| package org.bouncycastle.math.ec.rfc8032; |
| |
| import java.security.SecureRandom; |
| |
| import org.bouncycastle.crypto.Xof; |
| import org.bouncycastle.crypto.digests.SHAKEDigest; |
| import org.bouncycastle.math.ec.rfc7748.X448; |
| import org.bouncycastle.math.ec.rfc7748.X448Field; |
| import org.bouncycastle.math.raw.Nat; |
| import org.bouncycastle.util.Arrays; |
| import org.bouncycastle.util.Strings; |
| |
| public abstract class Ed448 |
| { |
| public static final class Algorithm |
| { |
| public static final int Ed448 = 0; |
| public static final int Ed448ph = 1; |
| } |
| |
| private static final long M26L = 0x03FFFFFFL; |
| private static final long M28L = 0x0FFFFFFFL; |
| private static final long M32L = 0xFFFFFFFFL; |
| |
| private static final int POINT_BYTES = 57; |
| private static final int SCALAR_INTS = 14; |
| private static final int SCALAR_BYTES = SCALAR_INTS * 4 + 1; |
| |
| public static final int PREHASH_SIZE = 64; |
| public static final int PUBLIC_KEY_SIZE = POINT_BYTES; |
| public static final int SECRET_KEY_SIZE = 57; |
| public static final int SIGNATURE_SIZE = POINT_BYTES + SCALAR_BYTES; |
| |
| private static final byte[] DOM4_PREFIX = Strings.toByteArray("SigEd448"); |
| |
| private static final int[] P = new int[] { 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, |
| 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF }; |
| private static final int[] L = new int[] { 0xAB5844F3, 0x2378C292, 0x8DC58F55, 0x216CC272, 0xAED63690, 0xC44EDB49, 0x7CCA23E9, |
| 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x3FFFFFFF }; |
| |
| private static final int L_0 = 0x04A7BB0D; // L_0:26/24 |
| private static final int L_1 = 0x0873D6D5; // L_1:27/23 |
| private static final int L_2 = 0x0A70AADC; // L_2:27/26 |
| private static final int L_3 = 0x03D8D723; // L_3:26/-- |
| private static final int L_4 = 0x096FDE93; // L_4:27/25 |
| private static final int L_5 = 0x0B65129C; // L_5:27/26 |
| private static final int L_6 = 0x063BB124; // L_6:27/-- |
| private static final int L_7 = 0x08335DC1; // L_7:27/22 |
| |
| private static final int L4_0 = 0x029EEC34; // L4_0:25/24 |
| private static final int L4_1 = 0x01CF5B55; // L4_1:25/-- |
| private static final int L4_2 = 0x09C2AB72; // L4_2:27/25 |
| private static final int L4_3 = 0x0F635C8E; // L4_3:28/-- |
| private static final int L4_4 = 0x05BF7A4C; // L4_4:26/25 |
| private static final int L4_5 = 0x0D944A72; // L4_5:28/-- |
| private static final int L4_6 = 0x08EEC492; // L4_6:27/24 |
| private static final int L4_7 = 0x20CD7705; // L4_7:29/24 |
| |
| private static final int[] B_x = new int[] { 0x070CC05E, 0x026A82BC, 0x00938E26, 0x080E18B0, 0x0511433B, 0x0F72AB66, 0x0412AE1A, |
| 0x0A3D3A46, 0x0A6DE324, 0x00F1767E, 0x04657047, 0x036DA9E1, 0x05A622BF, 0x0ED221D1, 0x066BED0D, 0x04F1970C }; |
| private static final int[] B_y = new int[] { 0x0230FA14, 0x008795BF, 0x07C8AD98, 0x0132C4ED, 0x09C4FDBD, 0x01CE67C3, 0x073AD3FF, |
| 0x005A0C2D, 0x07789C1E, 0x0A398408, 0x0A73736C, 0x0C7624BE, 0x003756C9, 0x02488762, 0x016EB6BC, 0x0693F467 }; |
| private static final int C_d = -39081; |
| |
| private static final int WNAF_WIDTH_BASE = 7; |
| |
| private static final int PRECOMP_BLOCKS = 5; |
| private static final int PRECOMP_TEETH = 5; |
| private static final int PRECOMP_SPACING = 18; |
| private static final int PRECOMP_POINTS = 1 << (PRECOMP_TEETH - 1); |
| private static final int PRECOMP_MASK = PRECOMP_POINTS - 1; |
| |
| private static Object precompLock = new Object(); |
| // TODO[ed448] Convert to PointPrecomp |
| private static PointExt[] precompBaseTable = null; |
| private static int[] precompBase = null; |
| |
| private static class PointExt |
| { |
| int[] x = X448Field.create(); |
| int[] y = X448Field.create(); |
| int[] z = X448Field.create(); |
| } |
| |
| private static class PointPrecomp |
| { |
| int[] x = X448Field.create(); |
| int[] y = X448Field.create(); |
| } |
| |
| private static byte[] calculateS(byte[] r, byte[] k, byte[] s) |
| { |
| int[] t = new int[SCALAR_INTS * 2]; decodeScalar(r, 0, t); |
| int[] u = new int[SCALAR_INTS]; decodeScalar(k, 0, u); |
| int[] v = new int[SCALAR_INTS]; decodeScalar(s, 0, v); |
| |
| Nat.mulAddTo(14, u, v, t); |
| |
| byte[] result = new byte[SCALAR_BYTES * 2]; |
