += s16 * 666643;
+			s5 += s16 * 470296;
+			s6 += s16 * 654183;
+			s7 -= s16 * 997805;
+			s8 += s16 * 136657;
+			s9 -= s16 * 683901;
+
+			s3 += s15 * 666643;
+			s4 += s15 * 470296;
+			s5 += s15 * 654183;
+			s6 -= s15 * 997805;
+			s7 += s15 * 136657;
+			s8 -= s15 * 683901;
+
+			s2 += s14 * 666643;
+			s3 += s14 * 470296;
+			s4 += s14 * 654183;
+			s5 -= s14 * 997805;
+			s6 += s14 * 136657;
+			s7 -= s14 * 683901;
+
+			s1 += s13 * 666643;
+			s2 += s13 * 470296;
+			s3 += s13 * 654183;
+			s4 -= s13 * 997805;
+			s5 += s13 * 136657;
+			s6 -= s13 * 683901;
+
+			s0 += s12 * 666643;
+			s1 += s12 * 470296;
+			s2 += s12 * 654183;
+			s3 -= s12 * 997805;
+			s4 += s12 * 136657;
+			s5 -= s12 * 683901;
+			s12 = 0;
+
+			carry0 = (s0 + (1 << 20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
+			carry2 = (s2 + (1 << 20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
+			carry4 = (s4 + (1 << 20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
+			carry6 = (s6 + (1 << 20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+			carry8 = (s8 + (1 << 20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+			carry10 = (s10 + (1 << 20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+
+			carry1 = (s1 + (1 << 20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
+			carry3 = (s3 + (1 << 20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
+			carry5 = (s5 + (1 << 20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
+			carry7 = (s7 + (1 << 20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+			carry9 = (s9 + (1 << 20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+			carry11 = (s11 + (1 << 20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+			s0 += s12 * 666643;
+			s1 += s12 * 470296;
+			s2 += s12 * 654183;
+			s3 -= s12 * 997805;
+			s4 += s12 * 136657;
+			s5 -= s12 * 683901;
+			s12 = 0;
+
+			carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
+			carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
+			carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
+			carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
+			carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
+			carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
+			carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
+			carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
+			carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
+			carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
+			carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+			carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+			s0 += s12 * 666643;
+			s1 += s12 * 470296;
+			s2 += s12 * 654183;
+			s3 -= s12 * 997805;
+			s4 += s12 * 136657;
+			s5 -= s12 * 683901;
+
+
+			carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
+			carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
+			carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
+			carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
+			carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
+			carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
+			carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
+			carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
+			carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
+			carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
+			carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+
+			s[0] = (Byte)(s0 >> 0);
+			s[1] = (Byte)(s0 >> 8);
+			s[2] = (Byte)((s0 >> 16) | (s1 << 5));
+			s[3] = (Byte)(s1 >> 3);
+			s[4] = (Byte)(s1 >> 11);
+			s[5] = (Byte)((s1 >> 19) | (s2 << 2));
+			s[6] = (Byte)(s2 >> 6);
+			s[7] = (Byte)((s2 >> 14) | (s3 << 7));
+			s[8] = (Byte)(s3 >> 1);
+			s[9] = (Byte)(s3 >> 9);
+			s[10] = (Byte)((s3 >> 17) | (s4 << 4));
+			s[11] = (Byte)(s4 >> 4);
+			s[12] = (Byte)(s4 >> 12);
+			s[13] = (Byte)((s4 >> 20) | (s5 << 1));
+			s[14] = (Byte)(s5 >> 7);
+			s[15] = (Byte)((s5 >> 15) | (s6 << 6));
