/* Ported from C to Java by Dmitry Skiba [sahn0], 23/02/08.
* Original: http://cds.xs4all.nl:8081/ecdh/
*/
/* Generic 64-bit integer implementation of Curve25519 ECDH
* Written by Matthijs van Duin, 200608242056
* Public domain.
*
* Based on work by Daniel J Bernstein, http://cr.yp.to/ecdh.html
*/
package djb;
public class Curve25519 {
/* key size */
public static final int KEY_SIZE = 32;
/* 0 */
public static final byte[] ZERO = {
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
};
/* the prime 2^255-19 */
public static final byte[] PRIME = {
(byte)237, (byte)255, (byte)255, (byte)255,
(byte)255, (byte)255, (byte)255, (byte)255,
(byte)255, (byte)255, (byte)255, (byte)255,
(byte)255, (byte)255, (byte)255, (byte)255,
(byte)255, (byte)255, (byte)255, (byte)255,
(byte)255, (byte)255, (byte)255, (byte)255,
(byte)255, (byte)255, (byte)255, (byte)255,
(byte)255, (byte)255, (byte)255, (byte)127
};
/* group order (a prime near 2^252+2^124) */
public static final byte[] ORDER = {
(byte)237, (byte)211, (byte)245, (byte)92,
(byte)26, (byte)99, (byte)18, (byte)88,
(byte)214, (byte)156, (byte)247, (byte)162,
(byte)222, (byte)249, (byte)222, (byte)20,
(byte)0, (byte)0, (byte)0, (byte)0,
(byte)0, (byte)0, (byte)0, (byte)0,
(byte)0, (byte)0, (byte)0, (byte)0,
(byte)0, (byte)0, (byte)0, (byte)16
};
/********* KEY AGREEMENT *********/
/* Private key clamping
* k [out] your private key for key agreement
* k [in] 32 random bytes
*/
public static final void clamp(byte[] k) {
k[31] &= 0x7F;
k[31] |= 0x40;
k[ 0] &= 0xF8;
}
/* Key-pair generation
* P [out] your public key
* s [out] your private key for signing
* k [out] your private key for key agreement
* k [in] 32 random bytes
* s may be NULL if you don't care
*
* WARNING: if s is not NULL, this function has data-dependent timing */
public static final void keygen(byte[] P, byte[] s, byte[] k) {
clamp(k);
core(P, s, k, null);
}
/* Key agreement
* Z [out] shared secret (needs hashing before use)
* k [in] your private key for key agreement
* P [in] peer's public key
*/
public static final void curve(byte[] Z, byte[] k, byte[] P) {
core(Z, null, k, P);
}
/********* DIGITAL SIGNATURES *********/
/* deterministic EC-KCDSA
*
* s is the private key for signing
* P is the corresponding public key
* Z is the context data (signer public key or certificate, etc)
*
* signing:
*
* m = hash(Z, message)
* x = hash(m, s)
* keygen25519(Y, NULL, x);
* r = hash(Y);
* h = m XOR r
* sign25519(v, h, x, s);
*
* output (v,r) as the signature
*
* verification:
*
* m = hash(Z, message);
* h = m XOR r
* verify25519(Y, v, h, P)
*
* confirm r == hash(Y)
*
* It would seem to me that it would be simpler to have the signer directly do
* h = hash(m, Y) and send that to the recipient instead of r, who can verify
* the signature by checking h == hash(m, Y). If there are any problems with
* such a scheme, please let me know.
*
* Also, EC-KCDSA (like most DS algorithms) picks x random, which is a waste of
* perfectly good entropy, but does allow Y to be calculated in advance of (or
* parallel to) hashing the message.
*/
/* Signature generation primitive, calculates (x-h)s mod q
* v [out] signature value
* h [in] signature hash (of message, signature pub key, and context data)
* x [in] signature private key
* s [in] private key for signing
* returns true on success, false on failure (use different x or h)
*/
public static final boolean sign(byte[] v, byte[] h, byte[] x, byte[] s) {
// v = (x - h) s mod q
int w, i;
byte[] h1 = new byte[32], x1 = new byte[32];
byte[] tmp1 = new byte[64];
byte[] tmp2 = new byte[64];
// Don't clobber the arguments, be nice!
cpy32(h1, h);
cpy32(x1, x);
// Reduce modulo group order
byte[] tmp3=new byte[32];
divmod(tmp3, h1, 32, ORDER, 32);
divmod(tmp3, x1, 32, ORDER, 32);
// v = x1 - h1
// If v is negative, add the group order to it to become positive.