| for (int i = 0; i < t.length; ++i) |
| { |
| encode32(t[i], result, i * 4); |
| } |
| return reduceScalar(result); |
| } |
| |
| private static boolean checkContextVar(byte[] ctx) |
| { |
| return ctx != null && ctx.length < 256; |
| } |
| |
| private static boolean checkPointVar(byte[] p) |
| { |
| if ((p[POINT_BYTES - 1] & 0x7F) != 0x00) |
| { |
| return false; |
| } |
| |
| int[] t = new int[14]; |
| decode32(p, 0, t, 0, 14); |
| return !Nat.gte(14, t, P); |
| } |
| |
| private static boolean checkScalarVar(byte[] s) |
| { |
| if (s[SCALAR_BYTES - 1] != 0x00) |
| { |
| return false; |
| } |
| |
| int[] n = new int[SCALAR_INTS]; |
| decodeScalar(s, 0, n); |
| return !Nat.gte(SCALAR_INTS, n, L); |
| } |
| |
| public static Xof createPrehash() |
| { |
| return createXof(); |
| } |
| |
| private static Xof createXof() |
| { |
| return new SHAKEDigest(256); |
| } |
| |
| private static int decode16(byte[] bs, int off) |
| { |
| int n = bs[off] & 0xFF; |
| n |= (bs[++off] & 0xFF) << 8; |
| return n; |
| } |
| |
| private static int decode24(byte[] bs, int off) |
| { |
| int n = bs[ off] & 0xFF; |
| n |= (bs[++off] & 0xFF) << 8; |
| n |= (bs[++off] & 0xFF) << 16; |
| return n; |
| } |
| |
| private static int decode32(byte[] bs, int off) |
| { |
| int n = bs[off] & 0xFF; |
| n |= (bs[++off] & 0xFF) << 8; |
| n |= (bs[++off] & 0xFF) << 16; |
| n |= bs[++off] << 24; |
| return n; |
| } |
| |
| private static void decode32(byte[] bs, int bsOff, int[] n, int nOff, int nLen) |
| { |
| for (int i = 0; i < nLen; ++i) |
| { |
| n[nOff + i] = decode32(bs, bsOff + i * 4); |
| } |
| } |
| |
| private static boolean decodePointVar(byte[] p, int pOff, boolean negate, PointExt r) |
| { |
| byte[] py = Arrays.copyOfRange(p, pOff, pOff + POINT_BYTES); |
| if (!checkPointVar(py)) |
| { |
| return false; |
| } |
| |
| int x_0 = (py[POINT_BYTES - 1] & 0x80) >>> 7; |
| py[POINT_BYTES - 1] &= 0x7F; |
| |
| X448Field.decode(py, 0, r.y); |
| |
| int[] u = X448Field.create(); |
| int[] v = X448Field.create(); |
| |
| X448Field.sqr(r.y, u); |
| X448Field.mul(u, -C_d, v); |
| X448Field.negate(u, u); |
| X448Field.addOne(u); |
| X448Field.addOne(v); |
| |
| if (!X448Field.sqrtRatioVar(u, v, r.x)) |
| { |
| return false; |
| } |
| |
| X448Field.normalize(r.x); |
| if (x_0 == 1 && X448Field.isZeroVar(r.x)) |
| { |
| return false; |
| } |
| |
| if (negate ^ (x_0 != (r.x[0] & 1))) |
| { |
| X448Field.negate(r.x, r.x); |
| } |
| |
| pointExtendXY(r); |
| return true; |
| } |
| |
| private static void decodeScalar(byte[] k, int kOff, int[] n) |
| { |
| // assert k[kOff + SCALAR_BYTES - 1] == 0x00; |
| |
| decode32(k, kOff, n, 0, SCALAR_INTS); |
| } |
| |
| private static void dom4(Xof d, byte x, byte[] y) |
| { |
| d.update(DOM4_PREFIX, 0, DOM4_PREFIX.length); |
| d.update(x); |
| d.update((byte)y.length); |
| d.update(y, 0, y.length); |
| } |
| |
| private static void encode24(int n, byte[] bs, int off) |
| { |
| bs[ off] = (byte)(n ); |
| bs[++off] = (byte)(n >>> 8); |
| bs[++off] = (byte)(n >>> 16); |
| } |
| |
| private static void encode32(int n, byte[] bs, int off) |
| { |
| bs[ off] = (byte)(n ); |
| bs[++off] = (byte)(n >>> 8); |
| bs[++off] = (byte)(n >>> 16); |
| bs[++off] = (byte)(n >>> 24); |
| } |
| |
| private static void encode56(long n, byte[] bs, int off) |
| { |
| encode32((int)n, bs, off); |
| encode24((int)(n >>> 32), bs, off + 4); |
| } |
| |
| private static void encodePoint(PointExt p, byte[] r, int rOff) |
| { |
| int[] x = X448Field.create(); |
| int[] y = X448Field.create(); |
| |
| X448Field.inv(p.z, y); |
| X448Field.mul(p.x, y, x); |
| X448Field.mul(p.y, y, y); |
| X448Field.normalize(x); |
| X448Field.normalize(y); |
| |
| X448Field.encode(y, r, rOff); |
| r[rOff + POINT_BYTES - 1] = (byte)((x[0] & 1) << 7); |
| } |
| |
| public static void generatePrivateKey(SecureRandom random, byte[] k) |
| { |
| random.nextBytes(k); |
| } |
| |
| public static void generatePublicKey(byte[] sk, int skOff, byte[] pk, int pkOff) |
| { |
| Xof d = createXof(); |
| byte[] h = new byte[SCALAR_BYTES * 2]; |
| |
| d.update(sk, skOff, SECRET_KEY_SIZE); |
| d.doFinal(h, 0, h.length); |
| |
| byte[] s = new byte[SCALAR_BYTES]; |
| pruneScalar(h, 0, s); |
| |
| scalarMultBaseEncoded(s, pk, pkOff); |