+			s[16] = (Byte)(s6 >> 2);
+			s[17] = (Byte)(s6 >> 10);
+			s[18] = (Byte)((s6 >> 18) | (s7 << 3));
+			s[19] = (Byte)(s7 >> 5);
+			s[20] = (Byte)(s7 >> 13);
+			s[21] = (Byte)(s8 >> 0);
+			s[22] = (Byte)(s8 >> 8);
+			s[23] = (Byte)((s8 >> 16) | (s9 << 5));
+			s[24] = (Byte)(s9 >> 3);
+			s[25] = (Byte)(s9 >> 11);
+			s[26] = (Byte)((s9 >> 19) | (s10 << 2));
+			s[27] = (Byte)(s10 >> 6);
+			s[28] = (Byte)((s10 >> 14) | (s11 << 7));
+			s[29] = (Byte)(s11 >> 1);
+			s[30] = (Byte)(s11 >> 9);
+			s[31] = (Byte)(s11 >> 17);
+		}
+		static unsafe void sc_muladd(Byte* s, Byte* a, Byte* b, Byte* c) {
+			Int64 a0 = 2097151 & load_3(a);
+			Int64 a1 = 2097151 & (load_4(a + 2) >> 5);
+			Int64 a2 = 2097151 & (load_3(a + 5) >> 2);
+			Int64 a3 = 2097151 & (load_4(a + 7) >> 7);
+			Int64 a4 = 2097151 & (load_4(a + 10) >> 4);
+			Int64 a5 = 2097151 & (load_3(a + 13) >> 1);
+			Int64 a6 = 2097151 & (load_4(a + 15) >> 6);
+			Int64 a7 = 2097151 & (load_3(a + 18) >> 3);
+			Int64 a8 = 2097151 & load_3(a + 21);
+			Int64 a9 = 2097151 & (load_4(a + 23) >> 5);
+			Int64 a10 = 2097151 & (load_3(a + 26) >> 2);
+			Int64 a11 = (load_4(a + 28) >> 7);
+			Int64 b0 = 2097151 & load_3(b);
+			Int64 b1 = 2097151 & (load_4(b + 2) >> 5);
+			Int64 b2 = 2097151 & (load_3(b + 5) >> 2);
+			Int64 b3 = 2097151 & (load_4(b + 7) >> 7);
+			Int64 b4 = 2097151 & (load_4(b + 10) >> 4);
+			Int64 b5 = 2097151 & (load_3(b + 13) >> 1);
+			Int64 b6 = 2097151 & (load_4(b + 15) >> 6);
+			Int64 b7 = 2097151 & (load_3(b + 18) >> 3);
+			Int64 b8 = 2097151 & load_3(b + 21);
+			Int64 b9 = 2097151 & (load_4(b + 23) >> 5);
+			Int64 b10 = 2097151 & (load_3(b + 26) >> 2);
+			Int64 b11 = (load_4(b + 28) >> 7);
+			Int64 c0 = 2097151 & load_3(c);
+			Int64 c1 = 2097151 & (load_4(c + 2) >> 5);
+			Int64 c2 = 2097151 & (load_3(c + 5) >> 2);
+			Int64 c3 = 2097151 & (load_4(c + 7) >> 7);
+			Int64 c4 = 2097151 & (load_4(c + 10) >> 4);
+			Int64 c5 = 2097151 & (load_3(c + 13) >> 1);
+			Int64 c6 = 2097151 & (load_4(c + 15) >> 6);
+			Int64 c7 = 2097151 & (load_3(c + 18) >> 3);
+			Int64 c8 = 2097151 & load_3(c + 21);
+			Int64 c9 = 2097151 & (load_4(c + 23) >> 5);
+			Int64 c10 = 2097151 & (load_3(c + 26) >> 2);
+			Int64 c11 = (load_4(c + 28) >> 7);
+			Int64 s0;
+			Int64 s1;
+			Int64 s2;
+			Int64 s3;
+			Int64 s4;
+			Int64 s5;
+			Int64 s6;
+			Int64 s7;
+			Int64 s8;
+			Int64 s9;
+			Int64 s10;
+			Int64 s11;
+			Int64 s12;
+			Int64 s13;
+			Int64 s14;
+			Int64 s15;
+			Int64 s16;
+			Int64 s17;
+			Int64 s18;
+			Int64 s19;
+			Int64 s20;
+			Int64 s21;
+			Int64 s22;
+			Int64 s23;
+			Int64 carry0;
+			Int64 carry1;
+			Int64 carry2;
+			Int64 carry3;
+			Int64 carry4;
+			Int64 carry5;
+			Int64 carry6;
+			Int64 carry7;
+			Int64 carry8;
+			Int64 carry9;
+			Int64 carry10;
+			Int64 carry11;
+			Int64 carry12;
+			Int64 carry13;
+			Int64 carry14;
+			Int64 carry15;
+			Int64 carry16;
+			Int64 carry17;
+			Int64 carry18;
+			Int64 carry19;
+			Int64 carry20;
+			Int64 carry21;
+			Int64 carry22;
+
+			s0 = c0 + a0 * b0;
+			s1 = c1 + a0 * b1 + a1 * b0;
+			s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
+			s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
+			s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
+			s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
+			s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
+			s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0;
+			s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0;
+			s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
+			s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
+			s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
+			s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
+			s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2;
+			s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3;
+			s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4;
+			s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