// If v was already positive we don't have to worry about overflow
// when adding the order because v < ORDER and 2*ORDER < 2^256
mula_small(v, x1, 0, h1, 32, -1);
mula_small(v, v , 0, ORDER, 32, 1);
// tmp1 = (x-h)*s mod q
mula32(tmp1, v, s, 32, 1);
divmod(tmp2, tmp1, 64, ORDER, 32);
for (w = 0, i = 0; i < 32; i++)
w |= v[i] = tmp1[i];
return w != 0;
}
/* Signature verification primitive, calculates Y = vP + hG
* Y [out] signature public key
* v [in] signature value
* h [in] signature hash
* P [in] public key
*/
public static final void verify(byte[] Y, byte[] v, byte[] h, byte[] P) {
/* Y = v abs(P) + h G */
byte[] d=new byte[32];
long10[]
p=new long10[]{new long10(),new long10()},
s=new long10[]{new long10(),new long10()},
yx=new long10[]{new long10(),new long10(),new long10()},
yz=new long10[]{new long10(),new long10(),new long10()},
t1=new long10[]{new long10(),new long10(),new long10()},
t2=new long10[]{new long10(),new long10(),new long10()};
int vi = 0, hi = 0, di = 0, nvh=0, i, j, k;
/* set p[0] to G and p[1] to P */
set(p[0], 9);
unpack(p[1], P);
/* set s[0] to P+G and s[1] to P-G */
/* s[0] = (Py^2 + Gy^2 - 2 Py Gy)/(Px - Gx)^2 - Px - Gx - 486662 */
/* s[1] = (Py^2 + Gy^2 + 2 Py Gy)/(Px - Gx)^2 - Px - Gx - 486662 */
x_to_y2(t1[0], t2[0], p[1]); /* t2[0] = Py^2 */
sqrt(t1[0], t2[0]); /* t1[0] = Py or -Py */
j = is_negative(t1[0]); /* ... check which */
t2[0]._0 += 39420360; /* t2[0] = Py^2 + Gy^2 */
mul(t2[1], BASE_2Y, t1[0]);/* t2[1] = 2 Py Gy or -2 Py Gy */
sub(t1[j], t2[0], t2[1]); /* t1[0] = Py^2 + Gy^2 - 2 Py Gy */
add(t1[1-j], t2[0], t2[1]);/* t1[1] = Py^2 + Gy^2 + 2 Py Gy */
cpy(t2[0], p[1]); /* t2[0] = Px */
t2[0]._0 -= 9; /* t2[0] = Px - Gx */
sqr(t2[1], t2[0]); /* t2[1] = (Px - Gx)^2 */
recip(t2[0], t2[1], 0); /* t2[0] = 1/(Px - Gx)^2 */
mul(s[0], t1[0], t2[0]); /* s[0] = t1[0]/(Px - Gx)^2 */
sub(s[0], s[0], p[1]); /* s[0] = t1[0]/(Px - Gx)^2 - Px */
s[0]._0 -= 9 + 486662; /* s[0] = X(P+G) */
mul(s[1], t1[1], t2[0]); /* s[1] = t1[1]/(Px - Gx)^2 */
sub(s[1], s[1], p[1]); /* s[1] = t1[1]/(Px - Gx)^2 - Px */
s[1]._0 -= 9 + 486662; /* s[1] = X(P-G) */
mul_small(s[0], s[0], 1); /* reduce s[0] */
mul_small(s[1], s[1], 1); /* reduce s[1] */
/* prepare the chain */
for (i = 0; i < 32; i++) {
vi = (vi >> 8) ^ (v[i] & 0xFF) ^ ((v[i] & 0xFF) << 1);
hi = (hi >> 8) ^ (h[i] & 0xFF) ^ ((h[i] & 0xFF) << 1);
nvh = ~(vi ^ hi);
di = (nvh & (di & 0x80) >> 7) ^ vi;
di ^= nvh & (di & 0x01) << 1;
di ^= nvh & (di & 0x02) << 1;
di ^= nvh & (di & 0x04) << 1;
di ^= nvh & (di & 0x08) << 1;
di ^= nvh & (di & 0x10) << 1;
di ^= nvh & (di & 0x20) << 1;
di ^= nvh & (di & 0x40) << 1;
d[i] = (byte)di;
}
di = ((nvh & (di & 0x80) << 1) ^ vi) >> 8;
/* initialize state */
set(yx[0], 1);
cpy(yx[1], p[di]);
cpy(yx[2], s[0]);
set(yz[0], 0);
set(yz[1], 1);
set(yz[2], 1);
/* y[0] is (even)P + (even)G
* y[1] is (even)P + (odd)G if current d-bit is 0
* y[1] is (odd)P + (even)G if current d-bit is 1
* y[2] is (odd)P + (odd)G
*/
