org.bouncycastle.math.ec.rfc8032.Ed448 Maven / Gradle / Ivy
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The Bouncy Castle Crypto package is a Java implementation of cryptographic algorithms. This jar contains JCE provider and lightweight API for the Bouncy Castle Cryptography APIs for JDK 1.5 to JDK 1.8.
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;
public abstract class Ed448
{
// x^2 + y^2 == 1 - 39081 * x^2 * y^2
public static final class Algorithm
{
public static final int Ed448 = 0;
public static final int Ed448ph = 1;
}
private static class F extends X448Field {};
private static final long M26L = 0x03FFFFFFL;
private static final long M28L = 0x0FFFFFFFL;
private static final long M32L = 0xFFFFFFFFL;
private static final int COORD_INTS = 14;
private static final int POINT_BYTES = COORD_INTS * 4 + 1;
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;
// "SigEd448"
private static final byte[] DOM4_PREFIX = new byte[]{ 0x53, 0x69, 0x67, 0x45, 0x64, 0x34, 0x34, 0x38 };
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;
// scalarMultBase supports varying blocks, teeth, spacing so long as their product is in range [449, 479]
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_RANGE = PRECOMP_BLOCKS * PRECOMP_TEETH * PRECOMP_SPACING; // 448 < range < 480
private static final int PRECOMP_POINTS = 1 << (PRECOMP_TEETH - 1);
private static final int PRECOMP_MASK = PRECOMP_POINTS - 1;
private static final 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 = F.create();
int[] y = F.create();
int[] z = F.create();
}
private static class PointPrecomp
{
int[] x = F.create();
int[] y = 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);
Nat.mulAddTo(SCALAR_INTS, 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 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.add(u, v, u);
F.mul(t, -C_d, t);
F.subOne(t);
F.add(t, u, 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.add(u, v, u);
F.mul(u, w, u);
F.sqr(w, w);
F.mul(t, -C_d, t);
F.sub(t, w, t);
F.add(t, u, t);
F.normalize(t);
return F.isZero(t);
}
private static boolean checkPointVar(byte[] p)
{
if ((p[POINT_BYTES - 1] & 0x7F) != 0x00)
{
return false;
}
int[] t = new int[COORD_INTS];
decode32(p, 0, t, 0, COORD_INTS);
return !Nat.gte(COORD_INTS, t, P);
}
private static boolean checkScalarVar(byte[] s, int[] n)
{
if (s[SCALAR_BYTES - 1] != 0x00)
{
return false;
}
decodeScalar(s, 0, n);
return !Nat.gte(SCALAR_INTS, 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;
}
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 = 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(u, -C_d, v);
F.negate(u, u);
F.addOne(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);
}
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 phflag, byte[] ctx)
{
int n = DOM4_PREFIX.length;
byte[] t = new byte[n + 2 + ctx.length];
System.arraycopy(DOM4_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(PointExt 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] = (byte)((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)
{
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 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[447];
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(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 = 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;
}
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[] nA = new int[SCALAR_INTS];
decodeScalar(k, 0, nA);
PointExt pR = new PointExt();
scalarMultStrausVar(nS, nA, pA, pR);
byte[] check = new byte[POINT_BYTES];
return 0 != encodePoint(pR, check, 0) && Arrays.areEqual(check, R);
}
private static boolean isNeutralElementVar(int[] x, int[] y, int[] z)
{
return F.isZeroVar(x) && F.areEqualVar(y, z);
}
private static void pointAdd(PointExt p, PointExt r)
{
int[] a = F.create();
int[] b = F.create();
int[] c = F.create();
int[] d = F.create();
int[] e = F.create();
int[] f = F.create();
int[] g = F.create();
int[] h = F.create();
F.mul(p.z, r.z, a);
F.sqr(a, b);
F.mul(p.x, r.x, c);
F.mul(p.y, r.y, d);
F.mul(c, d, e);
F.mul(e, -C_d, e);
// F.apm(b, e, f, g);
F.add(b, e, f);
F.sub(b, e, g);
F.add(p.x, p.y, b);