| } |
| |
| private static byte[] getWNAF(int[] n, int width) |
| { |
| // assert n[SCALAR_INTS - 1] >>> 31 == 0; |
| |
| int[] t = new int[SCALAR_INTS * 2]; |
| { |
| int tPos = t.length, c = 0; |
| int i = SCALAR_INTS; |
| while (--i >= 0) |
| { |
| int next = n[i]; |
| t[--tPos] = (next >>> 16) | (c << 16); |
| t[--tPos] = c = next; |
| } |
| } |
| |
| byte[] ws = new byte[448]; |
| |
| final int pow2 = 1 << width; |
| final int mask = pow2 - 1; |
| final int sign = pow2 >>> 1; |
| |
| int j = 0, carry = 0; |
| for (int i = 0; i < t.length; ++i, j -= 16) |
| { |
| int word = t[i]; |
| while (j < 16) |
| { |
| int word16 = word >>> j; |
| int bit = word16 & 1; |
| |
| if (bit == carry) |
| { |
| ++j; |
| continue; |
| } |
| |
| int digit = (word16 & mask) + carry; |
| carry = digit & sign; |
| digit -= (carry << 1); |
| carry >>>= (width - 1); |
| |
| ws[(i << 4) + j] = (byte)digit; |
| |
| j += width; |
| } |
| } |
| |
| // assert carry == 0; |
| |
| return ws; |
| } |
| |
| private static void implSign(Xof d, byte[] h, byte[] s, byte[] pk, int pkOff, byte[] ctx, byte phflag, |
| byte[] m, int mOff, int mLen, byte[] sig, int sigOff) |
| { |
| dom4(d, phflag, ctx); |
| d.update(h, SCALAR_BYTES, SCALAR_BYTES); |
| d.update(m, mOff, mLen); |
| d.doFinal(h, 0, h.length); |
| |
| byte[] r = reduceScalar(h); |
| byte[] R = new byte[POINT_BYTES]; |
| scalarMultBaseEncoded(r, R, 0); |
| |
| dom4(d, phflag, ctx); |
| d.update(R, 0, POINT_BYTES); |
| d.update(pk, pkOff, POINT_BYTES); |
| d.update(m, mOff, mLen); |
| d.doFinal(h, 0, h.length); |
| |
| byte[] k = reduceScalar(h); |
| byte[] S = calculateS(r, k, s); |
| |
| System.arraycopy(R, 0, sig, sigOff, POINT_BYTES); |
| System.arraycopy(S, 0, sig, sigOff + POINT_BYTES, SCALAR_BYTES); |
| } |
| |
| private static void implSign(byte[] sk, int skOff, byte[] ctx, byte phflag, byte[] m, int mOff, int mLen, |
| byte[] sig, int sigOff) |
| { |
| if (!checkContextVar(ctx)) |
| { |
| throw new IllegalArgumentException("ctx"); |
| } |
| |
| Xof d = createXof(); |
| byte[] h = new byte[SCALAR_BYTES * 2]; |
| |
| d.update(sk, skOff, SECRET_KEY_SIZE); |
| d.doFinal(h, 0, h.length); |
| |
| byte[] s = new byte[SCALAR_BYTES]; |
| pruneScalar(h, 0, s); |
| |
| byte[] pk = new byte[POINT_BYTES]; |
| scalarMultBaseEncoded(s, pk, 0); |
| |
| implSign(d, h, s, pk, 0, ctx, phflag, m, mOff, mLen, sig, sigOff); |
| } |
| |
| private static void implSign(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, byte phflag, |
| byte[] m, int mOff, int mLen, byte[] sig, int sigOff) |
| { |
| if (!checkContextVar(ctx)) |
| { |
| throw new IllegalArgumentException("ctx"); |
| } |
| |
| Xof d = createXof(); |
| byte[] h = new byte[SCALAR_BYTES * 2]; |
| |
| d.update(sk, skOff, SECRET_KEY_SIZE); |
| d.doFinal(h, 0, h.length); |
| |
| byte[] s = new byte[SCALAR_BYTES]; |
| pruneScalar(h, 0, s); |
| |
| implSign(d, h, s, pk, pkOff, ctx, phflag, m, mOff, mLen, sig, sigOff); |
| } |
| |
| private static boolean implVerify(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] ctx, byte phflag, |
| byte[] m, int mOff, int mLen) |
| { |
| if (!checkContextVar(ctx)) |
| { |
| throw new IllegalArgumentException("ctx"); |
| } |
| |
| byte[] R = Arrays.copyOfRange(sig, sigOff, sigOff + POINT_BYTES); |
| byte[] S = Arrays.copyOfRange(sig, sigOff + POINT_BYTES, sigOff + SIGNATURE_SIZE); |
| |
| if (!checkPointVar(R)) |
| { |
| return false; |
| } |
| if (!checkScalarVar(S)) |
| { |
| return false; |
| } |
| |
| PointExt pA = new PointExt(); |
| if (!decodePointVar(pk, pkOff, true, pA)) |
| { |
| return false; |
| } |
| |
| Xof d = createXof(); |
| byte[] h = new byte[SCALAR_BYTES * 2]; |
| |
| dom4(d, phflag, ctx); |
| d.update(R, 0, POINT_BYTES); |
| d.update(pk, pkOff, POINT_BYTES); |
| d.update(m, mOff, mLen); |
| d.doFinal(h, 0, h.length); |
| |
| byte[] k = reduceScalar(h); |
| |
| int[] nS = new int[SCALAR_INTS]; |
| decodeScalar(S, 0, nS); |
| |
| int[] nA = new int[SCALAR_INTS]; |
| decodeScalar(k, 0, nA); |
| |
| PointExt pR = new PointExt(); |
| scalarMultStraussVar(nS, nA, pA, pR); |
| |
| byte[] check = new byte[POINT_BYTES]; |
| encodePoint(pR, check, 0); |
| |
| return Arrays.areEqual(check, R); |
| } |
| |
| private static void pointAddVar(boolean negate, PointExt p, PointExt r) |
