org.bouncycastle.math.ec.rfc8032.Ed25519 Maven / Gradle / Ivy
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package org.bouncycastle.math.ec.rfc8032;
import java.security.SecureRandom;
import org.bouncycastle.crypto.Digest;
import org.bouncycastle.crypto.digests.SHA512Digest;
import org.bouncycastle.math.ec.rfc7748.X25519;
import org.bouncycastle.math.ec.rfc7748.X25519Field;
import org.bouncycastle.math.raw.Interleave;
import org.bouncycastle.math.raw.Nat;
import org.bouncycastle.math.raw.Nat256;
import org.bouncycastle.util.Arrays;
/**
* A low-level implementation of the Ed25519, Ed25519ctx, and Ed25519ph instantiations of the Edwards-Curve
* Digital Signature Algorithm specified in RFC 8032.
*
* The implementation strategy is mostly drawn from Mike Hamburg, "Fast and
* compact elliptic-curve cryptography", notably the "signed multi-comb" algorithm (for scalar
* multiplication by a fixed point), the "half Niels coordinates" (for precomputed points), and the
* "extensible coordinates" (for accumulators). Standard
* extended coordinates are used
* during precomputations, needing only a single extra point addition formula.
*/
public abstract class Ed25519
{
// -x^2 + y^2 == 1 + 0x52036CEE2B6FFE738CC740797779E89800700A4D4141D8AB75EB4DCA135978A3 * x^2 * y^2
public static final class Algorithm
{
public static final int Ed25519 = 0;
public static final int Ed25519ctx = 1;
public static final int Ed25519ph = 2;
}
private static class F extends X25519Field {};
private static final long M08L = 0x000000FFL;
private static final long M28L = 0x0FFFFFFFL;
private static final long M32L = 0xFFFFFFFFL;
private static final int COORD_INTS = 8;
private static final int POINT_BYTES = COORD_INTS * 4;
private static final int SCALAR_INTS = 8;
private static final int SCALAR_BYTES = SCALAR_INTS * 4;
public static final int PREHASH_SIZE = 64;
public static final int PUBLIC_KEY_SIZE = POINT_BYTES;
public static final int SECRET_KEY_SIZE = 32;
public static final int SIGNATURE_SIZE = POINT_BYTES + SCALAR_BYTES;
// "SigEd25519 no Ed25519 collisions"
private static final byte[] DOM2_PREFIX = new byte[]{ 0x53, 0x69, 0x67, 0x45, 0x64, 0x32, 0x35, 0x35, 0x31, 0x39,
0x20, 0x6e, 0x6f, 0x20, 0x45, 0x64, 0x32, 0x35, 0x35, 0x31, 0x39, 0x20, 0x63, 0x6f, 0x6c, 0x6c, 0x69, 0x73,
0x69, 0x6f, 0x6e, 0x73 };
private static final int[] P = new int[]{ 0xFFFFFFED, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
0xFFFFFFFF, 0x7FFFFFFF };
private static final int[] L = new int[]{ 0x5CF5D3ED, 0x5812631A, 0xA2F79CD6, 0x14DEF9DE, 0x00000000, 0x00000000,
0x00000000, 0x10000000 };
private static final int L0 = -0x030A2C13; // L0:26/--
private static final int L1 = 0x012631A6; // L1:24/22
private static final int L2 = 0x079CD658; // L2:27/--
private static final int L3 = -0x006215D1; // L3:23/--
private static final int L4 = 0x000014DF; // L4:12/11
private static final int[] B_x = new int[]{ 0x0325D51A, 0x018B5823, 0x007B2C95, 0x0304A92D, 0x00D2598E, 0x01D6DC5C,
0x01388C7F, 0x013FEC0A, 0x029E6B72, 0x0042D26D };
private static final int[] B_y = new int[]{ 0x02666658, 0x01999999, 0x00666666, 0x03333333, 0x00CCCCCC, 0x02666666,
0x01999999, 0x00666666, 0x03333333, 0x00CCCCCC, };
// Note that d == -121665/121666
private static final int[] C_d = new int[]{ 0x035978A3, 0x02D37284, 0x018AB75E, 0x026A0A0E, 0x0000E014, 0x0379E898,
0x01D01E5D, 0x01E738CC, 0x03715B7F, 0x00A406D9 };
private static final int[] C_d2 = new int[]{ 0x02B2F159, 0x01A6E509, 0x01156EBD, 0x00D4141D, 0x0001C029, 0x02F3D130,
0x03A03CBB, 0x01CE7198, 0x02E2B6FF, 0x00480DB3 };
private static final int[] C_d4 = new int[]{ 0x0165E2B2, 0x034DCA13, 0x002ADD7A, 0x01A8283B, 0x00038052, 0x01E7A260,
0x03407977, 0x019CE331, 0x01C56DFF, 0x00901B67 };
private static final int WNAF_WIDTH = 5;
private static final int WNAF_WIDTH_BASE = 7;
// scalarMultBase is hard-coded for these values of blocks, teeth, spacing so they can't be freely changed