+			s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
+			s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
+			s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
+			s20 = a9 * b11 + a10 * b10 + a11 * b9;
+			s21 = a10 * b11 + a11 * b10;
+			s22 = a11 * b11;
+			s23 = 0;
+
+			carry0 = (s0 + (1 << 20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
+			carry2 = (s2 + (1 << 20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
+			carry4 = (s4 + (1 << 20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
+			carry6 = (s6 + (1 << 20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+			carry8 = (s8 + (1 << 20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+			carry10 = (s10 + (1 << 20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+			carry12 = (s12 + (1 << 20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
+			carry14 = (s14 + (1 << 20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
+			carry16 = (s16 + (1 << 20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
+			carry18 = (s18 + (1 << 20)) >> 21; s19 += carry18; s18 -= carry18 << 21;
+			carry20 = (s20 + (1 << 20)) >> 21; s21 += carry20; s20 -= carry20 << 21;
+			carry22 = (s22 + (1 << 20)) >> 21; s23 += carry22; s22 -= carry22 << 21;
+
+			carry1 = (s1 + (1 << 20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
+			carry3 = (s3 + (1 << 20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
+			carry5 = (s5 + (1 << 20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
+			carry7 = (s7 + (1 << 20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+			carry9 = (s9 + (1 << 20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+			carry11 = (s11 + (1 << 20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+			carry13 = (s13 + (1 << 20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
+			carry15 = (s15 + (1 << 20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
+			carry17 = (s17 + (1 << 20)) >> 21; s18 += carry17; s17 -= carry17 << 21;
+			carry19 = (s19 + (1 << 20)) >> 21; s20 += carry19; s19 -= carry19 << 21;
+			carry21 = (s21 + (1 << 20)) >> 21; s22 += carry21; s21 -= carry21 << 21;
+
+			s11 += s23 * 666643;
+			s12 += s23 * 470296;
+			s13 += s23 * 654183;
+			s14 -= s23 * 997805;
+			s15 += s23 * 136657;
+			s16 -= s23 * 683901;
+
+
+			s10 += s22 * 666643;
+			s11 += s22 * 470296;
+			s12 += s22 * 654183;
+			s13 -= s22 * 997805;
+			s14 += s22 * 136657;
+			s15 -= s22 * 683901;
+
+
+			s9 += s21 * 666643;
+			s10 += s21 * 470296;
+			s11 += s21 * 654183;
+			s12 -= s21 * 997805;
+			s13 += s21 * 136657;
+			s14 -= s21 * 683901;
+
+
+			s8 += s20 * 666643;
+			s9 += s20 * 470296;
+			s10 += s20 * 654183;
+			s11 -= s20 * 997805;
+			s12 += s20 * 136657;
+			s13 -= s20 * 683901;
+
+
+			s7 += s19 * 666643;
+			s8 += s19 * 470296;
+			s9 += s19 * 654183;
+			s10 -= s19 * 997805;
+			s11 += s19 * 136657;
+			s12 -= s19 * 683901;
+
+
+			s6 += s18 * 666643;
+			s7 += s18 * 470296;
+			s8 += s18 * 654183;
+			s9 -= s18 * 997805;
+			s10 += s18 * 136657;
+			s11 -= s18 * 683901;
+
+
+			carry6 = (s6 + (1 << 20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+			carry8 = (s8 + (1 << 20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+			carry10 = (s10 + (1 << 20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+			carry12 = (s12 + (1 << 20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
+			carry14 = (s14 + (1 << 20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
+			carry16 = (s16 + (1 << 20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
+
+			carry7 = (s7 + (1 << 20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+			carry9 = (s9 + (1 << 20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+			carry11 = (s11 + (1 << 20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+			carry13 = (s13 + (1 << 20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
+			carry15 = (s15 + (1 << 20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
+
+			s5 += s17 * 666643;