vi = 0;
hi = 0;
/* and go for it! */
for (i = 32; i--!=0; ) {
vi = (vi << 8) | (v[i] & 0xFF);
hi = (hi << 8) | (h[i] & 0xFF);
di = (di << 8) | (d[i] & 0xFF);
for (j = 8; j--!=0; ) {
mont_prep(t1[0], t2[0], yx[0], yz[0]);
mont_prep(t1[1], t2[1], yx[1], yz[1]);
mont_prep(t1[2], t2[2], yx[2], yz[2]);
k = ((vi ^ vi >> 1) >> j & 1)
+ ((hi ^ hi >> 1) >> j & 1);
mont_dbl(yx[2], yz[2], t1[k], t2[k], yx[0], yz[0]);
k = (di >> j & 2) ^ ((di >> j & 1) << 1);
mont_add(t1[1], t2[1], t1[k], t2[k], yx[1], yz[1],
p[di >> j & 1]);
mont_add(t1[2], t2[2], t1[0], t2[0], yx[2], yz[2],
s[((vi ^ hi) >> j & 2) >> 1]);
}
}
k = (vi & 1) + (hi & 1);
recip(t1[0], yz[k], 0);
mul(t1[1], yx[k], t1[0]);
pack(t1[1], Y);
}
///////////////////////////////////////////////////////////////////////////
/* sahn0:
* Using this class instead of long[10] to avoid bounds checks. */
private static final class long10 {
public long10() {}
public long10(
long _0, long _1, long _2, long _3, long _4,
long _5, long _6, long _7, long _8, long _9)
{
this._0=_0; this._1=_1; this._2=_2;
this._3=_3; this._4=_4; this._5=_5;
this._6=_6; this._7=_7; this._8=_8;
this._9=_9;
}
public long _0,_1,_2,_3,_4,_5,_6,_7,_8,_9;
}
/********************* radix 2^8 math *********************/
private static final void cpy32(byte[] d, byte[] s) {
int i;
for (i = 0; i < 32; i++)
d[i] = s[i];
}
/* p[m..n+m-1] = q[m..n+m-1] + z * x */
/* n is the size of x */
/* n+m is the size of p and q */
private static final int mula_small(byte[] p,byte[] q,int m,byte[] x,int n,int z) {
int v=0;
for (int i=0;i<n;++i) {
v+=(q[i+m] & 0xFF)+z*(x[i] & 0xFF);
p[i+m]=(byte)v;
v>>=8;
}
return v;
}
/* p += x * y * z where z is a small integer
* x is size 32, y is size t, p is size 32+t
* y is allowed to overlap with p+32 if you don't care about the upper half */
private static final int mula32(byte[] p, byte[] x, byte[] y, int t, int z) {
final int n = 31;
int w = 0;
int i = 0;
for (; i < t; i++) {
int zy = z * (y[i] & 0xFF);
w += mula_small(p, p, i, x, n, zy) +
(p[i+n] & 0xFF) + zy * (x[n] & 0xFF);
p[i+n] = (byte)w;
w >>= 8;
}
p[i+n] = (byte)(w + (p[i+n] & 0xFF));
return w >> 8;
}
/* divide r (size n) by d (size t), returning quotient q and remainder r
* quotient is size n-t+1, remainder is size t
* requires t > 0 && d[t-1] != 0
* requires that r[-1] and d[-1] are valid memory locations
* q may overlap with r+t */
private static final void divmod(byte[] q, byte[] r, int n, byte[] d, int t) {
int rn = 0;
int dt = ((d[t-1] & 0xFF) << 8);
if (t>1) {
dt |= (d[t-2] & 0xFF);
}
while (n-- >= t) {
int z = (rn << 16) | ((r[n] & 0xFF) << 8);
if (n>0) {
z |= (r[n-1] & 0xFF);
}
z/=dt;
rn += mula_small(r,r, n-t+1, d, t, -z);
q[n-t+1] = (byte)((z + rn) & 0xFF); /* rn is 0 or -1 (underflow) */
mula_small(r,r, n-t+1, d, t, -rn);
rn = (r[n] & 0xFF);
r[n] = 0;
}
r[t-1] = (byte)rn;
}
private static final int numsize(byte[] x,int n) {
while (n--!=0 && x[n]==0)
;
return n+1;
}
/* Returns x if a contains the gcd, y if b.