private static final int PRECOMP_BLOCKS = 8;
private static final int PRECOMP_TEETH = 4;
private static final int PRECOMP_SPACING = 8;
// private static final int PRECOMP_RANGE = PRECOMP_BLOCKS * PRECOMP_TEETH * PRECOMP_SPACING; // range == 256
private static final int PRECOMP_POINTS = 1 << (PRECOMP_TEETH - 1);
private static final int PRECOMP_MASK = PRECOMP_POINTS - 1;
private static final Object PRECOMP_LOCK = new Object();
private static PointPrecomp[] PRECOMP_BASE_WNAF = null;
private static int[] PRECOMP_BASE_COMB = null;
private static class PointAccum
{
int[] x = F.create();
int[] y = F.create();
int[] z = F.create();
int[] u = F.create();
int[] v = F.create();
}
private static class PointAffine
{
int[] x = F.create();
int[] y = F.create();
}
private static class PointExtended
{
int[] x = F.create();
int[] y = F.create();
int[] z = F.create();
int[] t = F.create();
}
private static class PointPrecomp
{
int[] ymx_h = F.create(); // (y - x)/2
int[] ypx_h = F.create(); // (y + x)/2
int[] xyd = F.create(); // x.y.d
}
private static class PointPrecompZ
{
int[] ymx_h = F.create(); // (y - x)/2
int[] ypx_h = F.create(); // (y + x)/2
int[] xyd = F.create(); // x.y.d
int[] z = F.create();
}
// Temp space to avoid allocations in point formulae.
private static class PointTemp
{
int[] r0 = F.create();
int[] r1 = F.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);
Nat256.mulAddTo(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 , byte phflag)
{
return ctx == null && phflag == 0x00
|| ctx != null && ctx.length < 256;
}
private static int checkPoint(int[] x, int[] y)
{
int[] t = F.create();
int[] u = F.create();
int[] v = F.create();
F.sqr(x, u);
F.sqr(y, v);
F.mul(u, v, t);
F.sub(v, u, v);
F.mul(t, C_d, t);
F.addOne(t);
F.sub(t, v, t);
F.normalize(t);
return F.isZero(t);
}
private static int checkPoint(int[] x, int[] y, int[] z)
{
int[] t = F.create();
int[] u = F.create();
int[] v = F.create();
int[] w = F.create();
F.sqr(x, u);
F.sqr(y, v);
F.sqr(z, w);
F.mul(u, v, t);
F.sub(v, u, v);
F.mul(v, w, v);
F.sqr(w, w);
F.mul(t, C_d, t);
F.add(t, w, t);
F.sub(t, v, t);
F.normalize(t);
return F.isZero(t);
}
private static boolean checkPointVar(byte[] p)
{
int[] t = new int[COORD_INTS];
decode32(p, 0, t, 0, COORD_INTS);
t[COORD_INTS - 1] &= 0x7FFFFFFF;
return !Nat256.gte(t, P);
}
private static boolean checkScalarVar(byte[] s, int[] n)
{
decodeScalar(s, 0, n);
return !Nat256.gte(n, L);
}
private static byte[] copy(byte[] buf, int off, int len)
{
byte[] result = new byte[len];
System.arraycopy(buf, off, result, 0, len);
return result;
}
private static Digest createDigest()
{
return new SHA512Digest();
}
public static Digest createPrehash()
{
return createDigest();
}
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, PointAffine r)
{
byte[] py = copy(p, pOff, POINT_BYTES);
if (!checkPointVar(py))
{
return false;
}
int x_0 = (py[POINT_BYTES - 1] & 0x80) >>> 7;
py[POINT_BYTES - 1] &= 0x7F;
F.decode(py, 0, r.y);
int[] u = F.create();
int[] v = F.create();
F.sqr(r.y, u);
F.mul(C_d, u, v);
F.subOne(u);
F.addOne(v);
if (!F.sqrtRatioVar(u, v, r.x))
{
return false;
}
F.normalize(r.x);
if (x_0 == 1 && F.isZeroVar(r.x))
{
return false;
}
if (negate ^ (x_0 != (r.x[0] & 1)))
{
F.negate(r.x, r.x);
}
return true;
}
private static void decodeScalar(byte[] k, int kOff, int[] n)
{
decode32(k, kOff, n, 0, SCALAR_INTS);
}
private static void dom2(Digest d, byte phflag, byte[] ctx)
{
if (ctx != null)
{
int n = DOM2_PREFIX.length;
byte[] t = new byte[n + 2 + ctx.length];
System.arraycopy(DOM2_PREFIX, 0, t, 0, n);
t[n] = phflag;
t[n + 1] = (byte)ctx.length;
System.arraycopy(ctx, 0, t, n + 2, ctx.length);
d.update(t, 0, t.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 int encodePoint(PointAccum p, byte[] r, int rOff)
{
int[] x = F.create();
int[] y = F.create();
F.inv(p.z, y);