| { |
| int[] A = X448Field.create(); |
| int[] B = X448Field.create(); |
| int[] C = X448Field.create(); |
| int[] D = X448Field.create(); |
| int[] E = X448Field.create(); |
| int[] F = X448Field.create(); |
| int[] G = X448Field.create(); |
| int[] H = X448Field.create(); |
| |
| int[] b, e, f, g; |
| if (negate) |
| { |
| b = E; e = B; f = G; g = F; |
| X448Field.sub(p.y, p.x, H); |
| } |
| else |
| { |
| b = B; e = E; f = F; g = G; |
| X448Field.add(p.y, p.x, H); |
| } |
| |
| X448Field.mul(p.z, r.z, A); |
| X448Field.sqr(A, B); |
| X448Field.mul(p.x, r.x, C); |
| X448Field.mul(p.y, r.y, D); |
| X448Field.mul(C, D, E); |
| X448Field.mul(E, -C_d, E); |
| // X448Field.apm(B, E, F, G); |
| X448Field.add(B, E, f); |
| X448Field.sub(B, E, g); |
| X448Field.add(r.x, r.y, E); |
| X448Field.mul(H, E, H); |
| // X448Field.apm(D, C, B, E); |
| X448Field.add(D, C, b); |
| X448Field.sub(D, C, e); |
| X448Field.carry(b); |
| X448Field.sub(H, B, H); |
| X448Field.mul(H, A, H); |
| X448Field.mul(E, A, E); |
| X448Field.mul(F, H, r.x); |
| X448Field.mul(E, G, r.y); |
| X448Field.mul(F, G, r.z); |
| } |
| |
| private static void pointAddPrecomp(PointPrecomp p, PointExt r) |
| { |
| int[] B = X448Field.create(); |
| int[] C = X448Field.create(); |
| int[] D = X448Field.create(); |
| int[] E = X448Field.create(); |
| int[] F = X448Field.create(); |
| int[] G = X448Field.create(); |
| int[] H = X448Field.create(); |
| |
| X448Field.sqr(r.z, B); |
| X448Field.mul(p.x, r.x, C); |
| X448Field.mul(p.y, r.y, D); |
| X448Field.mul(C, D, E); |
| X448Field.mul(E, -C_d, E); |
| // X448Field.apm(B, E, F, G); |
| X448Field.add(B, E, F); |
| X448Field.sub(B, E, G); |
| X448Field.add(p.x, p.y, B); |
| X448Field.add(r.x, r.y, E); |
| X448Field.mul(B, E, H); |
| // X448Field.apm(D, C, B, E); |
| X448Field.add(D, C, B); |
| X448Field.sub(D, C, E); |
| X448Field.carry(B); |
| X448Field.sub(H, B, H); |
| X448Field.mul(H, r.z, H); |
| X448Field.mul(E, r.z, E); |
| X448Field.mul(F, H, r.x); |
| X448Field.mul(E, G, r.y); |
| X448Field.mul(F, G, r.z); |
| } |
| |
| private static PointExt pointCopy(PointExt p) |
| { |
| PointExt r = new PointExt(); |
| X448Field.copy(p.x, 0, r.x, 0); |
| X448Field.copy(p.y, 0, r.y, 0); |
| X448Field.copy(p.z, 0, r.z, 0); |
| return r; |
| } |
| |
| private static void pointDouble(PointExt r) |
| { |
| int[] B = X448Field.create(); |
| int[] C = X448Field.create(); |
| int[] D = X448Field.create(); |
| int[] E = X448Field.create(); |
| int[] H = X448Field.create(); |
| int[] J = X448Field.create(); |
| |
| X448Field.add(r.x, r.y, B); |
| X448Field.sqr(B, B); |
| X448Field.sqr(r.x, C); |
| X448Field.sqr(r.y, D); |
| X448Field.add(C, D, E); |
| X448Field.carry(E); |
| X448Field.sqr(r.z, H); |
| X448Field.add(H, H, H); |
| X448Field.carry(H); |
| X448Field.sub(E, H, J); |
| X448Field.sub(B, E, B); |
| X448Field.sub(C, D, C); |
| X448Field.mul(B, J, r.x); |
| X448Field.mul(E, C, r.y); |
| X448Field.mul(E, J, r.z); |
| } |
| |
| private static void pointExtendXY(PointExt p) |
| { |
| X448Field.one(p.z); |
| } |
| |
| private static void pointLookup(int block, int index, PointPrecomp p) |
| { |
| // assert 0 <= block && block < PRECOMP_BLOCKS; |
| // assert 0 <= index && index < PRECOMP_POINTS; |
| |
| int off = block * PRECOMP_POINTS * 2 * X448Field.SIZE; |
| |
| for (int i = 0; i < PRECOMP_POINTS; ++i) |
| { |
| int mask = ((i ^ index) - 1) >> 31; |
| Nat.cmov(X448Field.SIZE, mask, precompBase, off, p.x, 0); off += X448Field.SIZE; |
| Nat.cmov(X448Field.SIZE, mask, precompBase, off, p.y, 0); off += X448Field.SIZE; |
| } |
| } |
| |
| private static PointExt[] pointPrecompVar(PointExt p, int count) |
| { |
| // assert count > 0; |
| |
| PointExt d = pointCopy(p); |
| pointDouble(d); |
| |
| PointExt[] table = new PointExt[count]; |
| table[0] = pointCopy(p); |
| for (int i = 1; i < count; ++i) |
| { |
| table[i] = pointCopy(table[i - 1]); |
| pointAddVar(false, d, table[i]); |
| } |
| return table; |
| } |
| |
| private static void pointSetNeutral(PointExt p) |
| { |
| X448Field.zero(p.x); |
| X448Field.one(p.y); |
| X448Field.one(p.z); |
| } |
| |
| public static void precompute() |
| { |
| synchronized (precompLock) |
| { |
| if (precompBase != null) |
| { |
| return; |