* Also, the returned buffer contains the inverse of a mod b,
* as 32-byte signed.
* x and y must have 64 bytes space for temporary use.
* requires that a[-1] and b[-1] are valid memory locations */
private static final byte[] egcd32(byte[] x,byte[] y,byte[] a,byte[] b) {
int an, bn = 32, qn, i;
for (i = 0; i < 32; i++)
x[i] = y[i] = 0;
x[0] = 1;
an = numsize(a, 32);
if (an==0)
return y; /* division by zero */
byte[] temp=new byte[32];
while (true) {
qn = bn - an + 1;
divmod(temp, b, bn, a, an);
bn = numsize(b, bn);
if (bn==0)
return x;
mula32(y, x, temp, qn, -1);
qn = an - bn + 1;
divmod(temp, a, an, b, bn);
an = numsize(a, an);
if (an==0)
return y;
mula32(x, y, temp, qn, -1);
}
}
/********************* radix 2^25.5 GF(2^255-19) math *********************/
private static final int P25=33554431; /* (1 << 25) - 1 */
private static final int P26=67108863; /* (1 << 26) - 1 */
/* Convert to internal format from little-endian byte format */
private static final void unpack(long10 x,byte[] m) {
x._0 = ((m[0] & 0xFF)) | ((m[1] & 0xFF))<<8 |
(m[2] & 0xFF)<<16 | ((m[3] & 0xFF)& 3)<<24;
x._1 = ((m[3] & 0xFF)&~ 3)>>2 | (m[4] & 0xFF)<<6 |
(m[5] & 0xFF)<<14 | ((m[6] & 0xFF)& 7)<<22;
x._2 = ((m[6] & 0xFF)&~ 7)>>3 | (m[7] & 0xFF)<<5 |
(m[8] & 0xFF)<<13 | ((m[9] & 0xFF)&31)<<21;
x._3 = ((m[9] & 0xFF)&~31)>>5 | (m[10] & 0xFF)<<3 |
(m[11] & 0xFF)<<11 | ((m[12] & 0xFF)&63)<<19;
x._4 = ((m[12] & 0xFF)&~63)>>6 | (m[13] & 0xFF)<<2 |
(m[14] & 0xFF)<<10 | (m[15] & 0xFF) <<18;
x._5 = (m[16] & 0xFF) | (m[17] & 0xFF)<<8 |
(m[18] & 0xFF)<<16 | ((m[19] & 0xFF)& 1)<<24;
x._6 = ((m[19] & 0xFF)&~ 1)>>1 | (m[20] & 0xFF)<<7 |
(m[21] & 0xFF)<<15 | ((m[22] & 0xFF)& 7)<<23;
x._7 = ((m[22] & 0xFF)&~ 7)>>3 | (m[23] & 0xFF)<<5 |
(m[24] & 0xFF)<<13 | ((m[25] & 0xFF)&15)<<21;
x._8 = ((m[25] & 0xFF)&~15)>>4 | (m[26] & 0xFF)<<4 |
(m[27] & 0xFF)<<12 | ((m[28] & 0xFF)&63)<<20;
x._9 = ((m[28] & 0xFF)&~63)>>6 | (m[29] & 0xFF)<<2 |
(m[30] & 0xFF)<<10 | (m[31] & 0xFF) <<18;
}
/* Check if reduced-form input >= 2^255-19 */
private static final boolean is_overflow(long10 x) {
return (
((x._0 > P26-19)) &&
((x._1 & x._3 & x._5 & x._7 & x._9) == P25) &&
((x._2 & x._4 & x._6 & x._8) == P26)
) || (x._9 > P25);
}
/* Convert from internal format to little-endian byte format. The
* number must be in a reduced form which is output by the following ops:
* unpack, mul, sqr
* set -- if input in range 0 .. P25
* If you're unsure if the number is reduced, first multiply it by 1. */