+			s6 += s17 * 470296;
+			s7 += s17 * 654183;
+			s8 -= s17 * 997805;
+			s9 += s17 * 136657;
+			s10 -= s17 * 683901;
+
+
+			s4 += s16 * 666643;
+			s5 += s16 * 470296;
+			s6 += s16 * 654183;
+			s7 -= s16 * 997805;
+			s8 += s16 * 136657;
+			s9 -= s16 * 683901;
+
+
+			s3 += s15 * 666643;
+			s4 += s15 * 470296;
+			s5 += s15 * 654183;
+			s6 -= s15 * 997805;
+			s7 += s15 * 136657;
+			s8 -= s15 * 683901;
+
+
+			s2 += s14 * 666643;
+			s3 += s14 * 470296;
+			s4 += s14 * 654183;
+			s5 -= s14 * 997805;
+			s6 += s14 * 136657;
+			s7 -= s14 * 683901;
+
+
+			s1 += s13 * 666643;
+			s2 += s13 * 470296;
+			s3 += s13 * 654183;
+			s4 -= s13 * 997805;
+			s5 += s13 * 136657;
+			s6 -= s13 * 683901;
+
+
+			s0 += s12 * 666643;
+			s1 += s12 * 470296;
+			s2 += s12 * 654183;
+			s3 -= s12 * 997805;
+			s4 += s12 * 136657;
+			s5 -= s12 * 683901;
+			s12 = 0;
+
+			carry0 = (s0 + (1 << 20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
+			carry2 = (s2 + (1 << 20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
+			carry4 = (s4 + (1 << 20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
+			carry6 = (s6 + (1 << 20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+			carry8 = (s8 + (1 << 20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+			carry10 = (s10 + (1 << 20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+
+			carry1 = (s1 + (1 << 20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
+			carry3 = (s3 + (1 << 20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
+			carry5 = (s5 + (1 << 20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
+			carry7 = (s7 + (1 << 20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+			carry9 = (s9 + (1 << 20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+			carry11 = (s11 + (1 << 20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+			s0 += s12 * 666643;
+			s1 += s12 * 470296;
+			s2 += s12 * 654183;
+			s3 -= s12 * 997805;
+			s4 += s12 * 136657;
+			s5 -= s12 * 683901;
+			s12 = 0;
+
+			carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
+			carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
+			carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
+			carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
+			carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
+			carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
+			carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
+			carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
+			carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
+			carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
+			carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+			carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+			s0 += s12 * 666643;
+			s1 += s12 * 470296;
+			s2 += s12 * 654183;
+			s3 -= s12 * 997805;
+			s4 += s12 * 136657;
+			s5 -= s12 * 683901;
+
+
+			carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
+			carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
+			carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
+			carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
+			carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
+			carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
+			carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
+			carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
+			carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
+			carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
+			carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+
+			s[0] = (Byte)(s0 >> 0);
+			s[1] = (Byte)(s0 >> 8);
+			s[2] = (Byte)((s0 >> 16) | (s1 << 5));
+			s[3] = (Byte)(s1 >> 3);
+			s[4] = (Byte)(s1 >> 11);
+			s[5] = (Byte)((s1 >> 19) | (s2 << 2));
+			s[6] = (Byte)(s2 >> 6);
+			s[7] = (Byte)((s2 >> 14) | (s3 << 7));
+			s[8] = (Byte)(s3 >> 1);
+			s[9] = (Byte)(s3 >> 9);
+			s[10] = (Byte)((s3 >> 17) | (s4 << 4));
+			s[11] = (Byte)(s4 >> 4);
+			s[12] = (Byte)(s4 >> 12);