F.mul(p.x, y, x);
F.mul(p.y, y, y);
F.normalize(x);
F.normalize(y);
int result = checkPoint(x, y);
F.encode(y, r, rOff);
r[rOff + POINT_BYTES - 1] |= ((x[0] & 1) << 7);
return result;
}
public static void generatePrivateKey(SecureRandom random, byte[] k)
{
random.nextBytes(k);
}
public static void generatePublicKey(byte[] sk, int skOff, byte[] pk, int pkOff)
{
Digest d = createDigest();
byte[] h = new byte[d.getDigestSize()];
d.update(sk, skOff, SECRET_KEY_SIZE);
d.doFinal(h, 0);
byte[] s = new byte[SCALAR_BYTES];
pruneScalar(h, 0, s);
scalarMultBaseEncoded(s, pk, pkOff);
}
private static int getWindow4(int[] x, int n)
{
int w = n >>> 3, b = (n & 7) << 2;
return (x[w] >>> b) & 15;
}
private static byte[] getWnafVar(int[] n, int width)
{
// assert 0 <= n[SCALAR_INTS - 1] && n[SCALAR_INTS - 1] <= L[SCALAR_INTS - 1];
// assert 2 <= width && width <= 8;
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[253];
final int lead = 32 - width;
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 | 1) << lead;
carry = digit >>> 31;
ws[(i << 4) + j] = (byte)(digit >> lead);
j += width;
}
}
// assert carry == 0;
return ws;
}
private static void implSign(Digest d, byte[] h, byte[] s, byte[] pk, int pkOff, byte[] ctx, byte phflag, byte[] m,
int mOff, int mLen, byte[] sig, int sigOff)
{
dom2(d, phflag, ctx);
d.update(h, SCALAR_BYTES, SCALAR_BYTES);
d.update(m, mOff, mLen);
d.doFinal(h, 0);
byte[] r = reduceScalar(h);
byte[] R = new byte[POINT_BYTES];
scalarMultBaseEncoded(r, R, 0);
dom2(d, phflag, ctx);
d.update(R, 0, POINT_BYTES);
d.update(pk, pkOff, POINT_BYTES);
d.update(m, mOff, mLen);
d.doFinal(h, 0);
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, phflag))
{
throw new IllegalArgumentException("ctx");
}
Digest d = createDigest();
byte[] h = new byte[d.getDigestSize()];
d.update(sk, skOff, SECRET_KEY_SIZE);
d.doFinal(h, 0);
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, phflag))
{
throw new IllegalArgumentException("ctx");
}
Digest d = createDigest();
byte[] h = new byte[d.getDigestSize()];
d.update(sk, skOff, SECRET_KEY_SIZE);
d.doFinal(h, 0);
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, phflag))
{
throw new IllegalArgumentException("ctx");
}
byte[] R = copy(sig, sigOff, POINT_BYTES);
byte[] S = copy(sig, sigOff + POINT_BYTES, SCALAR_BYTES);
if (!checkPointVar(R))
{
return false;
}
int[] nS = new int[SCALAR_INTS];
if (!checkScalarVar(S, nS))
{
return false;
}
PointAffine pA = new PointAffine();
if (!decodePointVar(pk, pkOff, true, pA))
{
return false;
}
Digest d = createDigest();
byte[] h = new byte[d.getDigestSize()];
dom2(d, phflag, ctx);
d.update(R, 0, POINT_BYTES);
d.update(pk, pkOff, POINT_BYTES);
d.update(m, mOff, mLen);
d.doFinal(h, 0);
byte[] k = reduceScalar(h);
int[] nA = new int[SCALAR_INTS];
decodeScalar(k, 0, nA);
PointAccum pR = new PointAccum();
scalarMultStrausVar(nS, nA, pA, pR);
byte[] check = new byte[POINT_BYTES];
return 0 != encodePoint(pR, check, 0) && Arrays.areEqual(check, R);
}
private static void invertDoubleZs(PointExtended[] points)
{
int count = points.length;
int[] cs = F.createTable(count);
int[] u = F.create();
F.copy(points[0].z, 0, u, 0);
F.copy(u, 0, cs, 0);
int i = 0;
while (++i < count)
{
F.mul(u, points[i].z, u);
F.copy(u, 0, cs, i * F.SIZE);
}
F.add(u, u, u);
F.invVar(u, u);
--i;
int[] t = F.create();
while (i > 0)
{
int j = i--;
F.copy(cs, i * F.SIZE, t, 0);
F.mul(t, u, t);
F.mul(u, points[j].z, u);
F.copy(t, 0, points[j].z, 0);
}
F.copy(u, 0, points[0].z, 0);
}
private static boolean isNeutralElementVar(int[] x, int[] y)
{
return F.isZeroVar(x) && F.isOneVar(y);
}
private static boolean isNeutralElementVar(int[] x, int[] y, int[] z)
{
return F.isZeroVar(x) && F.areEqualVar(y, z);
}
private static void pointAdd(PointExtended p, PointExtended q, PointExtended r, PointTemp t)
{
// p may ref the same point as r (or q), but q may not ref the same point as r.