| } |
| |
| PointExt p = new PointExt(); |
| X448Field.copy(B_x, 0, p.x, 0); |
| X448Field.copy(B_y, 0, p.y, 0); |
| pointExtendXY(p); |
| |
| precompBaseTable = pointPrecompVar(p, 1 << (WNAF_WIDTH_BASE - 2)); |
| |
| precompBase = new int[PRECOMP_BLOCKS * PRECOMP_POINTS * 2 * X448Field.SIZE]; |
| |
| int off = 0; |
| for (int b = 0; b < PRECOMP_BLOCKS; ++b) |
| { |
| PointExt[] ds = new PointExt[PRECOMP_TEETH]; |
| |
| PointExt sum = new PointExt(); |
| pointSetNeutral(sum); |
| |
| for (int t = 0; t < PRECOMP_TEETH; ++t) |
| { |
| pointAddVar(true, p, sum); |
| pointDouble(p); |
| |
| ds[t] = pointCopy(p); |
| |
| if (b + t != PRECOMP_BLOCKS + PRECOMP_TEETH - 2) |
| { |
| for (int s = 1; s < PRECOMP_SPACING; ++s) |
| { |
| pointDouble(p); |
| } |
| } |
| } |
| |
| PointExt[] points = new PointExt[PRECOMP_POINTS]; |
| int k = 0; |
| points[k++] = sum; |
| |
| for (int t = 0; t < (PRECOMP_TEETH - 1); ++t) |
| { |
| int size = 1 << t; |
| for (int j = 0; j < size; ++j, ++k) |
| { |
| points[k] = pointCopy(points[k - size]); |
| pointAddVar(false, ds[t], points[k]); |
| } |
| } |
| |
| // assert k == PRECOMP_POINTS; |
| |
| for (int i = 0; i < PRECOMP_POINTS; ++i) |
| { |
| PointExt q = points[i]; |
| // TODO[ed448] Batch inversion |
| X448Field.inv(q.z, q.z); |
| X448Field.mul(q.x, q.z, q.x); |
| X448Field.mul(q.y, q.z, q.y); |
| |
| // X448Field.normalize(q.x); |
| // X448Field.normalize(q.y); |
| |
| X448Field.copy(q.x, 0, precompBase, off); off += X448Field.SIZE; |
| X448Field.copy(q.y, 0, precompBase, off); off += X448Field.SIZE; |
| } |
| } |
| |
| // assert off == precompBase.length; |
| } |
| } |
| |
| private static void pruneScalar(byte[] n, int nOff, byte[] r) |
| { |
| System.arraycopy(n, nOff, r, 0, SCALAR_BYTES - 1); |
| |
| r[0] &= 0xFC; |
| r[SCALAR_BYTES - 2] |= 0x80; |
| r[SCALAR_BYTES - 1] = 0x00; |
| } |
| |
| private static byte[] reduceScalar(byte[] n) |
| { |
| long x00 = decode32(n, 0) & M32L; // x00:32/-- |
| long x01 = (decode24(n, 4) << 4) & M32L; // x01:28/-- |
| long x02 = decode32(n, 7) & M32L; // x02:32/-- |
| long x03 = (decode24(n, 11) << 4) & M32L; // x03:28/-- |
| long x04 = decode32(n, 14) & M32L; // x04:32/-- |
| long x05 = (decode24(n, 18) << 4) & M32L; // x05:28/-- |
| long x06 = decode32(n, 21) & M32L; // x06:32/-- |
| long x07 = (decode24(n, 25) << 4) & M32L; // x07:28/-- |
| long x08 = decode32(n, 28) & M32L; // x08:32/-- |
| long x09 = (decode24(n, 32) << 4) & M32L; // x09:28/-- |
| long x10 = decode32(n, 35) & M32L; // x10:32/-- |
| long x11 = (decode24(n, 39) << 4) & M32L; // x11:28/-- |
| long x12 = decode32(n, 42) & M32L; // x12:32/-- |
| long x13 = (decode24(n, 46) << 4) & M32L; // x13:28/-- |
| long x14 = decode32(n, 49) & M32L; // x14:32/-- |
| long x15 = (decode24(n, 53) << 4) & M32L; // x15:28/-- |
| long x16 = decode32(n, 56) & M32L; // x16:32/-- |
| long x17 = (decode24(n, 60) << 4) & M32L; // x17:28/-- |
| long x18 = decode32(n, 63) & M32L; // x18:32/-- |
| long x19 = (decode24(n, 67) << 4) & M32L; // x19:28/-- |
| long x20 = decode32(n, 70) & M32L; // x20:32/-- |
| long x21 = (decode24(n, 74) << 4) & M32L; // x21:28/-- |
| long x22 = decode32(n, 77) & M32L; // x22:32/-- |
| long x23 = (decode24(n, 81) << 4) & M32L; // x23:28/-- |
| long x24 = decode32(n, 84) & M32L; // x24:32/-- |
| long x25 = (decode24(n, 88) << 4) & M32L; // x25:28/-- |
| long x26 = decode32(n, 91) & M32L; // x26:32/-- |
| long x27 = (decode24(n, 95) << 4) & M32L; // x27:28/-- |
| long x28 = decode32(n, 98) & M32L; // x28:32/-- |
| long x29 = (decode24(n, 102) << 4) & M32L; // x29:28/-- |
| long x30 = decode32(n, 105) & M32L; // x30:32/-- |
| long x31 = (decode24(n, 109) << 4) & M32L; // x31:28/-- |
| long x32 = decode16(n, 112) & M32L; // x32:16/-- |
| |
| // x32 += (x31 >>> 28); x31 &= M28L; |
| x16 += x32 * L4_0; // x16:42/-- |
| x17 += x32 * L4_1; // x17:41/28 |
| x18 += x32 * L4_2; // x18:43/42 |
| x19 += x32 * L4_3; // x19:44/28 |
| x20 += x32 * L4_4; // x20:43/-- |
| x21 += x32 * L4_5; // x21:44/28 |
| x22 += x32 * L4_6; // x22:43/41 |
| x23 += x32 * L4_7; // x23:45/41 |
| |
| x31 += (x30 >>> 28); x30 &= M28L; // x31:28/--, x30:28/-- |
| x15 += x31 * L4_0; // x15:54/-- |
| x16 += x31 * L4_1; // x16:53/42 |
| x17 += x31 * L4_2; // x17:55/54 |