+			s[13] = (Byte)((s4 >> 20) | (s5 << 1));
+			s[14] = (Byte)(s5 >> 7);
+			s[15] = (Byte)((s5 >> 15) | (s6 << 6));
+			s[16] = (Byte)(s6 >> 2);
+			s[17] = (Byte)(s6 >> 10);
+			s[18] = (Byte)((s6 >> 18) | (s7 << 3));
+			s[19] = (Byte)(s7 >> 5);
+			s[20] = (Byte)(s7 >> 13);
+			s[21] = (Byte)(s8 >> 0);
+			s[22] = (Byte)(s8 >> 8);
+			s[23] = (Byte)((s8 >> 16) | (s9 << 5));
+			s[24] = (Byte)(s9 >> 3);
+			s[25] = (Byte)(s9 >> 11);
+			s[26] = (Byte)((s9 >> 19) | (s10 << 2));
+			s[27] = (Byte)(s10 >> 6);
+			s[28] = (Byte)((s10 >> 14) | (s11 << 7));
+			s[29] = (Byte)(s11 >> 1);
+			s[30] = (Byte)(s11 >> 9);
+			s[31] = (Byte)(s11 >> 17);
+		}
+		public static unsafe void crypto_sign(Byte[] sm, int smoffset, out UInt64 smlen, Byte[] m, int moffset, UInt64 mlen, Byte[] sk) {
+			if (smoffset + (int)mlen + 64 > sm.Length) throw new ArgumentException("signed message buffer is too small");
+			if (moffset + (int)mlen > m.Length) throw new ArgumentException("message buffer is too small");
+			if (64 > sk.Length) throw new ArgumentException("key buffer is too small");
+			fixed (Byte* smp = sm, mp = m, skp = sk) crypto_sign(smp + smoffset, out smlen, mp + moffset, mlen, skp);
+		}
+		public static unsafe void crypto_sign(Byte* sm, out UInt64 smlen, Byte* m, UInt64 mlen, Byte* sk) {
+			Byte* az = stackalloc Byte[64];
+			Byte* r = stackalloc Byte[64];
+			Byte* hram = stackalloc Byte[64];
+
+			crypto_hash.sha512.crypto_hash(az, sk, 32);
+			az[0] &= 248;
+			az[31] &= 63;
+			az[31] |= 64;
+
+			smlen = mlen + 64;
+			for (UInt64 i = 0; i < mlen; ++i) sm[64 + i] = m[i];
+			for (UInt64 i = 0; i < 32; ++i) sm[32 + i] = az[32 + i];
+			crypto_hash.sha512.crypto_hash(r, sm + 32, mlen + 32);
+			for (UInt64 i = 0; i < 32; ++i) sm[32 + i] = sk[32 + i];
+
+			sc_reduce(r);
+			ge_p3 R;
+			ge_scalarmult_base(out R, r);
+			ge_p3_tobytes(sm, ref R);
+
+			crypto_hash.sha512.crypto_hash(hram, sm, mlen + 64);
+			sc_reduce(hram);
+			sc_muladd(sm + 32, hram, az, r);
+		}
+
+		static unsafe void fe_frombytes(out fe h, Byte* s) {
+			Int64 h0 = load_4(s);
+			Int64 h1 = load_3(s + 4) << 6;
+			Int64 h2 = load_3(s + 7) << 5;
+			Int64 h3 = load_3(s + 10) << 3;
+			Int64 h4 = load_3(s + 13) << 2;
+			Int64 h5 = load_4(s + 16);
+			Int64 h6 = load_3(s + 20) << 7;
+			Int64 h7 = load_3(s + 23) << 5;
+			Int64 h8 = load_3(s + 26) << 4;
+			Int64 h9 = (load_3(s + 29) & 8388607) << 2;
+			Int64 carry0;
+			Int64 carry1;
+			Int64 carry2;
+			Int64 carry3;
+			Int64 carry4;
+			Int64 carry5;
+			Int64 carry6;
+			Int64 carry7;
+			Int64 carry8;
+			Int64 carry9;
+
+			carry9 = (h9 + (Int64)(1 << 24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+			carry1 = (h1 + (Int64)(1 << 24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+			carry3 = (h3 + (Int64)(1 << 24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+			carry5 = (h5 + (Int64)(1 << 24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+			carry7 = (h7 + (Int64)(1 << 24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+			carry0 = (h0 + (Int64)(1 << 25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+			carry2 = (h2 + (Int64)(1 << 25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+			carry4 = (h4 + (Int64)(1 << 25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+			carry6 = (h6 + (Int64)(1 << 25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+			carry8 = (h8 + (Int64)(1 << 25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+			h = new fe();
+			h[0] = (Int32)h0;
+			h[1] = (Int32)h1;
+			h[2] = (Int32)h2;
+			h[3] = (Int32)h3;
+			h[4] = (Int32)h4;
+			h[5] = (Int32)h5;
+			h[6] = (Int32)h6;
+			h[7] = (Int32)h7;
+			h[8] = (Int32)h8;
+			h[9] = (Int32)h9;
+		}
+		static Byte[] zero = new Byte[32];
+		static unsafe int fe_isnonzero(ref fe f) {
+			Byte* s = stackalloc Byte[32];
+			fe_tobytes(s, ref f);
+			fixed (Byte* zerop = zero) return crypto_verify._32.crypto_verify(s, zerop);
+		}