// assert q != r;
int[] a = r.x;
int[] b = r.y;
int[] c = t.r0;
int[] d = t.r1;
int[] e = a;
int[] f = c;
int[] g = d;
int[] h = b;
F.apm(p.y, p.x, b, a);
F.apm(q.y, q.x, d, c);
F.mul(a, c, a);
F.mul(b, d, b);
F.mul(p.t, q.t, c);
F.mul(c, C_d2, c);
F.add(p.z, p.z, d);
F.mul(d, q.z, d);
F.apm(b, a, h, e);
F.apm(d, c, g, f);
F.mul(e, h, r.t);
F.mul(f, g, r.z);
F.mul(e, f, r.x);
F.mul(h, g, r.y);
}
private static void pointAdd(PointPrecomp p, PointAccum r, PointTemp t)
{
int[] a = r.x;
int[] b = r.y;
int[] c = t.r0;
int[] e = r.u;
int[] f = a;
int[] g = b;
int[] h = r.v;
F.apm(r.y, r.x, b, a);
F.mul(a, p.ymx_h, a);
F.mul(b, p.ypx_h, b);
F.mul(r.u, r.v, c);
F.mul(c, p.xyd, c);
F.apm(b, a, h, e);
F.apm(r.z, c, g, f);
F.mul(f, g, r.z);
F.mul(f, e, r.x);
F.mul(g, h, r.y);
}
private static void pointAdd(PointPrecompZ p, PointAccum r, PointTemp t)
{
int[] a = r.x;
int[] b = r.y;
int[] c = t.r0;
int[] d = r.z;
int[] e = r.u;
int[] f = a;
int[] g = b;
int[] h = r.v;
F.apm(r.y, r.x, b, a);
F.mul(a, p.ymx_h, a);
F.mul(b, p.ypx_h, b);
F.mul(r.u, r.v, c);
F.mul(c, p.xyd, c);
F.mul(r.z, p.z, d);
F.apm(b, a, h, e);
F.apm(d, c, g, f);
F.mul(f, g, r.z);
F.mul(f, e, r.x);
F.mul(g, h, r.y);
}
private static void pointAddVar(boolean negate, PointPrecomp p, PointAccum r, PointTemp t)
{
int[] a = r.x;
int[] b = r.y;
int[] c = t.r0;
int[] e = r.u;
int[] f = a;
int[] g = b;
int[] h = r.v;
int[] na, nb;
if (negate)
{
na = b; nb = a;
}
else
{
na = a; nb = b;
}
int[] nf = na, ng = nb;
F.apm(r.y, r.x, b, a);
F.mul(na, p.ymx_h, na);
F.mul(nb, p.ypx_h, nb);
F.mul(r.u, r.v, c);
F.mul(c, p.xyd, c);
F.apm(b, a, h, e);
F.apm(r.z, c, ng, nf);
F.mul(f, g, r.z);
F.mul(f, e, r.x);
F.mul(g, h, r.y);
}
private static void pointAddVar(boolean negate, PointPrecompZ p, PointAccum r, PointTemp t)
{
int[] a = r.x;
int[] b = r.y;
int[] c = t.r0;
int[] d = r.z;
int[] e = r.u;
int[] f = a;
int[] g = b;
int[] h = r.v;
int[] na, nb;
if (negate)
{
na = b; nb = a;
}
else
{
na = a; nb = b;
}
int[] nf = na, ng = nb;
F.apm(r.y, r.x, b, a);
F.mul(na, p.ymx_h, na);
F.mul(nb, p.ypx_h, nb);
F.mul(r.u, r.v, c);
F.mul(c, p.xyd, c);
F.mul(r.z, p.z, d);
F.apm(b, a, h, e);
F.apm(d, c, ng, nf);
F.mul(f, g, r.z);
F.mul(f, e, r.x);
F.mul(g, h, r.y);
}
private static void pointCopy(PointAccum p, PointExtended r)
{
F.copy(p.x, 0, r.x, 0);
F.copy(p.y, 0, r.y, 0);
F.copy(p.z, 0, r.z, 0);
F.mul(p.u, p.v, r.t);
}
private static void pointCopy(PointAffine p, PointExtended r)
{
F.copy(p.x, 0, r.x, 0);
F.copy(p.y, 0, r.y, 0);
F.one(r.z);
F.mul(p.x, p.y, r.t);
}
private static void pointCopy(PointExtended p, PointPrecompZ r)
{
// To avoid halving x and y, we double t and z instead.
