(() => { let _0 = new Uint8Array(16); let _9 = new Uint8Array(32); _9[0] = 9; function gf(init) { var i, r = new Float64Array(16); if (init) for (i = 0; i < init.length; i++) r[i] = init[i]; return r; } ; const gf0 = gf(), gf1 = gf([1]), _121665 = gf([0xdb41, 1]), D = gf([ 0x78a3, 0x1359, 0x4dca, 0x75eb, 0xd8ab, 0x4141, 0x0a4d, 0x0070, 0xe898, 0x7779, 0x4079, 0x8cc7, 0xfe73, 0x2b6f, 0x6cee, 0x5203, ]), D2 = gf([ 0xf159, 0x26b2, 0x9b94, 0xebd6, 0xb156, 0x8283, 0x149a, 0x00e0, 0xd130, 0xeef3, 0x80f2, 0x198e, 0xfce7, 0x56df, 0xd9dc, 0x2406, ]), X = gf([ 0xd51a, 0x8f25, 0x2d60, 0xc956, 0xa7b2, 0x9525, 0xc760, 0x692c, 0xdc5c, 0xfdd6, 0xe231, 0xc0a4, 0x53fe, 0xcd6e, 0x36d3, 0x2169, ]), Y = gf([ 0x6658, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, ]), I = gf([ 0xa0b0, 0x4a0e, 0x1b27, 0xc4ee, 0xe478, 0xad2f, 0x1806, 0x2f43, 0xd7a7, 0x3dfb, 0x0099, 0x2b4d, 0xdf0b, 0x4fc1, 0x2480, 0x2b83, ]); function ts64(x, i, h, l) { x[i] = (h >> 24) & 0xff; x[i + 1] = (h >> 16) & 0xff; x[i + 2] = (h >> 8) & 0xff; x[i + 3] = h & 0xff; x[i + 4] = (l >> 24) & 0xff; x[i + 5] = (l >> 16) & 0xff; x[i + 6] = (l >> 8) & 0xff; x[i + 7] = l & 0xff; } function vn(x, xi, y, yi, n) { var i, d = 0; for (i = 0; i < n; i++) d |= x[xi + i] ^ y[yi + i]; return (1 & ((d - 1) >>> 8)) - 1; } function crypto_verify_32(x, xi, y, yi) { return vn(x, xi, y, yi, 32); } function set25519(r, a) { var i; for (i = 0; i < 16; i++) r[i] = a[i] | 0; } function car25519(o) { var i, v, c = 1; for (i = 0; i < 16; i++) { v = o[i] + c + 65535; c = Math.floor(v / 65536); o[i] = v - c * 65536; } o[0] += c - 1 + 37 * (c - 1); } function sel25519(p, q, b) { var t, c = ~(b - 1); for (var i = 0; i < 16; i++) { t = c & (p[i] ^ q[i]); p[i] ^= t; q[i] ^= t; } } function pack25519(o, n) { var i, j, b; var m = gf(), t = gf(); for (i = 0; i < 16; i++) t[i] = n[i]; car25519(t); car25519(t); car25519(t); for (j = 0; j < 2; j++) { m[0] = t[0] - 0xffed; for (i = 1; i < 15; i++) { m[i] = t[i] - 0xffff - ((m[i - 1] >> 16) & 1); m[i - 1] &= 0xffff; } m[15] = t[15] - 0x7fff - ((m[14] >> 16) & 1); b = (m[15] >> 16) & 1; m[14] &= 0xffff; sel25519(t, m, 1 - b); } for (i = 0; i < 16; i++) { o[2 * i] = t[i] & 0xff; o[2 * i + 1] = t[i] >> 8; } } function neq25519(a, b) { var c = new Uint8Array(32), d = new Uint8Array(32); pack25519(c, a); pack25519(d, b); return crypto_verify_32(c, 0, d, 0); } function par25519(a) { var d = new Uint8Array(32); pack25519(d, a); return d[0] & 1; } function unpack25519(o, n) { var i; for (i = 0; i < 16; i++) o[i] = n[2 * i] + (n[2 * i + 1] << 8); o[15] &= 0x7fff; } function A(o, a, b) { for (var i = 0; i < 16; i++) o[i] = a[i] + b[i]; } function Z(o, a, b) { for (var i = 0; i < 16; i++) o[i] = a[i] - b[i]; } function M(o, a, b) { var v, c, t0 = 0, t1 = 0, t2 = 0, t3 = 0, t4 = 0, t5 = 0, t6 = 0, t7 = 0, t8 = 0, t9 = 0, t10 = 0, t11 = 0, t12 = 0, t13 = 0, t14 = 0, t15 = 0, t16 = 0, t17 = 0, t18 = 0, t19 = 0, t20 = 0, t21 = 0, t22 = 0, t23 = 0, t24 = 0, t25 = 0, t26 = 0, t27 = 0, t28 = 0, t29 = 0, t30 = 0, b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3], b4 = b[4], b5 = b[5], b6 = b[6], b7 = b[7], b8 = b[8], b9 = b[9], b10 = b[10], b11 = b[11], b12 = b[12], b13 = b[13], b14 = b[14], b15 = b[15]; v = a[0]; t0 += v * b0; t1 += v * b1; t2 += v * b2; t3 += v * b3; t4 += v * b4; t5 += v * b5; t6 += v * b6; t7 += v * b7; t8 += v * b8; t9 += v * b9; t10 += v * b10; t11 += v * b11; t12 += v * b12; t13 += v * b13; t14 += v * b14; t15 += v * b15; v = a[1]; t1 += v * b0; t2 += v * b1; t3 += v * b2; t4 += v * b3; t5 += v * b4; t6 += v * b5; t7 += v * b6; t8 += v * b7; t9 += v * b8; t10 += v * b9; t11 += v * b10; t12 += v * b11; t13 += v * b12; t14 += v * b13; t15 += v * b14; t16 += v * b15; v = a[2]; t2 += v * b0; t3 += v * b1; t4 += v * b2; t5 += v * b3; t6 += v * b4; t7 += v * b5; t8 += v * b6; t9 += v * b7; t10 += v * b8; t11 += v * b9; t12 += v * b10; t13 += v * b11; t14 += v * b12; t15 += v * b13; t16 += v * b14; t17 += v * b15; v = a[3]; t3 += v * b0; t4 += v * b1; t5 += v * b2; t6 += v * b3; t7 += v * b4; t8 += v * b5; t9 += v * b6; t10 += v * b7; t11 += v * b8; t12 += v * b9; t13 += v * b10; t14 += v * b11; t15 += v * b12; t16 += v * b13; t17 += v * b14; t18 += v * b15; v = a[4]; t4 += v * b0; t5 += v * b1; t6 += v * b2; t7 += v * b3; t8 += v * b4; t9 += v * b5; t10 += v * b6; t11 += v * b7; t12 += v * b8; t13 += v * b9; t14 += v * b10; t15 += v * b11; t16 += v * b12; t17 += v * b13; t18 += v * b14; t19 += v * b15; v = a[5]; t5 += v * b0; t6 += v * b1; t7 += v * b2; t8 += v * b3; t9 += v * b4; t10 += v * b5; t11 += v * b6; t12 += v * b7; t13 += v * b8; t14 += v * b9; t15 += v * b10; t16 += v * b11; t17 += v * b12; t18 += v * b13; t19 += v * b14; t20 += v * b15; v = a[6]; t6 += v * b0; t7 += v * b1; t8 += v * b2; t9 += v * b3; t10 += v * b4; t11 += v * b5; t12 += v * b6; t13 += v * b7; t14 += v * b8; t15 += v * b9; t16 += v * b10; t17 += v * b11; t18 += v * b12; t19 += v * b13; t20 += v * b14; t21 += v * b15; v = a[7]; t7 += v * b0; t8 += v * b1; t9 += v * b2; t10 += v * b3; t11 += v * b4; t12 += v * b5; t13 += v * b6; t14 += v * b7; t15 += v * b8; t16 += v * b9; t17 += v * b10; t18 += v * b11; t19 += v * b12; t20 += v * b13; t21 += v * b14; t22 += v * b15; v = a[8]; t8 += v * b0; t9 += v * b1; t10 += v * b2; t11 += v * b3; t12 += v * b4; t13 += v * b5; t14 += v * b6; t15 += v * b7; t16 += v * b8; t17 += v * b9; t18 += v * b10; t19 += v * b11; t20 += v * b12; t21 += v * b13; t22 += v * b14; t23 += v * b15; v = a[9]; t9 += v * b0; t10 += v * b1; t11 += v * b2; t12 += v * b3; t13 += v * b4; t14 += v * b5; t15 += v * b6; t16 += v * b7; t17 += v * b8; t18 += v * b9; t19 += v * b10; t20 += v * b11; t21 += v * b12; t22 += v * b13; t23 += v * b14; t24 += v * b15; v = a[10]; t10 += v * b0; t11 += v * b1; t12 += v * b2; t13 += v * b3; t14 += v * b4; t15 += v * b5; t16 += v * b6; t17 += v * b7; t18 += v * b8; t19 += v * b9; t20 += v * b10; t21 += v * b11; t22 += v * b12; t23 += v * b13; t24 += v * b14; t25 += v * b15; v = a[11]; t11 += v * b0; t12 += v * b1; t13 += v * b2; t14 += v * b3; t15 += v * b4; t16 += v * b5; t17 += v * b6; t18 += v * b7; t19 += v * b8; t20 += v * b9; t21 += v * b10; t22 += v * b11; t23 += v * b12; t24 += v * b13; t25 += v * b14; t26 += v * b15; v = a[12]; t12 += v * b0; t13 += v * b1; t14 += v * b2; t15 += v * b3; t16 += v * b4; t17 += v * b5; t18 += v * b6; t19 += v * b7; t20 += v * b8; t21 += v * b9; t22 += v * b10; t23 += v * b11; t24 += v * b12; t25 += v * b13; t26 += v * b14; t27 += v * b15; v = a[13]; t13 += v * b0; t14 += v * b1; t15 += v * b2; t16 += v * b3; t17 += v * b4; t18 += v * b5; t19 += v * b6; t20 += v * b7; t21 += v * b8; t22 += v * b9; t23 += v * b10; t24 += v * b11; t25 += v * b12; t26 += v * b13; t27 += v * b14; t28 += v * b15; v = a[14]; t14 += v * b0; t15 += v * b1; t16 += v * b2; t17 += v * b3; t18 += v * b4; t19 += v * b5; t20 += v * b6; t21 += v * b7; t22 += v * b8; t23 += v * b9; t24 += v * b10; t25 += v * b11; t26 += v * b12; t27 += v * b13; t28 += v * b14; t29 += v * b15; v = a[15]; t15 += v * b0; t16 += v * b1; t17 += v * b2; t18 += v * b3; t19 += v * b4; t20 += v * b5; t21 += v * b6; t22 += v * b7; t23 += v * b8; t24 += v * b9; t25 += v * b10; t26 += v * b11; t27 += v * b12; t28 += v * b13; t29 += v * b14; t30 += v * b15; t0 += 38 * t16; t1 += 38 * t17; t2 += 38 * t18; t3 += 38 * t19; t4 += 38 * t20; t5 += 38 * t21; t6 += 38 * t22; t7 += 38 * t23; t8 += 38 * t24; t9 += 38 * t25; t10 += 38 * t26; t11 += 38 * t27; t12 += 38 * t28; t13 += 38 * t29; t14 += 38 * t30; // t15 left as is // first car c = 1; v = t0 + c + 65535; c = Math.floor(v / 65536); t0 = v - c * 65536; v = t1 + c + 65535; c = Math.floor(v / 65536); t1 = v - c * 65536; v = t2 + c + 65535; c = Math.floor(v / 65536); t2 = v - c * 65536; v = t3 + c + 65535; c = Math.floor(v / 65536); t3 = v - c * 65536; v = t4 + c + 65535; c = Math.floor(v / 65536); t4 = v - c * 