F.add(r.x, r.y, e);
F.mul(b, e, h);
// F.apm(d, c, b, e);
F.add(d, c, b);
F.sub(d, c, e);
F.carry(b);
F.sub(h, b, h);
F.mul(h, a, h);
F.mul(e, a, e);
F.mul(f, h, r.x);
F.mul(e, g, r.y);
F.mul(f, g, r.z);
}
private static void pointAddVar(boolean negate, PointExt p, PointExt r)
{
int[] a = F.create();
int[] b = F.create();
int[] c = F.create();
int[] d = F.create();
int[] e = F.create();
int[] f = F.create();
int[] g = F.create();
int[] h = F.create();
int[] nb, ne, nf, ng;
if (negate)
{
nb = e; ne = b; nf = g; ng = f;
F.sub(p.y, p.x, h);
}
else
{
nb = b; ne = e; nf = f; ng = g;
F.add(p.y, p.x, h);
}
F.mul(p.z, r.z, a);
F.sqr(a, b);
F.mul(p.x, r.x, c);
F.mul(p.y, r.y, d);
F.mul(c, d, e);
F.mul(e, -C_d, e);
// F.apm(b, e, f, g);
F.add(b, e, nf);
F.sub(b, e, ng);
F.add(r.x, r.y, e);
F.mul(h, e, h);
// F.apm(d, c, b, e);
F.add(d, c, nb);
F.sub(d, c, ne);
F.carry(nb);
F.sub(h, b, h);
F.mul(h, a, h);
F.mul(e, a, e);
F.mul(f, h, r.x);
F.mul(e, g, r.y);
F.mul(f, g, r.z);
}
private static void pointAddPrecomp(PointPrecomp p, PointExt r)
{
int[] b = F.create();
int[] c = F.create();
int[] d = F.create();
int[] e = F.create();
int[] f = F.create();
int[] g = F.create();
int[] h = F.create();
F.sqr(r.z, b);
F.mul(p.x, r.x, c);
F.mul(p.y, r.y, d);
F.mul(c, d, e);
F.mul(e, -C_d, e);
// F.apm(b, e, f, g);
F.add(b, e, f);
F.sub(b, e, g);
F.add(p.x, p.y, b);
F.add(r.x, r.y, e);
F.mul(b, e, h);
// F.apm(d, c, b, e);
F.add(d, c, b);
F.sub(d, c, e);
F.carry(b);
F.sub(h, b, h);
F.mul(h, r.z, h);
F.mul(e, r.z, e);
F.mul(f, h, r.x);
F.mul(e, g, r.y);
F.mul(f, g, r.z);
}
private static PointExt pointCopy(PointExt p)
{
PointExt r = new PointExt();
pointCopy(p, r);
return r;
}
private static void pointCopy(PointExt p, PointExt 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);
}
private static void pointDouble(PointExt r)
{
int[] b = F.create();
int[] c = F.create();
int[] d = F.create();
int[] e = F.create();
int[] h = F.create();
int[] j = F.create();
F.add(r.x, r.y, b);
F.sqr(b, b);
F.sqr(r.x, c);
F.sqr(r.y, d);
F.add(c, d, e);
F.carry(e);
F.sqr(r.z, h);
F.add(h, h, h);
F.carry(h);
F.sub(e, h, j);
F.sub(b, e, b);
F.sub(c, d, c);
F.mul(b, j, r.x);
F.mul(e, c, r.y);
F.mul(e, j, r.z);
}
private static void pointExtendXY(PointExt p)
{
F.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 * F.SIZE;
for (int i = 0; i < PRECOMP_POINTS; ++i)
{
int cond = ((i ^ index) - 1) >> 31;
F.cmov(cond, precompBase, off, p.x, 0); off += F.SIZE;
F.cmov(cond, precompBase, off, p.y, 0); off += F.SIZE;
}
}
private static void pointLookup(int[] x, int n, int[] table, PointExt r)
{
// TODO This method is currently hardcoded 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.x, 0); off += F.SIZE;
F.cmov(cond, table, off, r.y, 0); off += F.SIZE;
F.cmov(cond, table, off, r.z, 0); off += F.SIZE;
}
F.cnegate(sign, r.x);
}
private static void pointLookup15(int[] table, PointExt r)
{
int off = F.SIZE * 3 * 7;
F.copy(table, off, r.x, 0); off += F.SIZE;
F.copy(table, off, r.y, 0); off += F.SIZE;
F.copy(table, off, r.z, 0);
}
private static int[] pointPrecompute(PointExt p, int count)
{
// assert count > 0;
PointExt q = pointCopy(p);
PointExt d = pointCopy(q);
pointDouble(d);
int[] table = F.createTable(count * 3);
int off = 0;
int i = 0;
for (;;)
{
F.copy(q.x, 0, table, off); off += F.SIZE;
F.copy(q.y, 0, table, off); off += F.SIZE;
F.copy(q.z, 0, table, off); off += F.SIZE;
if (++i == count)
{
break;
}
pointAdd(d, q);
}
return table;
}
private static PointExt[] pointPrecomputeVar(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)
{
F.zero(p.x);
F.one(p.y);
F.one(p.z);
}
public static void precompute()
{
synchronized (precompLock)
{
if (precompBase != null)
{
return;
}
// assert PRECOMP_RANGE > 448;
// assert PRECOMP_RANGE < 480;
PointExt p = new PointExt();
F.copy(B_x, 0, p.x, 0);
F.copy(B_y, 0, p.y, 0);
pointExtendXY(p);
precompBaseTable = pointPrecomputeVar(p, 1 << (WNAF_WIDTH_BASE - 2));
precompBase = F.createTable(PRECOMP_BLOCKS * PRECOMP_POINTS * 2);
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;
int[] cs = F.createTable(PRECOMP_POINTS);
// TODO[ed448] A single batch inversion across all blocks?