F.apm(p.y, p.x, r.ypx_h, r.ymx_h);
F.mul(p.t, C_d2, r.xyd);
F.add(p.z, p.z, r.z);
}
private static void pointDouble(PointAccum r)
{
int[] a = r.x;
int[] b = r.y;
int[] c = r.z;
int[] e = r.u;
int[] f = a;
int[] g = b;
int[] h = r.v;
F.add(r.x, r.y, e);
F.sqr(r.x, a);
F.sqr(r.y, b);
F.sqr(r.z, c);
F.add(c, c, c);
F.apm(a, b, h, g);
F.sqr(e, e);
F.sub(h, e, e);
F.add(c, g, f);
F.carry(f); // Probably unnecessary, but keep until better bounds analysis available
F.mul(f, g, r.z);
F.mul(f, e, r.x);
F.mul(g, h, r.y);
}
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 * 3 * F.SIZE;
for (int i = 0; i < PRECOMP_POINTS; ++i)
{
int cond = ((i ^ index) - 1) >> 31;
F.cmov(cond, PRECOMP_BASE_COMB, off, p.ymx_h, 0); off += F.SIZE;
F.cmov(cond, PRECOMP_BASE_COMB, off, p.ypx_h, 0); off += F.SIZE;
F.cmov(cond, PRECOMP_BASE_COMB, off, p.xyd, 0); off += F.SIZE;
}
}
private static void pointLookupZ(int[] x, int n, int[] table, PointPrecompZ r)
{
// TODO This method is currently hard-coded to 4-bit windows and 8 precomputed points
int w = getWindow4(x, n);
int sign = (w >>> (4 - 1)) ^ 1;
int abs = (w ^ -sign) & 7;
// assert sign == 0 || sign == 1;
// assert 0 <= abs && abs < 8;
for (int i = 0, off = 0; i < 8; ++i)
{
int cond = ((i ^ abs) - 1) >> 31;
F.cmov(cond, table, off, r.ymx_h, 0); off += F.SIZE;
F.cmov(cond, table, off, r.ypx_h, 0); off += F.SIZE;
F.cmov(cond, table, off, r.xyd , 0); off += F.SIZE;
F.cmov(cond, table, off, r.z , 0); off += F.SIZE;
}
F.cswap(sign, r.ymx_h, r.ypx_h);
F.cnegate(sign, r.xyd);
}
private static void pointPrecompute(PointAffine p, PointExtended[] points, int count, PointTemp t)
{
// assert count > 0;
pointCopy(p, points[0] = new PointExtended());
PointExtended d = new PointExtended();
pointAdd(points[0], points[0], d, t);
for (int i = 1; i < count; ++i)
{
pointAdd(points[i - 1], d, points[i] = new PointExtended(), t);
}
}
private static int[] pointPrecomputeZ(PointAffine p, int count, PointTemp t)
{
// assert count > 0;
PointExtended q = new PointExtended();
pointCopy(p, q);
PointExtended d = new PointExtended();
pointAdd(q, q, d, t);
PointPrecompZ r = new PointPrecompZ();
int[] table = F.createTable(count * 4);
int off = 0;
int i = 0;
for (;;)
{
pointCopy(q, r);
F.copy(r.ymx_h, 0, table, off); off += F.SIZE;
F.copy(r.ypx_h, 0, table, off); off += F.SIZE;
F.copy(r.xyd , 0, table, off); off += F.SIZE;
F.copy(r.z , 0, table, off); off += F.SIZE;
if (++i == count)
{
break;
}
pointAdd(q, d, q, t);
}
return table;
}
private static void pointPrecomputeZ(PointAffine p, PointPrecompZ[] points, int count, PointTemp t)
{
// assert count > 0;
PointExtended q = new PointExtended();
pointCopy(p, q);
PointExtended d = new PointExtended();
pointAdd(q, q, d, t);
int i = 0;
for (;;)
{
PointPrecompZ r = points[i] = new PointPrecompZ();
pointCopy(q, r);
if (++i == count)
{
break;
}
pointAdd(q, d, q, t);
}
}
private static void pointSetNeutral(PointAccum p)
{
F.zero(p.x);
F.one(p.y);
F.one(p.z);
F.zero(p.u);
F.one(p.v);
}
public static void precompute()
{
synchronized (PRECOMP_LOCK)
{
if (PRECOMP_BASE_WNAF != null && PRECOMP_BASE_COMB != null)
{
return;
}
int wnafPoints = 1 << (WNAF_WIDTH_BASE - 2);
int combPoints = PRECOMP_BLOCKS * PRECOMP_POINTS;
int totalPoints = wnafPoints + combPoints;
PointExtended[] points = new PointExtended[totalPoints];
PointTemp t = new PointTemp();