65536; v = t5 + c + 65535; c = Math.floor(v / 65536); t5 = v - c * 65536; v = t6 + c + 65535; c = Math.floor(v / 65536); t6 = v - c * 65536; v = t7 + c + 65535; c = Math.floor(v / 65536); t7 = v - c * 65536; v = t8 + c + 65535; c = Math.floor(v / 65536); t8 = v - c * 65536; v = t9 + c + 65535; c = Math.floor(v / 65536); t9 = v - c * 65536; v = t10 + c + 65535; c = Math.floor(v / 65536); t10 = v - c * 65536; v = t11 + c + 65535; c = Math.floor(v / 65536); t11 = v - c * 65536; v = t12 + c + 65535; c = Math.floor(v / 65536); t12 = v - c * 65536; v = t13 + c + 65535; c = Math.floor(v / 65536); t13 = v - c * 65536; v = t14 + c + 65535; c = Math.floor(v / 65536); t14 = v - c * 65536; v = t15 + c + 65535; c = Math.floor(v / 65536); t15 = v - c * 65536; t0 += c - 1 + 37 * (c - 1); // second car c = 1; v = t0 + c + 65535; c = Math.floor(v / 65536); t0 = v - c * 65536; v = t1 + c + 65535; c = Math.floor(v / 65536); t1 = v - c * 65536; v = t2 + c + 65535; c = Math.floor(v / 65536); t2 = v - c * 65536; v = t3 + c + 65535; c = Math.floor(v / 65536); t3 = v - c * 65536; v = t4 + c + 65535; c = Math.floor(v / 65536); t4 = v - c * 65536; v = t5 + c + 65535; c = Math.floor(v / 65536); t5 = v - c * 65536; v = t6 + c + 65535; c = Math.floor(v / 65536); t6 = v - c * 65536; v = t7 + c + 65535; c = Math.floor(v / 65536); t7 = v - c * 65536; v = t8 + c + 65535; c = Math.floor(v / 65536); t8 = v - c * 65536; v = t9 + c + 65535; c = Math.floor(v / 65536); t9 = v - c * 65536; v = t10 + c + 65535; c = Math.floor(v / 65536); t10 = v - c * 65536; v = t11 + c + 65535; c = Math.floor(v / 65536); t11 = v - c * 65536; v = t12 + c + 65535; c = Math.floor(v / 65536); t12 = v - c * 65536; v = t13 + c + 65535; c = Math.floor(v / 65536); t13 = v - c * 65536; v = t14 + c + 65535; c = Math.floor(v / 65536); t14 = v - c * 65536; v = t15 + c + 65535; c = Math.floor(v / 65536); t15 = v - c * 65536; t0 += c - 1 + 37 * (c - 1); o[0] = t0; o[1] = t1; o[2] = t2; o[3] = t3; o[4] = t4; o[5] = t5; o[6] = t6; o[7] = t7; o[8] = t8; o[9] = t9; o[10] = t10; o[11] = t11; o[12] = t12; o[13] = t13; o[14] = t14; o[15] = t15; } function S(o, a) { M(o, a, a); } function inv25519(o, i) { var c = gf(); var a; for (a = 0; a < 16; a++) c[a] = i[a]; for (a = 253; a >= 0; a--) { S(c, c); if (a !== 2 && a !== 4) M(c, c, i); } for (a = 0; a < 16; a++) o[a] = c[a]; } function pow2523(o, i) { var c = gf(); var a; for (a = 0; a < 16; a++) c[a] = i[a]; for (a = 250; a >= 0; a--) { S(c, c); if (a !== 1) M(c, c, i); } for (a = 0; a < 16; a++) o[a] = c[a]; } function crypto_scalarmult(q, n, p) { var z = new Uint8Array(32); var x = new Float64Array(80), r, i; var a = gf(), b = gf(), c = gf(), d = gf(), e = gf(), f = gf(); for (i = 0; i < 31; i++) z[i] = n[i]; z[31] = (n[31] & 127) | 64; z[0] &= 248; unpack25519(x, p); for (i = 0; i < 16; i++) { b[i] = x[i]; d[i] = a[i] = c[i] = 0; } a[0] = d[0] = 1; for (i = 254; i >= 0; --i) { r = (z[i >>> 3] >>> (i & 7)) & 1; sel25519(a, b, r); sel25519(c, d, r); A(e, a, c); Z(a, a, c); A(c, b, d); Z(b, b, d); S(d, e); S(f, a); M(a, c, a); M(c, b, e); A(e, a, c); Z(a, a, c); S(b, a); Z(c, d, f); M(a, c, _121665); A(a, a, d); M(c, c, a); M(a, d, f); M(d, b, x); S(b, e); sel25519(a, b, r); sel25519(c, d, r); } for (i = 0; i < 16; i++) { x[i + 16] = a[i]; x[i + 32] = c[i]; x[i + 48] = b[i]; x[i + 64] = d[i]; } var x32 = x.subarray(32); var x16 = x.subarray(16); inv25519(x32, x32); M(x16, x16, x32); pack25519(q, x16); return 0; } function crypto_scalarmult_base(q, n) { return crypto_scalarmult(q, n, _9); } var K = [ 0x428a2f98, 0xd728ae22, 0x71374491, 0x23ef65cd, 0xb5c0fbcf, 0xec4d3b2f, 0xe9b5dba5, 0x8189dbbc, 0x3956c25b, 0xf348b538, 0x59f111f1, 0xb605d019, 0x923f82a4, 0xaf194f9b, 0xab1c5ed5, 0xda6d8118, 0xd807aa98, 0xa3030242, 0x12835b01, 0x45706fbe, 0x243185be, 0x4ee4b28c, 0x550c7dc3, 0xd5ffb4e2, 0x72be5d74, 0xf27b896f, 0x80deb1fe, 0x3b1696b1, 0x9bdc06a7, 0x25c71235, 0xc19bf174, 0xcf692694, 0xe49b69c1, 