+		static fe d = fe_unpack(0, new Int32[10] { -10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116 });
+		static fe sqrtm1 = fe_unpack(0, new Int32[10] { -32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482 });
+		static void fe_pow22523(out fe outv, ref fe z) {
+			fe t0;
+			fe t1;
+			fe t2;
+			fe_sq(out t0, ref z); for (int i = 1; i < 1; ++i) fe_sq(out t0, ref t0);
+			fe_sq(out t1, ref t0); for (int i = 1; i < 2; ++i) fe_sq(out t1, ref t1);
+			fe_mul(out t1, ref z, ref t1);
+			fe_mul(out t0, ref t0, ref t1);
+			fe_sq(out t0, ref t0); for (int i = 1; i < 1; ++i) fe_sq(out t0, ref t0);
+			fe_mul(out t0, ref t1, ref t0);
+			fe_sq(out t1, ref t0); for (int i = 1; i < 5; ++i) fe_sq(out t1, ref t1);
+			fe_mul(out t0, ref t1, ref t0);
+			fe_sq(out t1, ref t0); for (int i = 1; i < 10; ++i) fe_sq(out t1, ref t1);
+			fe_mul(out t1, ref t1, ref t0);
+			fe_sq(out t2, ref t1); for (int i = 1; i < 20; ++i) fe_sq(out t2, ref t2);
+			fe_mul(out t1, ref t2, ref t1);
+			fe_sq(out t1, ref t1); for (int i = 1; i < 10; ++i) fe_sq(out t1, ref t1);
+			fe_mul(out t0, ref t1, ref t0);
+			fe_sq(out t1, ref t0); for (int i = 1; i < 50; ++i) fe_sq(out t1, ref t1);
+			fe_mul(out t1, ref t1, ref t0);
+			fe_sq(out t2, ref t1); for (int i = 1; i < 100; ++i) fe_sq(out t2, ref t2);
+			fe_mul(out t1, ref t2, ref t1);
+			fe_sq(out t1, ref t1); for (int i = 1; i < 50; ++i) fe_sq(out t1, ref t1);
+			fe_mul(out t0, ref t1, ref t0);
+			fe_sq(out t0, ref t0); for (int i = 1; i < 2; ++i) fe_sq(out t0, ref t0);
+			fe_mul(out outv, ref t0, ref z);
+		}
+		static unsafe Boolean ge_frombytes_negate_vartime(out ge_p3 h, Byte* s) {
+			fe u;
+			fe v;
+			fe v3;
+			fe vxx;
+			fe check;
+
+			fe_frombytes(out h.Y, s);
+			fe_1(out h.Z);
+			fe_sq(out u, ref h.Y);
+			fe_mul(out v, ref u, ref d);
+			fe_sub(out u, ref u, ref h.Z); /* u = y^2-1 */
+			fe_add(out v, ref v, ref h.Z); /* v = dy^2+1 */
+
+			fe_sq(out v3, ref v);
+			fe_mul(out v3, ref v3, ref v); /* v3 = v^3 */
+			fe_sq(out h.X, ref v3);
+			fe_mul(out h.X, ref h.X, ref v);
+			fe_mul(out h.X, ref h.X, ref u); /* x = uv^7 */
+
+			fe_pow22523(out h.X, ref h.X); /* x = (uv^7)^((q-5)/8) */
+			fe_mul(out h.X, ref h.X, ref v3);
+			fe_mul(out h.X, ref h.X, ref u); /* x = uv^3(uv^7)^((q-5)/8) */
+
+			fe_sq(out vxx, ref h.X);
+			fe_mul(out vxx, ref vxx, ref v);
+			fe_sub(out check, ref vxx, ref u); /* vx^2-u */
+			if (fe_isnonzero(ref check) != 0) {
+				fe_add(out check, ref vxx, ref u); /* vx^2+u */
+				if (fe_isnonzero(ref check) != 0) return false;
+				fe_mul(out h.X, ref h.X, ref sqrtm1);
+			}
+
+			if (fe_isnegative(ref h.X) == (s[31] >> 7))
+				fe_neg(out h.X, ref h.X);
+
+			fe_mul(out h.T, ref h.X, ref h.Y);
+			return true;
+		}
+		struct ge_cached {
+			public fe YplusX;
+			public fe YminusX;
+			public fe Z;
+			public fe T2d;
+		}
+		static unsafe void slide(SByte* r, Byte* a) {
+			for (int i = 0; i < 256; ++i) r[i] = (SByte)(1 & (a[i >> 3] >> (i & 7)));
+
+			for (int i = 0; i < 256; ++i)
+				if (r[i] != 0) {
+					for (int b = 1; b <= 6 && i + b < 256; ++b) {
+						if (r[i + b] != 0) {
+							if (r[i] + (r[i + b] << b) <= 15) {
+								r[i] += (SByte)(r[i + b] << b); r[i + b] = 0;
+							} else if (r[i] - (r[i + b] << b) >= -15) {
+								r[i] -= (SByte)(r[i + b] << b);
+								for (int k = i + b; k < 256; ++k) {
+									if (r[k] == 0) {
+										r[k] = 1;
+										break;
+									}
+									r[k] = 0;
+								}
+							} else
+								break;
+						}
+					}
+				}
+		}
+		static ge_precomp[] Bi = base_unpack(8, 0, new Int32[8 * 3 * 10] {
+#region Base number
+25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605,
+-12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378,
+-8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546,
+15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024,
+16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574,
+30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357,
+10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380,