PointAffine b = new PointAffine();
F.copy(B_x, 0, b.x, 0);
F.copy(B_y, 0, b.y, 0);
pointPrecompute(b, points, wnafPoints, t);
PointAccum p = new PointAccum();
F.copy(B_x, 0, p.x, 0);
F.copy(B_y, 0, p.y, 0);
F.one(p.z);
F.copy(p.x, 0, p.u, 0);
F.copy(p.y, 0, p.v, 0);
int pointsIndex = wnafPoints;
PointExtended[] toothPowers = new PointExtended[PRECOMP_TEETH];
for (int tooth = 0; tooth < PRECOMP_TEETH; ++tooth)
{
toothPowers[tooth] = new PointExtended();
}
PointExtended u = new PointExtended();
for (int block = 0; block < PRECOMP_BLOCKS; ++block)
{
PointExtended sum = points[pointsIndex++] = new PointExtended();
for (int tooth = 0; tooth < PRECOMP_TEETH; ++tooth)
{
if (tooth == 0)
{
pointCopy(p, sum);
}
else
{
pointCopy(p, u);
pointAdd(sum, u, sum, t);
}
pointDouble(p);
pointCopy(p, toothPowers[tooth]);
if (block + tooth != PRECOMP_BLOCKS + PRECOMP_TEETH - 2)
{
for (int spacing = 1; spacing < PRECOMP_SPACING; ++spacing)
{
pointDouble(p);
}
}
}
F.negate(sum.x, sum.x);
F.negate(sum.t, sum.t);
for (int tooth = 0; tooth < (PRECOMP_TEETH - 1); ++tooth)
{
int size = 1 << tooth;
for (int j = 0; j < size; ++j, ++pointsIndex)
{
points[pointsIndex] = new PointExtended();
pointAdd(points[pointsIndex - size], toothPowers[tooth], points[pointsIndex], t);
}
}
}
// assert pointsIndex == totalPoints;
// Set each z coordinate to 1/(2.z) to avoid calculating halves of x, y in the following code
invertDoubleZs(points);
PRECOMP_BASE_WNAF = new PointPrecomp[wnafPoints];
for (int i = 0; i < wnafPoints; ++i)
{
PointExtended q = points[i];
PointPrecomp r = PRECOMP_BASE_WNAF[i] = new PointPrecomp();
// Calculate x/2 and y/2 (because the z value holds half the inverse; see above).
F.mul(q.x, q.z, q.x);
F.mul(q.y, q.z, q.y);
// y/2 +/- x/2
F.apm(q.y, q.x, r.ypx_h, r.ymx_h);
// x/2 * y/2 * (4.d) == x.y.d
F.mul(q.x, q.y, r.xyd);
F.mul(r.xyd, C_d4, r.xyd);
F.normalize(r.ymx_h);
F.normalize(r.ypx_h);
F.normalize(r.xyd);
}
PRECOMP_BASE_COMB = F.createTable(combPoints * 3);
PointPrecomp s = new PointPrecomp();
int off = 0;
for (int i = wnafPoints; i < totalPoints; ++i)
{
PointExtended q = points[i];
// Calculate x/2 and y/2 (because the z value holds half the inverse; see above).
F.mul(q.x, q.z, q.x);
F.mul(q.y, q.z, q.y);
// y/2 +/- x/2
F.apm(q.y, q.x, s.ypx_h, s.ymx_h);
// x/2 * y/2 * (4.d) == x.y.d
F.mul(q.x, q.y, s.xyd);
F.mul(s.xyd, C_d4, s.xyd);
F.normalize(s.ymx_h);
F.normalize(s.ypx_h);
F.normalize(s.xyd);
F.copy(s.ymx_h, 0, PRECOMP_BASE_COMB, off); off += F.SIZE;
F.copy(s.ypx_h, 0, PRECOMP_BASE_COMB, off); off += F.SIZE;
F.copy(s.xyd , 0, PRECOMP_BASE_COMB, off); off += F.SIZE;
}
// assert off == precompBaseComb.length;
}
}
private static void pruneScalar(byte[] n, int nOff, byte[] r)
{
System.arraycopy(n, nOff, r, 0, SCALAR_BYTES);
r[0] &= 0xF8;
r[SCALAR_BYTES - 1] &= 0x7F;
r[SCALAR_BYTES - 1] |= 0x40;
}
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 = n[63] & M08L; // x18:08/--
long t;
// x18 += (x17 >> 28); x17 &= M28L;
x09 -= x18 * L0; // x09:34/28
x10 -= x18 * L1; // x10:33/30
x11 -= x18 * L2; // x11:35/28
x12 -= x18 * L3; // x12:32/31
x13 -= x18 * L4; // x13:28/21
x17 += (x16 >> 28); x16 &= M28L; // x17:28/--, x16:28/--
x08 -= x17 * L0; // x08:54/32
x09 -= x17 * L1; // x09:52/51
x10 -= x17 * L2; // x10:55/34
x11 -= x17 * L3; // x11:51/36
x12 -= x17 * L4; // x12:41/--