0x9ef14ad2, 0xefbe4786, 0x384f25e3, 0x0fc19dc6, 0x8b8cd5b5, 0x240ca1cc, 0x77ac9c65, 0x2de92c6f, 0x592b0275, 0x4a7484aa, 0x6ea6e483, 0x5cb0a9dc, 0xbd41fbd4, 0x76f988da, 0x831153b5, 0x983e5152, 0xee66dfab, 0xa831c66d, 0x2db43210, 0xb00327c8, 0x98fb213f, 0xbf597fc7, 0xbeef0ee4, 0xc6e00bf3, 0x3da88fc2, 0xd5a79147, 0x930aa725, 0x06ca6351, 0xe003826f, 0x14292967, 0x0a0e6e70, 0x27b70a85, 0x46d22ffc, 0x2e1b2138, 0x5c26c926, 0x4d2c6dfc, 0x5ac42aed, 0x53380d13, 0x9d95b3df, 0x650a7354, 0x8baf63de, 0x766a0abb, 0x3c77b2a8, 0x81c2c92e, 0x47edaee6, 0x92722c85, 0x1482353b, 0xa2bfe8a1, 0x4cf10364, 0xa81a664b, 0xbc423001, 0xc24b8b70, 0xd0f89791, 0xc76c51a3, 0x0654be30, 0xd192e819, 0xd6ef5218, 0xd6990624, 0x5565a910, 0xf40e3585, 0x5771202a, 0x106aa070, 0x32bbd1b8, 0x19a4c116, 0xb8d2d0c8, 0x1e376c08, 0x5141ab53, 0x2748774c, 0xdf8eeb99, 0x34b0bcb5, 0xe19b48a8, 0x391c0cb3, 0xc5c95a63, 0x4ed8aa4a, 0xe3418acb, 0x5b9cca4f, 0x7763e373, 0x682e6ff3, 0xd6b2b8a3, 0x748f82ee, 0x5defb2fc, 0x78a5636f, 0x43172f60, 0x84c87814, 0xa1f0ab72, 0x8cc70208, 0x1a6439ec, 0x90befffa, 0x23631e28, 0xa4506ceb, 0xde82bde9, 0xbef9a3f7, 0xb2c67915, 0xc67178f2, 0xe372532b, 0xca273ece, 0xea26619c, 0xd186b8c7, 0x21c0c207, 0xeada7dd6, 0xcde0eb1e, 0xf57d4f7f, 0xee6ed178, 0x06f067aa, 0x72176fba, 0x0a637dc5, 0xa2c898a6, 0x113f9804, 0xbef90dae, 0x1b710b35, 0x131c471b, 0x28db77f5, 0x23047d84, 0x32caab7b, 0x40c72493, 0x3c9ebe0a, 0x15c9bebc, 0x431d67c4, 0x9c100d4c, 0x4cc5d4be, 0xcb3e42b6, 0x597f299c, 0xfc657e2a, 0x5fcb6fab, 0x3ad6faec, 0x6c44198c, 0x4a475817, ]; function crypto_hashblocks_hl(hh, hl, m, n) { var wh = new Int32Array(16), wl = new Int32Array(16), bh0, bh1, bh2, bh3, bh4, bh5, bh6, bh7, bl0, bl1, bl2, bl3, bl4, bl5, bl6, bl7, th, tl, i, j, h, l, a, b, c, d; var ah0 = hh[0], ah1 = hh[1], ah2 = hh[2], ah3 = hh[3], ah4 = hh[4], ah5 = hh[5], ah6 = hh[6], ah7 = hh[7], al0 = hl[0], al1 = hl[1], al2 = hl[2], al3 = hl[3], al4 = hl[4], al5 = hl[5], al6 = hl[6], al7 = hl[7]; var pos = 0; while (n >= 128) { for (i = 0; i < 16; i++) { j = 8 * i + pos; wh[i] = (m[j + 0] << 24) | (m[j + 1] << 16) | (m[j + 2] << 8) | m[j + 3]; wl[i] = (m[j + 4] << 24) | (m[j + 5] << 16) | (m[j + 6] << 8) | m[j + 7]; } for (i = 0; i < 80; i++) { bh0 = ah0; bh1 = ah1; bh2 = ah2; bh3 = ah3; bh4 = ah4; bh5 = ah5; bh6 = ah6; bh7 = ah7; bl0 = al0; bl1 = al1; bl2 = al2; bl3 = al3; bl4 = al4; bl5 = al5; bl6 = al6; bl7 = al7; // add h = ah7; l = al7; a = l & 0xffff; b = l >>> 16; c = h & 0xffff; d = h >>> 16; // Sigma1 h = ((ah4 >>> 14) | (al4 << (32 - 14))) ^ ((ah4 >>> 18) | (al4 << (32 - 18))) ^ ((al4 >>> (41 - 32)) | (ah4 << (32 - (41 - 32)))); l = ((al4 >>> 14) | (ah4 << (32 - 14))) ^ ((al4 >>> 18) | (ah4 << (32 - 18))) ^ ((ah4 >>> (41 - 32)) | (al4 << (32 - (41 - 32)))); a += l & 0xffff; b += l >>> 16; c += h & 0xffff; d += h >>> 16; // Ch h = (ah4 & ah5) ^ (~ah4 & ah6); l = (al4 & al5) ^ (~al4 & al6); a += l & 0xffff; b += l >>> 16; c += h & 0xffff; d += h >>> 16; // K h = K[i * 2]; l = K[i * 2 + 1]; a += l & 0xffff; b += l >>> 16; c += h & 0xffff; d += h >>> 16; // w h = wh[i % 16]; l = wl[i % 16]; a += l & 0xffff; b += l >>> 16; c += h & 0xffff; d += h >>> 16; b += a >>> 16; c += b >>> 16; d += c >>> 16; th = (c & 0xffff) | (d << 16); tl = (a & 0xffff) | (b << 16); // add h = th; l = tl; a = l & 0xffff; b = l >>> 16; c = h & 0xffff; d = h >>> 16; // Sigma0 h = ((ah0 >>> 28) | (al0 << (32 - 28))) ^ ((al0 >>> (34 - 32)) | (ah0 << (32 - (34 - 32)))) ^ ((al0 >>> (39 - 32)) | (ah0 << (32 - (39 - 32)))); l = ((al0 >>> 28) | (ah0 << (32 - 28))) ^ ((ah0 >>> (34 - 32)) | (al0 << (32 - (34 - 32)))) ^ ((ah0 >>> (39 - 32)) | (al0 << (32 - (39 - 32)))); a += l & 0xffff; b += l >>> 16; c += h & 0xffff; d += h >>> 16; // Maj h = (ah0 & ah1) ^ (ah0 & ah2) ^ (ah1 & ah2); l = (al0 & al1) ^ (al0 & al2) ^ (al1 & al2); a += l & 0xffff; b += l >>> 16; c += h & 0xffff; d += h >>> 16; b += a >>> 16; c += b >>> 16; d += c >>> 16; bh7 = (c & 0xffff) | (d << 16); bl7 = (a & 0xffff) | (b << 16); // add h = bh3; l = bl3; a = l & 0xffff; b = l >>> 16; c = h & 0xffff; d = h >>> 16; h = th; l = tl; a += l & 0xffff; b += l >>> 16; c += h & 0xffff; d += h >>> 16; b += a >>> 16; c += b >>> 16; d += c >>> 16; bh3 = (c & 0xffff) | (d << 16); bl3 = (a & 0xffff) | (b << 16); ah1 = bh0; ah2 = bh1; ah3 = bh2; ah4 = bh3; ah5 = bh4; ah6 = bh5; ah7 = bh6; ah0 = bh7; al1 = bl0; al2 = bl1; al3 = bl2; al4 = bl3; al5 = bl4; al6 = bl5; al7 = bl6; al0 = bl7; if (i % 16 === 15) { for (j = 0; j < 16; j++) { // add h = wh[j]; l = wl[j]; a = l & 0xffff; b = l >>> 16; c = h & 0xffff; d = h >>> 16; h = wh[(j + 9) % 16]; l = wl[(j + 9) % 16]; a += l & 0xffff; b += l >>> 16; c += h & 0xffff; d += h >>> 16; // sigma0 th = wh[(j + 1) % 16]; tl = wl[(j + 1) % 16]; h = ((th >>> 1) | (tl << (32 - 1))) ^ ((th >>> 8) | (tl << (32 - 8))) ^ (th >>> 7); l = ((tl >>> 1) | (th << (32 - 1))) ^ ((tl >>> 8) | (th << (32 - 8))) ^ ((tl >>> 7) | (th << (32 - 7))); a += l & 0xffff; b += l >>> 16; c += h & 0xffff; d += h >>> 16; // sigma1 th = wh[(j + 14) % 16]; tl = wl[(j + 14) % 16]; h = ((th >>> 19) | (tl << (32 - 19))) ^ ((tl >>> (61 - 32)) | (th << (32 - (61 - 32)))) ^ (th >>> 6); l = ((tl >>> 19) | (th << (32 - 19))) ^ ((th >>> (61 - 32)) | (tl << (32 - (61 - 32)))) ^ ((tl >>> 6) | (th << (32 - 6))); a += l & 0xffff; b += l >>> 16; c += h & 0xffff; d += h >>> 16; b += a >>> 16; c += b >>> 16; d += c >>> 16; wh[j] = (c & 0xffff) | (d << 16); wl[j] = (a & 0xffff) | (b << 16); } } } // add h = ah0; l = al0; a = l & 0xffff; b = l >>> 16; c = h & 0xffff; d = h >>> 16; h = hh[0]; l = hl[0]; a += l & 0xffff; b += l >>> 16; c += h & 0xffff; d += h >>> 16; b += a >>> 16; c += b >>> 16; d += c >>> 16; hh[0] = ah0 = (c & 0xffff) | (d << 16); hl[0] = al0 = (a & 0xffff) | (b << 16); h = ah1; l = al1; a = l & 0xffff; b = l >>> 16; c = h & 0xffff; d = h >>> 16; h = hh[1]; l = hl[1]; a += l & 0xffff; b += l >>> 16; c += h & 0xffff; d += h >>> 16; b += a >>> 16; c += b >>> 16; d += c >>> 16; hh[1] = ah1 = (c & 0xffff) | (d << 16); hl[1] = al1 = (a & 0xffff) | (b << 16); h = ah2; l = al2; a = l & 0xffff; b = l >>> 16; c = h & 0xffff; d = h >>> 16; h = hh[2]; l = hl[2]; a += l & 0xffff; b += l >>> 16; c += h & 0xffff; d += h >>> 16; b += a >>> 16; c += b >>> 16; d += c >>> 16; hh[2] = ah2 = (c & 0xffff) | (d << 16); hl[2] = al2 = (a & 0xffff) | (b << 16); h = ah3; l = al3; a = l & 0xffff; b = l >>> 16; c = h & 0xffff; d = h >>> 16; h = hh[3]; l = hl[3]; a += l & 0xffff; b += l >>> 16; c += h & 0xffff; d += h >>> 16; b += a >>> 16; c += b >>> 16; d += c >>> 16; hh[3] = ah3 = (c & 0xffff) | (d << 16); hl[3] = al3 = (a & 0xffff) | (b << 16); h = ah4; l = al4; a = l & 0xffff; b = l >>> 16; c = h & 0xffff; d = h >>> 16; h = hh[4]; l = hl[4]; a += l & 0xffff; b += l >>> 16; c += h & 0xffff; d += h >>> 16; b += a >>> 16; c += b >>> 16; d += c >>> 16; hh[4] = ah4 = (c & 0xffff) | (d << 16); hl[4] = al4 = (a & 0xffff) | (b << 16); h = ah5; l = al5; a = l & 0xffff; b = l >>> 16; c = h & 0xffff; d = h >>> 16; h = hh[5]; l = hl[5]; a += l & 0xffff; b += l >>> 16; c += h & 0xffff; d += h >>> 16; b += a >>> 16; c += b >>> 16; d += c >>> 16; hh[5] = ah5 = (c & 0xffff) | (d << 16); hl[5] = al5 = (a & 0xffff) | (b << 16); h = ah6; l = al6; a = l & 0xffff; b = l >>> 16; c = h & 0xffff; d = h >>> 16; h = hh[6]; l = hl[6]; a += l & 0xffff; b += l >>> 16; c += h & 0xffff; d += h >>> 16; b += a >>> 16; c += b >>> 16; d += c >>> 16; hh[6] = ah6 = (c & 0xffff) | (d << 16); hl[6] = al6 = (a & 0xffff) | (b << 16); h = ah7; l = al7; a = l & 0xffff; b = l >>> 16; c = h & 0xffff; d = h >>> 16; h = hh[7]; l = hl[7]; a += l & 0xffff; b += l >>> 16; c += h & 0xffff; d += h >>> 16; b += a >>> 16; c += b >>> 16; d += c >>> 16; hh[7] = ah7 = (c & 0xffff) | (d << 16); hl[7] = al7 = (a & 0xffff) | (b << 16); pos += 128; n -= 128; } return n; } function crypto_hash(out, m, n) { var hh = new Int32Array(8), hl = new Int32Array(8), x = new Uint8Array(256), i, b = n; hh[0] = 0x6a09e667; hh[1] = 0xbb67ae85; hh[2] = 0x3c6ef372; hh[3] = 0xa54ff53a; hh[4] = 0x510e527f; hh[5] = 0x9b05688c; hh[6] = 0x1f83d9ab; hh[7] = 0x5be0cd19; hl[0] = 0xf3bcc908; hl[1] = 0x84caa73b; hl[2] = 0xfe94f82b; hl[3] = 0x5f1d36f1; hl[4] = 0xade682d1; hl[5] = 0x2b3e6c1f; hl[6] = 0xfb41bd6b; hl[7] = 0x137e2179; crypto_hashblocks_hl(hh, hl, m, n); n %= 128; for (i = 0; i < n; i++) x[i] = m[b - n + i]; x[n] = 128; n = 256 - 128 * (n < 112 ? 