+4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306,
+19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942,
+5153746,9909285,1723747,-2777874,30523605,5516873,19480852,5230134,-23952439,-15175766,
+-30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701,
+28881845,14381568,9657904,3680757,-20181635,7843316,-31400660,1370708,29794553,-1409300,
+-22518993,-6692182,14201702,-8745502,-23510406,8844726,18474211,-1361450,-13062696,13821877,
+-6455177,-7839871,3374702,-4740862,-27098617,-10571707,31655028,-7212327,18853322,-14220951,
+4566830,-12963868,-28974889,-12240689,-7602672,-2830569,-8514358,-10431137,2207753,-3209784,
+-25154831,-4185821,29681144,7868801,-6854661,-9423865,-12437364,-663000,-31111463,-16132436,
+25576264,-2703214,7349804,-11814844,16472782,9300885,3844789,15725684,171356,6466918,
+23103977,13316479,9739013,-16149481,817875,-15038942,8965339,-14088058,-30714912,16193877,
+-33521811,3180713,-2394130,14003687,-16903474,-16270840,17238398,4729455,-18074513,9256800,
+-25182317,-4174131,32336398,5036987,-21236817,11360617,22616405,9761698,-19827198,630305,
+-13720693,2639453,-24237460,-7406481,9494427,-5774029,-6554551,-15960994,-2449256,-14291300,
+-3151181,-5046075,9282714,6866145,-31907062,-863023,-18940575,15033784,25105118,-7894876,
+-24326370,15950226,-31801215,-14592823,-11662737,-5090925,1573892,-2625887,2198790,-15804619,
+-3099351,10324967,-2241613,7453183,-5446979,-2735503,-13812022,-16236442,-32461234,-12290683,
+#endregion
+});
+		static fe d2 = fe_unpack(0, new Int32[10] { -21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199 });
+		static void ge_p3_to_cached(out ge_cached r, ref ge_p3 p) {
+			fe_add(out r.YplusX, ref p.Y, ref p.X);
+			fe_sub(out r.YminusX, ref p.Y, ref p.X);
+			fe_copy(out r.Z, ref p.Z);
+			fe_mul(out r.T2d, ref p.T, ref d2);
+		}
+		static void ge_add(out ge_p1p1 r, ref ge_p3 p, ref ge_cached q) {
+			fe t0;
+			fe_add(out r.X, ref p.Y, ref p.X);
+			fe_sub(out r.Y, ref p.Y, ref p.X);
+			fe_mul(out r.Z, ref r.X, ref q.YplusX);
+			fe_mul(out r.Y, ref r.Y, ref q.YminusX);
+			fe_mul(out r.T, ref q.T2d, ref p.T);
+			fe_mul(out r.X, ref p.Z, ref q.Z);
+			fe_add(out t0, ref r.X, ref r.X);
+			fe_sub(out r.X, ref r.Z, ref r.Y);
+			fe_add(out r.Y, ref r.Z, ref r.Y);
+			fe_add(out r.Z, ref t0, ref r.T);
+			fe_sub(out r.T, ref t0, ref r.T);
+		}
+		static void ge_p2_0(out ge_p2 h) {
+			fe_0(out h.X);
+			fe_1(out h.Y);
+			fe_1(out h.Z);
+		}
+		static void ge_sub(out ge_p1p1 r, ref ge_p3 p, ref ge_cached q) {
+			fe t0;
+			fe_add(out r.X, ref p.Y, ref p.X);
+			fe_sub(out r.Y, ref p.Y, ref p.X);
+			fe_mul(out r.Z, ref r.X, ref q.YminusX);
+			fe_mul(out r.Y, ref r.Y, ref q.YplusX);
+			fe_mul(out r.T, ref q.T2d, ref p.T);
+			fe_mul(out r.X, ref p.Z, ref q.Z);
+			fe_add(out t0, ref r.X, ref r.X);
+			fe_sub(out r.X, ref r.Z, ref r.Y);
+			fe_add(out r.Y, ref r.Z, ref r.Y);
+			fe_sub(out r.Z, ref t0, ref r.T);
+			fe_add(out r.T, ref t0, ref r.T);
+		}
+		static void ge_msub(out ge_p1p1 r, ref ge_p3 p, ref ge_precomp q) {
+			fe t0;
+			fe_add(out r.X, ref p.Y, ref p.X);
+			fe_sub(out r.Y, ref p.Y, ref p.X);
+			fe_mul(out r.Z, ref r.X, ref q.yminusx);
+			fe_mul(out r.Y, ref r.Y, ref q.yplusx);
+			fe_mul(out r.T, ref q.xy2d, ref p.T);
+			fe_add(out t0, ref p.Z, ref p.Z);
+			fe_sub(out r.X, ref r.Z, ref r.Y);
+			fe_add(out r.Y, ref r.Z, ref r.Y);
+			fe_sub(out r.Z, ref t0, ref r.T);
+			fe_add(out r.T, ref t0, ref r.T);
+		}
+		static unsafe void ge_double_scalarmult_vartime(out ge_p2 r, Byte* a, ref ge_p3 A, Byte* b) {
+			SByte* aslide = stackalloc SByte[256];
+			SByte* bslide = stackalloc SByte[256];
+			ge_cached* Ai = stackalloc ge_cached[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
+			ge_p1p1 t;
+			ge_p3 u;
+			ge_p3 A2;
+			int i;
+
+			slide(aslide, a);
+			slide(bslide, b);
+
+			ge_p3_to_cached(out Ai[0], ref A);
+			ge_p3_dbl(out t, ref A); ge_p1p1_to_p3(out A2, ref t);