private static final void pack(long10 x,byte[] m) {
int ld = 0, ud = 0;
long t;
ld = (is_overflow(x)?1:0) - ((x._9 < 0)?1:0);
ud = ld * -(P25+1);
ld *= 19;
t = ld + x._0 + (x._1 << 26);
m[ 0] = (byte)t;
m[ 1] = (byte)(t >> 8);
m[ 2] = (byte)(t >> 16);
m[ 3] = (byte)(t >> 24);
t = (t >> 32) + (x._2 << 19);
m[ 4] = (byte)t;
m[ 5] = (byte)(t >> 8);
m[ 6] = (byte)(t >> 16);
m[ 7] = (byte)(t >> 24);
t = (t >> 32) + (x._3 << 13);
m[ 8] = (byte)t;
m[ 9] = (byte)(t >> 8);
m[10] = (byte)(t >> 16);
m[11] = (byte)(t >> 24);
t = (t >> 32) + (x._4 << 6);
m[12] = (byte)t;
m[13] = (byte)(t >> 8);
m[14] = (byte)(t >> 16);
m[15] = (byte)(t >> 24);
t = (t >> 32) + x._5 + (x._6 << 25);
m[16] = (byte)t;
m[17] = (byte)(t >> 8);
m[18] = (byte)(t >> 16);
m[19] = (byte)(t >> 24);
t = (t >> 32) + (x._7 << 19);
m[20] = (byte)t;
m[21] = (byte)(t >> 8);
m[22] = (byte)(t >> 16);
m[23] = (byte)(t >> 24);
t = (t >> 32) + (x._8 << 12);
m[24] = (byte)t;
m[25] = (byte)(t >> 8);
m[26] = (byte)(t >> 16);
m[27] = (byte)(t >> 24);
t = (t >> 32) + ((x._9 + ud) << 6);
m[28] = (byte)t;
m[29] = (byte)(t >> 8);
m[30] = (byte)(t >> 16);
m[31] = (byte)(t >> 24);
}
/* Copy a number */
private static final void cpy(long10 out, long10 in) {
out._0=in._0; out._1=in._1;
out._2=in._2; out._3=in._3;
out._4=in._4; out._5=in._5;
out._6=in._6; out._7=in._7;
out._8=in._8; out._9=in._9;
}
/* Set a number to value, which must be in range -185861411 .. 185861411 */
private static final void set(long10 out, int in) {
out._0=in; out._1=0;
out._2=0; out._3=0;
out._4=0; out._5=0;
out._6=0; out._7=0;
out._8=0; out._9=0;
}
/* Add/subtract two numbers. The inputs must be in reduced form, and the
* output isn't, so to do another addition or subtraction on the output,
* first multiply it by one to reduce it. */
private static final void add(long10 xy, long10 x, long10 y) {
xy._0 = x._0 + y._0; xy._1 = x._1 + y._1;
xy._2 = x._2 + y._2; xy._3 = x._3 + y._3;
xy._4 = x._4 + y._4; xy._5 = x._5 + y._5;
xy._6 = x._6 + y._6; xy._7 = x._7 + y._7;
xy._8 = x._8 + y._8; xy._9 = x._9 + y._9;
}
private static final void sub(long10 xy, long10 x, long10 y) {
xy._0 = x._0 - y._0; xy._1 = x._1 - y._1;
xy._2 = x._2 - y._2; xy._3 = x._3 - y._3;
xy._4 = x._4 - y._4; xy._5 = x._5 - y._5;
xy._6 = x._6 - y._6; xy._7 = x._7 - y._7;
xy._8 = x._8 - y._8; xy._9 = x._9 - y._9;
}
/* Multiply a number by a small integer in range -185861411 .. 185861411.