// x16 += (x15 >> 28); x15 &= M28L;
x07 -= x16 * L0; // x07:54/28
x08 -= x16 * L1; // x08:54/53
x09 -= x16 * L2; // x09:55/53
x10 -= x16 * L3; // x10:55/52
x11 -= x16 * L4; // x11:51/41
x15 += (x14 >> 28); x14 &= M28L; // x15:28/--, x14:28/--
x06 -= x15 * L0; // x06:54/32
x07 -= x15 * L1; // x07:54/53
x08 -= x15 * L2; // x08:56/--
x09 -= x15 * L3; // x09:55/54
x10 -= x15 * L4; // x10:55/53
// x14 += (x13 >> 28); x13 &= M28L;
x05 -= x14 * L0; // x05:54/28
x06 -= x14 * L1; // x06:54/53
x07 -= x14 * L2; // x07:56/--
x08 -= x14 * L3; // x08:56/51
x09 -= x14 * L4; // x09:56/--
x13 += (x12 >> 28); x12 &= M28L; // x13:28/22, x12:28/--
x04 -= x13 * L0; // x04:54/49
x05 -= x13 * L1; // x05:54/53
x06 -= x13 * L2; // x06:56/--
x07 -= x13 * L3; // x07:56/52
x08 -= x13 * L4; // x08:56/52
x12 += (x11 >> 28); x11 &= M28L; // x12:28/24, x11:28/--
x03 -= x12 * L0; // x03:54/49
x04 -= x12 * L1; // x04:54/51
x05 -= x12 * L2; // x05:56/--
x06 -= x12 * L3; // x06:56/52
x07 -= x12 * L4; // x07:56/53
x11 += (x10 >> 28); x10 &= M28L; // x11:29/--, x10:28/--
x02 -= x11 * L0; // x02:55/32
x03 -= x11 * L1; // x03:55/--
x04 -= x11 * L2; // x04:56/55
x05 -= x11 * L3; // x05:56/52
x06 -= x11 * L4; // x06:56/53
x10 += (x09 >> 28); x09 &= M28L; // x10:29/--, x09:28/--
x01 -= x10 * L0; // x01:55/28
x02 -= x10 * L1; // x02:55/54
x03 -= x10 * L2; // x03:56/55
x04 -= x10 * L3; // x04:57/--
x05 -= x10 * L4; // x05:56/53
x08 += (x07 >> 28); x07 &= M28L; // x08:56/53, x07:28/--
x09 += (x08 >> 28); x08 &= M28L; // x09:29/25, x08:28/--
t = x08 >>> 27;
x09 += t; // x09:29/26
x00 -= x09 * L0; // x00:55/53
x01 -= x09 * L1; // x01:55/54
x02 -= x09 * L2; // x02:57/--
x03 -= x09 * L3; // x03:57/--
x04 -= x09 * L4; // x04:57/42
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;
x09 -= t;
// assert x09 == 0L || x09 == -1L;
x00 += x09 & L0;
x01 += x09 & L1;
x02 += x09 & L2;
x03 += x09 & L3;
x04 += x09 & L4;
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;
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);
encode32((int)x08, r, 28);
return r;
}
private static void scalarMult(byte[] k, PointAffine p, PointAccum r)
{
int[] n = new int[SCALAR_INTS];
decodeScalar(k, 0, n);
// Recode the scalar into signed-digit form
{
//int c1 =
Nat.cadd(SCALAR_INTS, ~n[0] & 1, n, L, n); //assert c1 == 0;
//int c2 =
Nat.shiftDownBit(SCALAR_INTS, n, 1); //assert c2 == (1 << 31);
}
PointPrecompZ q = new PointPrecompZ();
PointTemp t = new PointTemp();
int[] table = pointPrecomputeZ(p, 8, t);
pointSetNeutral(r);
int w = 63;
for (;;)
{
pointLookupZ(n, w, table, q);
pointAdd(q, r, t);
if (--w < 0)
{
break;
}
for (int i = 0; i < 4; ++i)
{
pointDouble(r);
}
}
}
private static void scalarMultBase(byte[] k, PointAccum r)
{
// Equivalent (but much slower)
// PointAffine p = new PointAffine();
// F.copy(B_x, 0, p.x, 0);
// F.copy(B_y, 0, p.y, 0);
// scalarMult(k, p, r);
precompute();
int[] n = new int[SCALAR_INTS];
decodeScalar(k, 0, n);
// Recode the scalar into signed-digit form, then group comb bits in each block
{
//int c1 =
Nat.cadd(SCALAR_INTS, ~n[0] & 1, n, L, n); //assert c1 == 0;
//int c2 =
Nat.shiftDownBit(SCALAR_INTS, n, 1); //assert c2 == (1 << 31);
/*
* Because we are using 4 teeth and 8 spacing, each limb of n corresponds to one of the 8 blocks.
* Therefore we can efficiently group the bits for each comb position using a (double) shuffle.