| x18 += x31 * L4_3; // x18:56/44 |
| x19 += x31 * L4_4; // x19:55/-- |
| x20 += x31 * L4_5; // x20:56/43 |
| x21 += x31 * L4_6; // x21:55/53 |
| x22 += x31 * L4_7; // x22:57/53 |
| |
| // x30 += (x29 >>> 28); x29 &= M28L; |
| x14 += x30 * L4_0; // x14:54/-- |
| x15 += x30 * L4_1; // x15:54/53 |
| x16 += x30 * L4_2; // x16:56/-- |
| x17 += x30 * L4_3; // x17:57/-- |
| x18 += x30 * L4_4; // x18:56/55 |
| x19 += x30 * L4_5; // x19:56/55 |
| x20 += x30 * L4_6; // x20:57/-- |
| x21 += x30 * L4_7; // x21:57/56 |
| |
| x29 += (x28 >>> 28); x28 &= M28L; // x29:28/--, x28:28/-- |
| x13 += x29 * L4_0; // x13:54/-- |
| x14 += x29 * L4_1; // x14:54/53 |
| x15 += x29 * L4_2; // x15:56/-- |
| x16 += x29 * L4_3; // x16:57/-- |
| x17 += x29 * L4_4; // x17:57/55 |
| x18 += x29 * L4_5; // x18:57/55 |
| x19 += x29 * L4_6; // x19:57/52 |
| x20 += x29 * L4_7; // x20:58/52 |
| |
| // x28 += (x27 >>> 28); x27 &= M28L; |
| x12 += x28 * L4_0; // x12:54/-- |
| x13 += x28 * L4_1; // x13:54/53 |
| x14 += x28 * L4_2; // x14:56/-- |
| x15 += x28 * L4_3; // x15:57/-- |
| x16 += x28 * L4_4; // x16:57/55 |
| x17 += x28 * L4_5; // x17:58/-- |
| x18 += x28 * L4_6; // x18:58/-- |
| x19 += x28 * L4_7; // x19:58/53 |
| |
| x27 += (x26 >>> 28); x26 &= M28L; // x27:28/--, x26:28/-- |
| x11 += x27 * L4_0; // x11:54/-- |
| x12 += x27 * L4_1; // x12:54/53 |
| x13 += x27 * L4_2; // x13:56/-- |
| x14 += x27 * L4_3; // x14:57/-- |
| x15 += x27 * L4_4; // x15:57/55 |
| x16 += x27 * L4_5; // x16:58/-- |
| x17 += x27 * L4_6; // x17:58/56 |
| x18 += x27 * L4_7; // x18:59/-- |
| |
| // x26 += (x25 >>> 28); x25 &= M28L; |
| x10 += x26 * L4_0; // x10:54/-- |
| x11 += x26 * L4_1; // x11:54/53 |
| x12 += x26 * L4_2; // x12:56/-- |
| x13 += x26 * L4_3; // x13:57/-- |
| x14 += x26 * L4_4; // x14:57/55 |
| x15 += x26 * L4_5; // x15:58/-- |
| x16 += x26 * L4_6; // x16:58/56 |
| x17 += x26 * L4_7; // x17:59/-- |
| |
| x25 += (x24 >>> 28); x24 &= M28L; // x25:28/--, x24:28/-- |
| x09 += x25 * L4_0; // x09:54/-- |
| x10 += x25 * L4_1; // x10:54/53 |
| x11 += x25 * L4_2; // x11:56/-- |
| x12 += x25 * L4_3; // x12:57/-- |
| x13 += x25 * L4_4; // x13:57/55 |
| x14 += x25 * L4_5; // x14:58/-- |
| x15 += x25 * L4_6; // x15:58/56 |
| x16 += x25 * L4_7; // x16:59/-- |
| |
| x21 += (x20 >>> 28); x20 &= M28L; // x21:58/--, x20:28/-- |
| x22 += (x21 >>> 28); x21 &= M28L; // x22:57/54, x21:28/-- |
| x23 += (x22 >>> 28); x22 &= M28L; // x23:45/42, x22:28/-- |
| x24 += (x23 >>> 28); x23 &= M28L; // x24:28/18, x23:28/-- |
| |
| x08 += x24 * L4_0; // x08:54/-- |
| x09 += x24 * L4_1; // x09:55/-- |
| x10 += x24 * L4_2; // x10:56/46 |
| x11 += x24 * L4_3; // x11:57/46 |
| x12 += x24 * L4_4; // x12:57/55 |
| x13 += x24 * L4_5; // x13:58/-- |
| x14 += x24 * L4_6; // x14:58/56 |
| x15 += x24 * L4_7; // x15:59/-- |
| |
| x07 += x23 * L4_0; // x07:54/-- |
| x08 += x23 * L4_1; // x08:54/53 |
| x09 += x23 * L4_2; // x09:56/53 |
| x10 += x23 * L4_3; // x10:57/46 |
| x11 += x23 * L4_4; // x11:57/55 |
| x12 += x23 * L4_5; // x12:58/-- |
| x13 += x23 * L4_6; // x13:58/56 |
| x14 += x23 * L4_7; // x14:59/-- |
| |
| x06 += x22 * L4_0; // x06:54/-- |
| x07 += x22 * L4_1; // x07:54/53 |
| x08 += x22 * L4_2; // x08:56/-- |
| x09 += x22 * L4_3; // x09:57/53 |
| x10 += x22 * L4_4; // x10:57/55 |
| x11 += x22 * L4_5; // x11:58/-- |
| x12 += x22 * L4_6; // x12:58/56 |
| x13 += x22 * L4_7; // x13:59/-- |
| |
| x18 += (x17 >>> 28); x17 &= M28L; // x18:59/31, x17:28/-- |
| x19 += (x18 >>> 28); x18 &= M28L; // x19:58/54, x18:28/-- |
| x20 += (x19 >>> 28); x19 &= M28L; // x20:30/29, x19:28/-- |
| x21 += (x20 >>> 28); x20 &= M28L; // x21:28/03, x20:28/-- |
| |
| x05 += x21 * L4_0; // x05:54/-- |
| x06 += x21 * L4_1; // x06:55/-- |
| x07 += x21 * L4_2; // x07:56/31 |
| x08 += x21 * L4_3; // x08:57/31 |
| x09 += x21 * L4_4; // x09:57/56 |
| x10 += x21 * L4_5; // x10:58/-- |
| x11 += x21 * L4_6; // x11:58/56 |
| x12 += x21 * L4_7; // x12:59/-- |
| |
| x04 += x20 * L4_0; // x04:54/-- |
| x05 += x20 * L4_1; // x05:54/53 |
| x06 += x20 * L4_2; // x06:56/53 |
| x07 += x20 * L4_3; // x07:57/31 |
| x08 += x20 * L4_4; // x08:57/55 |
| x09 += x20 * L4_5; // x09:58/-- |
| x10 += x20 * L4_6; // x10:58/56 |
| x11 += x20 * L4_7; // x11:59/-- |
| |
| x03 += x19 * L4_0; // x03:54/-- |
| x04 += x19 * L4_1; // x04:54/53 |