* The output is in reduced form, the input x need not be. x and xy may point
* to the same buffer. */
private static final long10 mul_small(long10 xy, long10 x, long y) {
long t;
t = (x._8*y);
xy._8 = (t & ((1 << 26) - 1));
t = (t >> 26) + (x._9*y);
xy._9 = (t & ((1 << 25) - 1));
t = 19 * (t >> 25) + (x._0*y);
xy._0 = (t & ((1 << 26) - 1));
t = (t >> 26) + (x._1*y);
xy._1 = (t & ((1 << 25) - 1));
t = (t >> 25) + (x._2*y);
xy._2 = (t & ((1 << 26) - 1));
t = (t >> 26) + (x._3*y);
xy._3 = (t & ((1 << 25) - 1));
t = (t >> 25) + (x._4*y);
xy._4 = (t & ((1 << 26) - 1));
t = (t >> 26) + (x._5*y);
xy._5 = (t & ((1 << 25) - 1));
t = (t >> 25) + (x._6*y);
xy._6 = (t & ((1 << 26) - 1));
t = (t >> 26) + (x._7*y);
xy._7 = (t & ((1 << 25) - 1));
t = (t >> 25) + xy._8;
xy._8 = (t & ((1 << 26) - 1));
xy._9 += (t >> 26);
return xy;
}
/* Multiply two numbers. The output is in reduced form, the inputs need not
* be. */
private static final long10 mul(long10 xy, long10 x, long10 y) {
/* sahn0:
* Using local variables to avoid class access.
* This seem to improve performance a bit...
*/
long
x_0=x._0,x_1=x._1,x_2=x._2,x_3=x._3,x_4=x._4,
x_5=x._5,x_6=x._6,x_7=x._7,x_8=x._8,x_9=x._9;
long
y_0=y._0,y_1=y._1,y_2=y._2,y_3=y._3,y_4=y._4,
y_5=y._5,y_6=y._6,y_7=y._7,y_8=y._8,y_9=y._9;
long t;
t = (x_0*y_8) + (x_2*y_6) + (x_4*y_4) + (x_6*y_2) +
(x_8*y_0) + 2 * ((x_1*y_7) + (x_3*y_5) +
(x_5*y_3) + (x_7*y_1)) + 38 *
(x_9*y_9);
xy._8 = (t & ((1 << 26) - 1));
t = (t >> 26) + (x_0*y_9) + (x_1*y_8) + (x_2*y_7) +
(x_3*y_6) + (x_4*y_5) + (x_5*y_4) +
(x_6*y_3) + (x_7*y_2) + (x_8*y_1) +
(x_9*y_0);
xy._9 = (t & ((1 << 25) - 1));
t = (x_0*y_0) + 19 * ((t >> 25) + (x_2*y_8) + (x_4*y_6)
+ (x_6*y_4) + (x_8*y_2)) + 38 *
((x_1*y_9) + (x_3*y_7) + (x_5*y_5) +
(x_7*y_3) + (x_9*y_1));
xy._0 = (t & ((1 << 26) - 1));
t = (t >> 26) + (x_0*y_1) + (x_1*y_0) + 19 * ((x_2*y_9)
+ (x_3*y_8) + (x_4*y_7) + (x_5*y_6) +
(x_6*y_5) + (x_7*y_4) + (x_8*y_3) +
(x_9*y_2));
xy._1 = (t & ((1 << 25) - 1));
t = (t >> 25) + (x_0*y_2) + (x_2*y_0) + 19 * ((x_4*y_8)
+ (x_6*y_6) + (x_8*y_4)) + 2 * (x_1*y_1)
+ 38 * ((x_3*y_9) + (x_5*y_7) +
(x_7*y_5) + (x_9*y_3));
xy._2 = (t & ((1 << 26) - 1));
t = (t >> 26) + (x_0*y_3) + (x_1*y_2) + (x_2*y_1) +
(x_3*y_0) + 19 * ((x_4*y_9) + (x_5*y_8) +
(x_6*y_7) + (x_7*y_6) +
(x_8*y_5) + (x_9*y_4));
xy._3 = (t & ((1 << 25) - 1));
t = (t >> 25) + (x_0*y_4) + (x_2*y_2) + (x_4*y_0) + 19 *
((x_6*y_8) + (x_8*y_6)) + 2 * ((x_1*y_3) +
(x_3*y_1)) + 38 *