*/
for (int i = 0; i < SCALAR_INTS; ++i)
{
n[i] = Interleave.shuffle2(n[i]);
}
}
PointPrecomp p = new PointPrecomp();
PointTemp t = new PointTemp();
pointSetNeutral(r);
int resultSign = 0;
int cOff = (PRECOMP_SPACING - 1) * PRECOMP_TEETH;
for (;;)
{
for (int b = 0; b < PRECOMP_BLOCKS; ++b)
{
int w = n[b] >>> cOff;
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);
F.cnegate(resultSign ^ sign, r.x);
F.cnegate(resultSign ^ sign, r.u);
resultSign = sign;
pointAdd(p, r, t);
}
if ((cOff -= PRECOMP_TEETH) < 0)
{
break;
}
pointDouble(r);
}
F.cnegate(resultSign, r.x);
F.cnegate(resultSign, r.u);
}
private static void scalarMultBaseEncoded(byte[] k, byte[] r, int rOff)
{
PointAccum p = new PointAccum();
scalarMultBase(k, p);
if (0 == encodePoint(p, r, rOff))
{
throw new IllegalStateException();
}
}
/**
* NOTE: Only for use by X25519
*/
public static void scalarMultBaseYZ(X25519.Friend friend, byte[] k, int kOff, int[] y, int[] z)
{
if (null == friend)
{
throw new NullPointerException("This method is only for use by X25519");
}
byte[] n = new byte[SCALAR_BYTES];
pruneScalar(k, kOff, n);
PointAccum p = new PointAccum();
scalarMultBase(n, p);
if (0 == checkPoint(p.x, p.y, p.z))
{
throw new IllegalStateException();
}
F.copy(p.y, 0, y, 0);
F.copy(p.z, 0, z, 0);
}
private static void scalarMultOrderVar(PointAffine p, PointAccum r)
{
byte[] ws_p = getWnafVar(L, WNAF_WIDTH);
int count = 1 << (WNAF_WIDTH - 2);
PointPrecompZ[] tp = new PointPrecompZ[count];
PointTemp t = new PointTemp();
pointPrecomputeZ(p, tp, count, t);
pointSetNeutral(r);
for (int bit = 252;;)
{
int wp = ws_p[bit];
if (wp != 0)
{
int sign = wp >> 31;
int index = (wp ^ sign) >>> 1;
pointAddVar((sign != 0), tp[index], r, t);
}
if (--bit < 0)
{
break;
}
pointDouble(r);
}
}
private static void scalarMultStrausVar(int[] nb, int[] np, PointAffine p, PointAccum r)
{
precompute();
byte[] ws_b = getWnafVar(nb, WNAF_WIDTH_BASE);
byte[] ws_p = getWnafVar(np, WNAF_WIDTH);
int count = 1 << (WNAF_WIDTH - 2);
PointPrecompZ[] tp = new PointPrecompZ[count];
PointTemp t = new PointTemp();
pointPrecomputeZ(p, tp, count, t);
pointSetNeutral(r);
for (int bit = 252;;)
{
int wb = ws_b[bit];
if (wb != 0)
{
int sign = wb >> 31;
int index = (wb ^ sign) >>> 1;
pointAddVar(sign != 0, PRECOMP_BASE_WNAF[index], r, t);
}
int wp = ws_p[bit];
if (wp != 0)
{
int sign = wp >> 31;
int index = (wp ^ sign) >>> 1;
pointAddVar(sign != 0, tp[index], r, t);
}
if (--bit < 0)
{
break;
}
pointDouble(r);
}
}
public static void sign(byte[] sk, int skOff, byte[] m, int mOff, int mLen, byte[] sig, int sigOff)
{
byte[] ctx = null;
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[] m, int mOff, int mLen, byte[] sig, int sigOff)
{
byte[] ctx = null;
byte phflag = 0x00;
implSign(sk, skOff, pk, pkOff, ctx, phflag, m, mOff, mLen, sig, sigOff);
}
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, Digest ph, byte[] sig, int sigOff)
{
byte[] m = new byte[PREHASH_SIZE];
if (PREHASH_SIZE != ph.doFinal(m, 0))
{
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, Digest ph, byte[] sig, int sigOff)
{
byte[] m = new byte[PREHASH_SIZE];
if (PREHASH_SIZE != ph.doFinal(m, 0))
{
throw new IllegalArgumentException("ph");
}
byte phflag = 0x01;
implSign(sk, skOff, pk, pkOff, ctx, phflag, m, 0, m.length, sig, sigOff);
}
public static boolean validatePublicKeyFull(byte[] pk, int pkOff)
{
PointAffine p = new PointAffine();
if (!decodePointVar(pk, pkOff, false, p))
{
return false;
}
F.normalize(p.x);
F.normalize(p.y);
if (isNeutralElementVar(p.x, p.y))
{
return false;
}
PointAccum r = new PointAccum();
scalarMultOrderVar(p, r);
F.normalize(r.x);
F.normalize(r.y);
F.normalize(r.z);
return isNeutralElementVar(r.x, r.y, r.z);
}
public static boolean validatePublicKeyPartial(byte[] pk, int pkOff)
{
PointAffine p = new PointAffine();
return decodePointVar(pk, pkOff, false, p);
}
public static boolean verify(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] m, int mOff, int mLen)
{
byte[] ctx = null;
byte phflag = 0x00;
return implVerify(sig, sigOff, pk, pkOff, ctx, phflag, m, mOff, mLen);
}
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, Digest ph)
{
byte[] m = new byte[PREHASH_SIZE];
if (PREHASH_SIZE != ph.doFinal(m, 0))
{
throw new IllegalArgumentException("ph");
}
byte phflag = 0x01;
return implVerify(sig, sigOff, pk, pkOff, ctx, phflag, m, 0, m.length);
}
}