+			ge_add(out t, ref A2, ref Ai[0]); ge_p1p1_to_p3(out u, ref t); ge_p3_to_cached(out Ai[1], ref u);
+			ge_add(out t, ref A2, ref Ai[1]); ge_p1p1_to_p3(out u, ref t); ge_p3_to_cached(out Ai[2], ref u);
+			ge_add(out t, ref A2, ref Ai[2]); ge_p1p1_to_p3(out u, ref t); ge_p3_to_cached(out Ai[3], ref u);
+			ge_add(out t, ref A2, ref Ai[3]); ge_p1p1_to_p3(out u, ref t); ge_p3_to_cached(out Ai[4], ref u);
+			ge_add(out t, ref A2, ref Ai[4]); ge_p1p1_to_p3(out u, ref t); ge_p3_to_cached(out Ai[5], ref u);
+			ge_add(out t, ref A2, ref Ai[5]); ge_p1p1_to_p3(out u, ref t); ge_p3_to_cached(out Ai[6], ref u);
+			ge_add(out t, ref A2, ref Ai[6]); ge_p1p1_to_p3(out u, ref t); ge_p3_to_cached(out Ai[7], ref u);
+
+			ge_p2_0(out r);
+
+			for (i = 255; i >= 0; --i) {
+				if ((aslide[i] != 0) || (bslide[i] != 0)) break;
+			}
+
+			for (; i >= 0; --i) {
+				ge_p2_dbl(out t, ref r);
+
+				if (aslide[i] > 0) {
+					ge_p1p1_to_p3(out u, ref t);
+					ge_add(out t, ref u, ref Ai[aslide[i] / 2]);
+				} else if (aslide[i] < 0) {
+					ge_p1p1_to_p3(out u, ref t);
+					ge_sub(out t, ref u, ref Ai[(-aslide[i]) / 2]);
+				}
+
+				if (bslide[i] > 0) {
+					ge_p1p1_to_p3(out u, ref t);
+					ge_madd(out t, ref u, ref Bi[bslide[i] / 2]);
+				} else if (bslide[i] < 0) {
+					ge_p1p1_to_p3(out u, ref t);
+					ge_msub(out t, ref u, ref Bi[(-bslide[i]) / 2]);
+				}
+
+				ge_p1p1_to_p2(out r, ref t);
+			}
+		}
+		static unsafe void ge_tobytes(Byte* s, ref ge_p2 h) {
+			fe recip;
+			fe x;
+			fe y;
+			fe_invert(out recip, ref h.Z);
+			fe_mul(out x, ref h.X, ref recip);
+			fe_mul(out y, ref h.Y, ref recip);
+			fe_tobytes(s, ref y);
+			s[31] ^= (Byte)(fe_isnegative(ref x) << 7);
+		}
+		public static unsafe Boolean crypto_sign_open(Byte[] m, int moffset, out UInt64 mlen, Byte[] sm, int smoffset, UInt64 smlen, Byte[] pk) {
+			if (smoffset + (int)smlen > sm.Length) throw new ArgumentException("signed message buffer is too small");
+			if (moffset + (int)smlen > m.Length) throw new ArgumentException("message buffer is too small");
+			if (32 > pk.Length) throw new ArgumentException("key buffer is too small");
+			fixed (Byte* mp = m, smp = sm, pkp = pk) return crypto_sign_open(mp + moffset, out mlen, smp + smoffset, smlen, pkp);
+		}
+		public static unsafe Boolean crypto_sign_open(Byte* m, out UInt64 mlen, Byte* sm, UInt64 smlen, Byte* pk) {
+			Byte* h = stackalloc Byte[64];
+			Byte* checkr = stackalloc Byte[32];
+			ge_p3 A;
+			ge_p2 R;
+
+			mlen = unchecked((UInt64)(-1));
+			if (smlen < 64) return false;
+			if ((sm[63] & 224) != 0) return false;
+			if (!ge_frombytes_negate_vartime(out A, pk)) return false;
+
+			for (UInt64 i = 0; i < smlen; ++i) m[i] = sm[i];
+			for (UInt64 i = 0; i < 32; ++i) m[32 + i] = pk[i];
+			crypto_hash.sha512.crypto_hash(h, m, smlen);
+			sc_reduce(h);
+
+			ge_double_scalarmult_vartime(out R, h, ref A, sm + 32);
+			ge_tobytes(checkr, ref R);
+			if (crypto_verify._32.crypto_verify(checkr, sm) != 0) {
+				for (UInt64 i = 0; i < smlen; ++i) m[i] = 0;
+				return false;
+			}
+
+			for (UInt64 i = 0; i < smlen - 64; ++i) m[i] = sm[64 + i];
+			for (UInt64 i = smlen - 64; i < smlen; ++i) m[i] = 0;
+			mlen = smlen - 64;
+			return true;
+		}
+	}
+}
--- a/NaCl/crypto_sign/edwards25519sha512batch.cs	Wed Oct 30 15:32:58 2013 +0100
+++ b/NaCl/crypto_sign/edwards25519sha512batch.cs	Fri Nov 01 00:07:36 2013 +0100
@@ -1,6 +1,4 @@
 using System;
-using UCIS.NaCl;
-using System.Runtime.InteropServices;
 
 namespace UCIS.NaCl.crypto_sign {
 	public static class edwards25519sha512batch {
--- a/UCIS.Core.csproj	Wed Oct 30 15:32:58 2013 +0100
+++ b/UCIS.Core.csproj	Fri Nov 01 00:07:36 2013 +0100
@@ -77,6 +77,7 @@
     <Compile Include="NaCl\crypto_secretbox\xsalsa20poly1305.cs">
       <SubType>Code</SubType>
     </Compile>
+    <Compile Include="NaCl\crypto_sign\ed25519.cs" />
     <Compile Include="NaCl\crypto_sign\edwards25519sha512batch.cs">
       <SubType>Code</SubType>
     </Compile>