1 : 0); x[n - 9] = 0; ts64(x, n - 8, (b / 0x20000000) | 0, b << 3); crypto_hashblocks_hl(hh, hl, x, n); for (i = 0; i < 8; i++) ts64(out, 8 * i, hh[i], hl[i]); return 0; } function add(p, q) { var a = gf(), b = gf(), c = gf(), d = gf(), e = gf(), f = gf(), g = gf(), h = gf(), t = gf(); Z(a, p[1], p[0]); Z(t, q[1], q[0]); M(a, a, t); A(b, p[0], p[1]); A(t, q[0], q[1]); M(b, b, t); M(c, p[3], q[3]); M(c, c, D2); M(d, p[2], q[2]); A(d, d, d); Z(e, b, a); Z(f, d, c); A(g, d, c); A(h, b, a); M(p[0], e, f); M(p[1], h, g); M(p[2], g, f); M(p[3], e, h); } function cswap(p, q, b) { var i; for (i = 0; i < 4; i++) { sel25519(p[i], q[i], b); } } function pack(r, p) { var tx = gf(), ty = gf(), zi = gf(); inv25519(zi, p[2]); M(tx, p[0], zi); M(ty, p[1], zi); pack25519(r, ty); r[31] ^= par25519(tx) << 7; } function scalarmult(p, q, s) { var b, i; set25519(p[0], gf0); set25519(p[1], gf1); set25519(p[2], gf1); set25519(p[3], gf0); for (i = 255; i >= 0; --i) { b = (s[(i / 8) | 0] >> (i & 7)) & 1; cswap(p, q, b); add(q, p); add(p, p); cswap(p, q, b); } } function scalarbase(p, s) { var q = [gf(), gf(), gf(), gf()]; set25519(q[0], X); set25519(q[1], Y); set25519(q[2], gf1); M(q[3], X, Y); scalarmult(p, q, s); } var L = new Float64Array([ 0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, 0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0x10, ]); function modL(r, x) { var carry, i, j, k; for (i = 63; i >= 32; --i) { carry = 0; for (j = i - 32, k = i - 12; j < k; ++j) { x[j] += carry - 16 * x[i] * L[j - (i - 32)]; carry = (x[j] + 128) >> 8; x[j] -= carry * 256; } x[j] += carry; x[i] = 0; } carry = 0; for (j = 0; j < 32; j++) { x[j] += carry - (x[31] >> 4) * L[j]; carry = x[j] >> 8; x[j] &= 255; } for (j = 0; j < 32; j++) x[j] -= carry * L[j]; for (i = 0; i < 32; i++) { x[i + 1] += x[i] >> 8; r[i] = x[i] & 255; } } function reduce(r) { var x = new Float64Array(64), i; for (i = 0; i < 64; i++) x[i] = r[i]; for (i = 0; i < 64; i++) r[i] = 0; modL(r, x); } // Like crypto_sign, but uses secret key directly in hash. function crypto_sign_direct(sm, m, n, sk) { var h = new Uint8Array(64), r = new Uint8Array(64); var i, j, x = new Float64Array(64); var p = [gf(), gf(), gf(), gf()]; for (i = 0; i < n; i++) sm[64 + i] = m[i]; for (i = 0; i < 32; i++) sm[32 + i] = sk[i]; crypto_hash(r, sm.subarray(32), n + 32); reduce(r); scalarbase(p, r); pack(sm, p); for (i = 0; i < 32; i++) sm[i + 32] = sk[32 + i]; crypto_hash(h, sm, n + 64); reduce(h); for (i = 0; i < 64; i++) x[i] = 0; for (i = 0; i < 32; i++) x[i] = r[i]; for (i = 0; i < 32; i++) { for (j = 0; j < 32; j++) { x[i + j] += h[i] * sk[j]; } } modL(sm.subarray(32), x); return n + 64; } // Note: sm must be n+128. function crypto_sign_direct_rnd(sm, m, n, sk, rnd) { var h = new Uint8Array(64), r = new Uint8Array(64); var i, j, x = new Float64Array(64); var p = [gf(), gf(), gf(), gf()]; // Hash separation. sm[0] = 0xfe; for (i = 1; i < 32; i++) sm[i] = 0xff; // Secret key. for (i = 0; i < 32; i++) sm[32 + i] = sk[i]; // Message. for (i = 0; i < n; i++) sm[64 + i] = m[i]; // Random suffix. for (i = 0; i < 64; i++) sm[n + 64 + i] = rnd[i]; crypto_hash(r, sm, n + 128); reduce(r); scalarbase(p, r); pack(sm, p); for (i = 0; i < 32; i++) sm[i + 32] = sk[32 + i]; crypto_hash(h, sm, n + 64); reduce(h); // Wipe out random suffix. for (i = 0; i < 64; i++) sm[n + 64 + i] = 0; for (i = 0; i < 64; i++) x[i] = 0; for (i = 0; i < 32; i++) x[i] = r[i]; for (i = 0; i < 32; i++) { for (j = 0; j < 32; j++) { x[i + j] += h[i] * sk[j]; } } modL(sm.subarray(32, n + 64), x); return n + 64; } function curve25519_sign(sm, m, n, sk, opt_rnd) { // If opt_rnd is provided, sm must have n + 128, // otherwise it must have n + 64 bytes. // Convert Curve25519 secret key into Ed25519 secret key (includes pub key). var edsk = new Uint8Array(64); var p = [gf(), gf(), gf(), gf()]; for (var i = 0; i < 32; i++) edsk[i] = sk[i]; // Ensure private key is in the correct format. edsk[0] &= 248; edsk[31] &= 127; edsk[31] |= 64; scalarbase(p, edsk); pack(edsk.subarray(32), p); // Remember sign bit. var signBit = edsk[63] & 128; var smlen; if (opt_rnd) { smlen = crypto_sign_direct_rnd(sm, m, n, edsk, opt_rnd); } else { smlen = crypto_sign_direct(sm, m, n, edsk); } // Copy sign bit from public key into signature. sm[63] |= signBit; return smlen; } function unpackneg(r, p) { var t = gf(), chk = gf(), num = gf(), den = gf(), den2 = gf(), den4 = gf(), den6 = gf(); set25519(r[2], gf1); unpack25519(r[1], p); S(num, r[1]); M(den, num, D); Z(num, num, r[2]); A(den, r[2], den); S(den2, den); S(den4, den2); M(den6, den4, den2); M(t, den6, num); M(t, t, den); pow2523(t, t); M(t, t, num); M(t, t, den); M(t, t, den); M(r[0], t, den); S(chk, r[0]); M(chk, chk, den); if (neq25519(chk, num)) M(r[0], r[0], I); S(chk, r[0]); M(chk, chk, den); if (neq25519(chk, num)) return -1; if (par25519(r[0]) === p[31] >> 7) Z(r[0], gf0, r[0]); M(r[3], r[0], r[1]); return 0; } function crypto_sign_open(m, sm, n, pk) { var i, mlen; var t = new Uint8Array(32), h = new Uint8Array(64); var p = [gf(), gf(), gf(), gf()], q = [gf(), gf(), gf(), gf()]; mlen = -1; if (n < 64) return -1; if (unpackneg(q, pk)) return -1; for (i = 0; i < n; i++) m[i] = sm[i]; for (i = 0; i < 32; i++) m[i + 32] = pk[i]; crypto_hash(h, m, n); reduce(h); scalarmult(p, q, h); scalarbase(q, sm.subarray(32)); add(p, q); pack(t, p); n -= 64; if (crypto_verify_32(sm, 0, t, 0)) { for (i = 0; i < n; i++) m[i] = 0; return -1; } for (i = 0; i < n; i++) m[i] = sm[i + 64]; mlen = n; return mlen; } // Converts Curve25519 public key back to Ed25519 public key. // edwardsY = (montgomeryX - 1) / (montgomeryX + 1) function convertPublicKey(pk) { var z = new Uint8Array(32), x = gf(), a = gf(), b = gf(); unpack25519(x, pk); A(a, x, gf1); Z(b, x, gf1); inv25519(a, a); M(a, a, b); pack25519(z, a); return z; } function curve25519_sign_open(m, sm, n, pk) { // Convert Curve25519 public key into Ed25519 public key. var edpk = convertPublicKey(pk); // Restore sign bit from signature. edpk[31] |= sm[63] & 128; // Remove sign bit from signature. sm[63] &= 127; // Verify signed message. return crypto_sign_open(m, sm, n, edpk); } /* High-level API */ function checkArrayTypes(...args) { var t, i; for (i = 0; i < arguments.length; i++) { if ((t = Object.prototype.toString.call(arguments[i])) !== '[object Uint8Array]') throw new TypeError('unexpected type ' + t + ', use Uint8Array'); } } /** * Returns a raw shared key between own private key and peer's public key (in other words, this is an ECC Diffie-Hellman function X25519, performing scalar multiplication). * * The result should not be used directly as a key, but should be processed with a one-way function (e.g. HSalsa20 as in NaCl, or any secure cryptographic hash function, such as SHA-256, or key derivation function, such as HKDF). * * @export * @param {Uint8Array} secretKey * @param {Uint8Array} publicKey * @returns Uint8Array */ function sharedKey(secretKey, publicKey) { checkArrayTypes(publicKey, secretKey); if (publicKey.length !== 32) throw new Error('wrong public key length'); if (secretKey.length !