((x_5*y_9) + (x_7*y_7) + (x_9*y_5));
xy._4 = (t & ((1 << 26) - 1));
t = (t >> 26) + (x_0*y_5) + (x_1*y_4) + (x_2*y_3) +
(x_3*y_2) + (x_4*y_1) + (x_5*y_0) + 19 *
((x_6*y_9) + (x_7*y_8) + (x_8*y_7) +
(x_9*y_6));
xy._5 = (t & ((1 << 25) - 1));
t = (t >> 25) + (x_0*y_6) + (x_2*y_4) + (x_4*y_2) +
(x_6*y_0) + 19 * (x_8*y_8) + 2 * ((x_1*y_5) +
(x_3*y_3) + (x_5*y_1)) + 38 *
((x_7*y_9) + (x_9*y_7));
xy._6 = (t & ((1 << 26) - 1));
t = (t >> 26) + (x_0*y_7) + (x_1*y_6) + (x_2*y_5) +
(x_3*y_4) + (x_4*y_3) + (x_5*y_2) +
(x_6*y_1) + (x_7*y_0) + 19 * ((x_8*y_9) +
(x_9*y_8));
xy._7 = (t & ((1 << 25) - 1));
t = (t >> 25) + xy._8;
xy._8 = (t & ((1 << 26) - 1));
xy._9 += (t >> 26);
return xy;
}
/* Square a number. Optimization of mul25519(x2, x, x) */
private static final long10 sqr(long10 x2, long10 x) {
long
x_0=x._0,x_1=x._1,x_2=x._2,x_3=x._3,x_4=x._4,
x_5=x._5,x_6=x._6,x_7=x._7,x_8=x._8,x_9=x._9;
long t;
t = (x_4*x_4) + 2 * ((x_0*x_8) + (x_2*x_6)) + 38 *
(x_9*x_9) + 4 * ((x_1*x_7) + (x_3*x_5));
x2._8 = (t & ((1 << 26) - 1));
t = (t >> 26) + 2 * ((x_0*x_9) + (x_1*x_8) + (x_2*x_7) +
(x_3*x_6) + (x_4*x_5));
x2._9 = (t & ((1 << 25) - 1));
t = 19 * (t >> 25) + (x_0*x_0) + 38 * ((x_2*x_8) +
(x_4*x_6) + (x_5*x_5)) + 76 * ((x_1*x_9)
+ (x_3*x_7));
x2._0 = (t & ((1 << 26) - 1));
t = (t >> 26) + 2 * (x_0*x_1) + 38 * ((x_2*x_9) +
(x_3*x_8) + (x_4*x_7) + (x_5*x_6));
x2._1 = (t & ((1 << 25) - 1));
t = (t >> 25) + 19 * (x_6*x_6) + 2 * ((x_0*x_2) +
(x_1*x_1)) + 38 * (x_4*x_8) + 76 *
((x_3*x_9) + (x_5*x_7));
x2._2 = (t & ((1 << 26) - 1));
t = (t >> 26) + 2 * ((x_0*x_3) + (x_1*x_2)) + 38 *
((x_4*x_9) + (x_5*x_8) + (x_6*x_7));
x2._3 = (t & ((1 << 25) - 1));
t = (t >> 25) + (x_2*x_2) + 2 * (x_0*x_4) + 38 *
((x_6*x_8) + (x_7*x_7)) + 4 * (x_1*x_3) + 76 *
(x_5*x_9);
x2._4 = (t & ((1 << 26) - 1));
t = (t >> 26) + 2 * ((x_0*x_5) + (x_1*x_4) + (x_2*x_3))
+ 38 * ((x_6*x_9) + (x_7*x_8));
x2._5 = (t & ((1 << 25) - 1));
t = (t >> 25) + 19 * (x_8*x_8) + 2 * ((x_0*x_6) +
(x_2*x_4) + (x_3*x_3)) + 4 * (x_1*x_5) +
76 * (x_7*x_9);
x2._6 = (t & ((1 << 26) - 1));
t = (t >> 26) + 2 * ((x_0*x_7) + (x_1*x_6) + (x_2*x_5) +
(x_3*x_4)) + 38 * (x_8*x_9);
x2._7 = (t & ((1 << 25) - 1));
t = (t >> 25) + x2._8;
x2._8 = (t & ((1 << 26) - 1));
x2._9 += (t >> 26);
return x2;
}
/* Calculates a reciprocal. The output is in reduced form, the inputs need not
* be. Simply calculates y = x^(p-2) so it's not too fast. */
/* When sqrtassist is true, it instead calculates y = x^((p-5)/8) */