| x05 += x19 * L4_2; // x05:56/-- |
| x06 += x19 * L4_3; // x06:57/53 |
| x07 += x19 * L4_4; // x07:57/55 |
| x08 += x19 * L4_5; // x08:58/-- |
| x09 += x19 * L4_6; // x09:58/56 |
| x10 += x19 * L4_7; // x10:59/-- |
| |
| x15 += (x14 >>> 28); x14 &= M28L; // x15:59/31, x14:28/-- |
| x16 += (x15 >>> 28); x15 &= M28L; // x16:59/32, x15:28/-- |
| x17 += (x16 >>> 28); x16 &= M28L; // x17:31/29, x16:28/-- |
| x18 += (x17 >>> 28); x17 &= M28L; // x18:28/04, x17:28/-- |
| |
| x02 += x18 * L4_0; // x02:54/-- |
| x03 += x18 * L4_1; // x03:55/-- |
| x04 += x18 * L4_2; // x04:56/32 |
| x05 += x18 * L4_3; // x05:57/32 |
| x06 += x18 * L4_4; // x06:57/56 |
| x07 += x18 * L4_5; // x07:58/-- |
| x08 += x18 * L4_6; // x08:58/56 |
| x09 += x18 * L4_7; // x09:59/-- |
| |
| x01 += x17 * L4_0; // x01:54/-- |
| x02 += x17 * L4_1; // x02:54/53 |
| x03 += x17 * L4_2; // x03:56/53 |
| x04 += x17 * L4_3; // x04:57/32 |
| x05 += x17 * L4_4; // x05:57/55 |
| x06 += x17 * L4_5; // x06:58/-- |
| x07 += x17 * L4_6; // x07:58/56 |
| x08 += x17 * L4_7; // x08:59/-- |
| |
| x16 *= 4; |
| x16 += (x15 >>> 26); x15 &= M26L; |
| x16 += 1; // x16:30/01 |
| |
| x00 += x16 * L_0; |
| x01 += x16 * L_1; |
| x02 += x16 * L_2; |
| x03 += x16 * L_3; |
| x04 += x16 * L_4; |
| x05 += x16 * L_5; |
| x06 += x16 * L_6; |
| x07 += x16 * L_7; |
| |
| x01 += (x00 >>> 28); x00 &= M28L; |
| x02 += (x01 >>> 28); x01 &= M28L; |
| x03 += (x02 >>> 28); x02 &= M28L; |
| x04 += (x03 >>> 28); x03 &= M28L; |
| x05 += (x04 >>> 28); x04 &= M28L; |
| x06 += (x05 >>> 28); x05 &= M28L; |
| x07 += (x06 >>> 28); x06 &= M28L; |
| x08 += (x07 >>> 28); x07 &= M28L; |
| x09 += (x08 >>> 28); x08 &= M28L; |
| x10 += (x09 >>> 28); x09 &= M28L; |
| x11 += (x10 >>> 28); x10 &= M28L; |
| x12 += (x11 >>> 28); x11 &= M28L; |
| x13 += (x12 >>> 28); x12 &= M28L; |
| x14 += (x13 >>> 28); x13 &= M28L; |
| x15 += (x14 >>> 28); x14 &= M28L; |
| x16 = (x15 >>> 26); x15 &= M26L; |
| |
| x16 -= 1; |
| |
| // assert x16 == 0L || x16 == -1L; |
| |
| x00 -= x16 & L_0; |
| x01 -= x16 & L_1; |
| x02 -= x16 & L_2; |
| x03 -= x16 & L_3; |
| x04 -= x16 & L_4; |
| x05 -= x16 & L_5; |
| x06 -= x16 & L_6; |
| x07 -= x16 & L_7; |
| |
| x01 += (x00 >> 28); x00 &= M28L; |
| x02 += (x01 >> 28); x01 &= M28L; |
| x03 += (x02 >> 28); x02 &= M28L; |
| x04 += (x03 >> 28); x03 &= M28L; |
| x05 += (x04 >> 28); x04 &= M28L; |
| x06 += (x05 >> 28); x05 &= M28L; |
| x07 += (x06 >> 28); x06 &= M28L; |
| x08 += (x07 >> 28); x07 &= M28L; |
| x09 += (x08 >> 28); x08 &= M28L; |
| x10 += (x09 >> 28); x09 &= M28L; |
| x11 += (x10 >> 28); x10 &= M28L; |
| x12 += (x11 >> 28); x11 &= M28L; |
| x13 += (x12 >> 28); x12 &= M28L; |
| x14 += (x13 >> 28); x13 &= M28L; |
| x15 += (x14 >> 28); x14 &= M28L; |
| |
| // assert x15 >>> 26 == 0L; |
| |
| byte[] r = new byte[SCALAR_BYTES]; |
| encode56(x00 | (x01 << 28), r, 0); |
| encode56(x02 | (x03 << 28), r, 7); |
| encode56(x04 | (x05 << 28), r, 14); |
| encode56(x06 | (x07 << 28), r, 21); |
| encode56(x08 | (x09 << 28), r, 28); |
| encode56(x10 | (x11 << 28), r, 35); |
| encode56(x12 | (x13 << 28), r, 42); |
| encode56(x14 | (x15 << 28), r, 49); |
| // r[SCALAR_BYTES - 1] = 0; |
| return r; |
| } |
| |
| private static void scalarMultBase(byte[] k, PointExt r) |
| { |
| precompute(); |
| |
| pointSetNeutral(r); |
| |
| int[] n = new int[SCALAR_INTS + 1]; |
| decodeScalar(k, 0, n); |
| |
| // Recode the scalar into signed-digit form |
| { |
| n[SCALAR_INTS] = 4 + Nat.cadd(SCALAR_INTS, ~n[0] & 1, n, L, n); |
| // int c = Nat.shiftDownBit(n.length, n, 0); assert c == (1 << 31); |
| Nat.shiftDownBit(n.length, n, 0); |
| } |
| |
| PointPrecomp p = new PointPrecomp(); |
| |
| int cOff = PRECOMP_SPACING - 1; |
| for (;;) |
| { |
| int tPos = cOff; |
| |
| for (int b = 0; b < PRECOMP_BLOCKS; ++b) |
| { |
| int w = 0; |
| for (int t = 0; t < PRECOMP_TEETH; ++t) |
| { |
| int tBit = n[tPos >>> 5] >>> (tPos & 0x1F); |
| w &= ~(1 << t); |
| w ^= (tBit << t); |
| tPos += PRECOMP_SPACING; |
| } |
| |
| int sign = (w >>> (PRECOMP_TEETH - 1)) & 1; |
| int abs = (w ^ -sign) & PRECOMP_MASK; |
| |
| // assert sign == 0 || sign == 1; |
| // assert 0 <= abs && abs < PRECOMP_POINTS; |
| |
| pointLookup(b, abs, p); |
| |
| X448Field.cnegate(sign, p.x); |
| |
| pointAddPrecomp(p, r); |