== 32) throw new Error('wrong secret key length'); var sharedKey = new Uint8Array(32); crypto_scalarmult(sharedKey, secretKey, publicKey); return sharedKey; } /** * Signs the given message using the private key and returns a signed message (signature concatenated with the message copy). * * Optional random data argument (which must have 64 random bytes) turns on hash separation and randomization to make signatures non-deterministic. * * @export * @param {Uint8Array} secretKey * @param {*} msg * @param {Uint8Array} opt_random * @returns */ function signMessage(secretKey, msg, opt_random) { checkArrayTypes(msg, secretKey); if (secretKey.length !== 32) throw new Error('wrong secret key length'); if (opt_random) { checkArrayTypes(opt_random); if (opt_random.length !== 64) throw new Error('wrong random data length'); var buf = new Uint8Array(128 + msg.length); curve25519_sign(buf, msg, msg.length, secretKey, opt_random); return new Uint8Array(buf.subarray(0, 64 + msg.length)); } else { var signedMsg = new Uint8Array(64 + msg.length); curve25519_sign(signedMsg, msg, msg.length, secretKey); return signedMsg; } } /** * Verifies signed message with the public key and returns the original message without signature if it's correct or null if verification fails. * * @export * @param {Uint8Array} publicKey * @param {*} signedMsg * @returns Message */ function openMessage(publicKey, signedMsg) { checkArrayTypes(signedMsg, publicKey); if (publicKey.length !== 32) throw new Error('wrong public key length'); var tmp = new Uint8Array(signedMsg.length); var mlen = curve25519_sign_open(tmp, signedMsg, signedMsg.length, publicKey); if (mlen < 0) return null; var m = new Uint8Array(mlen); for (var i = 0; i < m.length; i++) m[i] = tmp[i]; return m; } /** * Signs the given message using the private key and returns signature. * * Optional random data argument (which must have 64 random bytes) turns on hash separation and randomization to make signatures non-deterministic. * * @export * @param {Uint8Array} secretKey * @param {*} msg * @param {Uint8Array} opt_random * @returns */ function sign(secretKey, msg, opt_random) { checkArrayTypes(secretKey, msg); if (secretKey.length !== 32) throw new Error('wrong secret key length'); if (opt_random) { checkArrayTypes(opt_random); if (opt_random.length !== 64) throw new Error('wrong random data length'); } var buf = new Uint8Array((opt_random ? 128 : 64) + msg.length); curve25519_sign(buf, msg, msg.length, secretKey, opt_random); var signature = new Uint8Array(64); for (var i = 0; i < signature.length; i++) signature[i] = buf[i]; return signature; } /** * Verifies the given signature for the message using the given private key. Returns true if the signature is valid, false otherwise. * * @export * @param {Uint8Array} publicKey * @param {*} msg * @param {*} signature * @returns */ function verify(publicKey, msg, signature) { checkArrayTypes(msg, signature, publicKey); if (signature.length !== 64) throw new Error('wrong signature length'); if (publicKey.length !== 32) throw new Error('wrong public key length'); var sm = new Uint8Array(64 + msg.length); var m = new Uint8Array(64 + msg.length); var i; for (i = 0; i < 64; i++) sm[i] = signature[i]; for (i = 0; i < msg.length; i++) sm[i + 64] = msg[i]; return curve25519_sign_open(m, sm, sm.length, publicKey) >= 0; } /** * Generates a new key pair from the given 32-byte secret seed (which should be generated with a CSPRNG) and returns it as object. * * The returned keys can be used for signing and key agreement. * * @export * @param {Uint8Array} seed required * @returns */ function generateKeyPair(seed) { checkArrayTypes(seed); if (seed.length !== 32) throw new Error('wrong seed length'); var sk = new Uint8Array(32); var pk = new Uint8Array(32); for (var i = 0; i < 32; i++) sk[i] = seed[i]; crypto_scalarmult_base(pk, sk); // Turn secret key into the correct format. sk[0] &= 248; sk[31] &= 127; sk[31] |= 64; // Remove sign bit from public key. pk[31] &= 127; return { public: pk, private: sk, }; } globalThis.x25519 = { sharedKey, signMessage, openMessage, sign, verify, generateKeyPair, }; })();

Diving Deep

KSM, VMM & Gateway

DStack Component Architecture

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