{
int[] u = F.create();
F.copy(points[0].z, 0, u, 0);
F.copy(u, 0, cs, 0);
int i = 0;
while (++i < PRECOMP_POINTS)
{
F.mul(u, points[i].z, u);
F.copy(u, 0, cs, i * F.SIZE);
}
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.copy(t, 0, cs, j * F.SIZE);
F.mul(u, points[j].z, u);
}
F.copy(u, 0, cs, 0);
}
for (int i = 0; i < PRECOMP_POINTS; ++i)
{
PointExt q = points[i];
// F.invVar(q.z, q.z);
F.copy(cs, i * F.SIZE, q.z, 0);
F.mul(q.x, q.z, q.x);
F.mul(q.y, q.z, q.y);
// F.normalize(q.x);
// F.normalize(q.y);
F.copy(q.x, 0, precompBase, off); off += F.SIZE;
F.copy(q.y, 0, precompBase, off); off += F.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 scalarMult(byte[] k, PointExt p, PointExt 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);
//int c2 =
Nat.shiftDownBit(SCALAR_INTS, n, c1); //assert c2 == (1 << 31);
// NOTE: Bit 448 is implicitly set after the signed-digit recoding
}
int[] table = pointPrecompute(p, 8);
PointExt q = new PointExt();
// Replace first 4 doublings (2^4 * P) with 1 addition (P + 15 * P)
pointLookup15(table, r);
pointAdd(p, r);
int w = 111;
for (;;)
{
pointLookup(n, w, table, q);
pointAdd(q, r);
if (--w < 0)
{
break;
}
for (int i = 0; i < 4; ++i)
{
pointDouble(r);
}
}
}
private static void scalarMultBase(byte[] k, PointExt r)
{
// Equivalent (but much slower)
// PointExt p = new PointExt();
// F.copy(B_x, 0, p.x, 0);
// F.copy(B_y, 0, p.y, 0);
// pointExtendXY(p);
// scalarMult(k, p, r);
precompute();
int[] n = new int[SCALAR_INTS + 1];
decodeScalar(k, 0, n);
// Recode the scalar into signed-digit form
{
n[SCALAR_INTS] = (1 << (PRECOMP_RANGE - 448))
+ Nat.cadd(SCALAR_INTS, ~n[0] & 1, n, L, n);
//int c =
Nat.shiftDownBit(n.length, n, 0);
//assert c == (1 << 31);
}
PointPrecomp p = new PointPrecomp();
pointSetNeutral(r);
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);
F.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);
if (0 == encodePoint(p, r, rOff))
{
throw new IllegalStateException();
}
}
/**
* 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);
if (0 == checkPoint(p.x, p.y, p.z))
{
throw new IllegalStateException();
}
F.copy(p.x, 0, x, 0);
F.copy(p.y, 0, y, 0);
}
private static void scalarMultOrderVar(PointExt p, PointExt r)
{
final int width = 5;
byte[] ws_p = getWnafVar(L, width);
PointExt[] tp = pointPrecomputeVar(p, 1 << (width - 2));
pointSetNeutral(r);
for (int bit = 446;;)
{
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);
}
}
private static void scalarMultStrausVar(int[] nb, int[] np, PointExt p, PointExt r)
{
precompute();
final int width = 5;
byte[] ws_b = getWnafVar(nb, WNAF_WIDTH_BASE);
byte[] ws_p = getWnafVar(np, width);
PointExt[] tp = pointPrecomputeVar(p, 1 << (width - 2));
pointSetNeutral(r);
for (int bit = 446;;)
{
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 validatePublicKeyFull(byte[] pk, int pkOff)
{
PointExt p = new PointExt();
if (!decodePointVar(pk, pkOff, false, p))
{
return false;
}
F.normalize(p.x);
F.normalize(p.y);
F.normalize(p.z);
if (isNeutralElementVar(p.x, p.y, p.z))
{
return false;
}
PointExt r = new PointExt();
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)
{
PointExt p = new PointExt();
return decodePointVar(pk, pkOff, false, p);
}
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);
}
}