| } |
| |
| if (--cOff < 0) |
| { |
| break; |
| } |
| |
| pointDouble(r); |
| } |
| } |
| |
| private static void scalarMultBaseEncoded(byte[] k, byte[] r, int rOff) |
| { |
| PointExt p = new PointExt(); |
| scalarMultBase(k, p); |
| encodePoint(p, r, rOff); |
| } |
| |
| /** |
| * NOTE: Only for use by X448 |
| */ |
| public static void scalarMultBaseXY(X448.Friend friend, byte[] k, int kOff, int[] x, int[] y) |
| { |
| if (null == friend) |
| { |
| throw new NullPointerException("This method is only for use by X448"); |
| } |
| |
| byte[] n = new byte[SCALAR_BYTES]; |
| pruneScalar(k, kOff, n); |
| |
| PointExt p = new PointExt(); |
| scalarMultBase(n, p); |
| X448Field.copy(p.x, 0, x, 0); |
| X448Field.copy(p.y, 0, y, 0); |
| } |
| |
| private static void scalarMultStraussVar(int[] nb, int[] np, PointExt p, PointExt r) |
| { |
| precompute(); |
| |
| final int width = 5; |
| |
| byte[] ws_b = getWNAF(nb, WNAF_WIDTH_BASE); |
| byte[] ws_p = getWNAF(np, width); |
| |
| PointExt[] tp = pointPrecompVar(p, 1 << (width - 2)); |
| |
| pointSetNeutral(r); |
| |
| int bit = 447; |
| while (bit > 0 && (ws_b[bit] | ws_p[bit]) == 0) |
| { |
| --bit; |
| } |
| |
| for (;;) |
| { |
| int wb = ws_b[bit]; |
| if (wb != 0) |
| { |
| int sign = wb >> 31; |
| int index = (wb ^ sign) >>> 1; |
| |
| pointAddVar((sign != 0), precompBaseTable[index], r); |
| } |
| |
| int wp = ws_p[bit]; |
| if (wp != 0) |
| { |
| int sign = wp >> 31; |
| int index = (wp ^ sign) >>> 1; |
| |
| pointAddVar((sign != 0), tp[index], r); |
| } |
| |
| if (--bit < 0) |
| { |
| break; |
| } |
| |
| pointDouble(r); |
| } |
| } |
| |
| public static void sign(byte[] sk, int skOff, byte[] ctx, byte[] m, int mOff, int mLen, byte[] sig, int sigOff) |
| { |
| byte phflag = 0x00; |
| |
| implSign(sk, skOff, ctx, phflag, m, mOff, mLen, sig, sigOff); |
| } |
| |
| public static void sign(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, byte[] m, int mOff, int mLen, byte[] sig, int sigOff) |
| { |
| byte phflag = 0x00; |
| |
| implSign(sk, skOff, pk, pkOff, ctx, phflag, m, mOff, mLen, sig, sigOff); |
| } |
| |
| public static void signPrehash(byte[] sk, int skOff, byte[] ctx, byte[] ph, int phOff, byte[] sig, int sigOff) |
| { |
| byte phflag = 0x01; |
| |
| implSign(sk, skOff, ctx, phflag, ph, phOff, PREHASH_SIZE, sig, sigOff); |
| } |
| |
| public static void signPrehash(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, byte[] ph, int phOff, byte[] sig, int sigOff) |
| { |
| byte phflag = 0x01; |
| |
| implSign(sk, skOff, pk, pkOff, ctx, phflag, ph, phOff, PREHASH_SIZE, sig, sigOff); |
| } |
| |
| public static void signPrehash(byte[] sk, int skOff, byte[] ctx, Xof ph, byte[] sig, int sigOff) |
| { |
| byte[] m = new byte[PREHASH_SIZE]; |
| if (PREHASH_SIZE != ph.doFinal(m, 0, PREHASH_SIZE)) |
| { |
| throw new IllegalArgumentException("ph"); |
| } |
| |
| byte phflag = 0x01; |
| |
| implSign(sk, skOff, ctx, phflag, m, 0, m.length, sig, sigOff); |
| } |
| |
| public static void signPrehash(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, Xof ph, byte[] sig, int sigOff) |
| { |
| byte[] m = new byte[PREHASH_SIZE]; |
| if (PREHASH_SIZE != ph.doFinal(m, 0, PREHASH_SIZE)) |
| { |
| throw new IllegalArgumentException("ph"); |
| } |
| |
| byte phflag = 0x01; |
| |
| implSign(sk, skOff, pk, pkOff, ctx, phflag, m, 0, m.length, sig, sigOff); |
| } |
| |
| public static boolean verify(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] ctx, byte[] m, int mOff, int mLen) |
| { |
| byte phflag = 0x00; |
| |
| return implVerify(sig, sigOff, pk, pkOff, ctx, phflag, m, mOff, mLen); |
| } |
| |
| public static boolean verifyPrehash(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] ctx, byte[] ph, int phOff) |
| { |
| byte phflag = 0x01; |
| |
| return implVerify(sig, sigOff, pk, pkOff, ctx, phflag, ph, phOff, PREHASH_SIZE); |
| } |
| |
| public static boolean verifyPrehash(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] ctx, Xof ph) |
| { |
| byte[] m = new byte[PREHASH_SIZE]; |
| if (PREHASH_SIZE != ph.doFinal(m, 0, PREHASH_SIZE)) |
| { |
| throw new IllegalArgumentException("ph"); |
| } |
| |
| byte phflag = 0x01; |
| |
| return implVerify(sig, sigOff, pk, pkOff, ctx, phflag, m, 0, m.length); |
| } |
| } |