private static final void recip(long10 y, long10 x, int sqrtassist) {
long10
t0=new long10(),
t1=new long10(),
t2=new long10(),
t3=new long10(),
t4=new long10();
int i;
/* the chain for x^(2^255-21) is straight from djb's implementation */
sqr(t1, x); /* 2 == 2 * 1 */
sqr(t2, t1); /* 4 == 2 * 2 */
sqr(t0, t2); /* 8 == 2 * 4 */
mul(t2, t0, x); /* 9 == 8 + 1 */
mul(t0, t2, t1); /* 11 == 9 + 2 */
sqr(t1, t0); /* 22 == 2 * 11 */
mul(t3, t1, t2); /* 31 == 22 + 9
== 2^5 - 2^0 */
sqr(t1, t3); /* 2^6 - 2^1 */
sqr(t2, t1); /* 2^7 - 2^2 */
sqr(t1, t2); /* 2^8 - 2^3 */
sqr(t2, t1); /* 2^9 - 2^4 */
sqr(t1, t2); /* 2^10 - 2^5 */
mul(t2, t1, t3); /* 2^10 - 2^0 */
sqr(t1, t2); /* 2^11 - 2^1 */
sqr(t3, t1); /* 2^12 - 2^2 */
for (i = 1; i < 5; i++) {
sqr(t1, t3);
sqr(t3, t1);
} /* t3 */ /* 2^20 - 2^10 */
mul(t1, t3, t2); /* 2^20 - 2^0 */
sqr(t3, t1); /* 2^21 - 2^1 */
sqr(t4, t3); /* 2^22 - 2^2 */
for (i = 1; i < 10; i++) {
sqr(t3, t4);
sqr(t4, t3);
} /* t4 */ /* 2^40 - 2^20 */
mul(t3, t4, t1); /* 2^40 - 2^0 */
for (i = 0; i < 5; i++) {
sqr(t1, t3);
sqr(t3, t1);
} /* t3 */ /* 2^50 - 2^10 */
mul(t1, t3, t2); /* 2^50 - 2^0 */
sqr(t2, t1); /* 2^51 - 2^1 */
sqr(t3, t2); /* 2^52 - 2^2 */
for (i = 1; i < 25; i++) {
sqr(t2, t3);
sqr(t3, t2);
} /* t3 */ /* 2^100 - 2^50 */
mul(t2, t3, t1); /* 2^100 - 2^0 */
sqr(t3, t2); /* 2^101 - 2^1 */
sqr(t4, t3); /* 2^102 - 2^2 */
for (i = 1; i < 50; i++) {
sqr(t3, t4);
sqr(t4, t3);
} /* t4 */ /* 2^200 - 2^100 */
mul(t3, t4, t2); /* 2^200 - 2^0 */
for (i = 0; i < 25; i++) {
sqr(t4, t3);
sqr(t3, t4);
} /* t3 */ /* 2^250 - 2^50 */
mul(t2, t3, t1); /* 2^250 - 2^0 */
sqr(t1, t2); /* 2^251 - 2^1 */
sqr(t2, t1); /* 2^252 - 2^2 */
if (sqrtassist!=0) {
mul(y, x, t2); /* 2^252 - 3 */
} else {
sqr(t1, t2); /* 2^253 - 2^3 */
sqr(t2, t1); /* 2^254 - 2^4 */
sqr(t1, t2); /* 2^255 - 2^5 */
mul(y, t1, t0); /* 2^255 - 21 */
}
}
/* checks if x is "negative", requires reduced input */
private static final int is_negative(long10 x) {
return (int)(((is_overflow(x) || (x._9 < 0))?1:0) ^ (x._0 & 1));
}
/* a square root */
private static final void sqrt(long10 x, long10 u) {
long10 v=new long10(), t1=new long10(), t2=new long10();
add(t1, u, u); /* t1 = 2u */
recip(v, t1, 1); /* v = (2u)^((p-5)/8) */
sqr(x, v); /* x = v^2 */
mul(t2, t1, x); /* t2 = 2uv^2 */
t2._0--; /* t2 = 2uv^2-1 */
mul(t1, v, t2); /* t1 = v(2uv^2-1) */
mul(x, u, t1); /* x = uv(2uv^2-1) */
}
/********************* Elliptic curve *********************/
/* y^2 = x^3 + 486662 x^2 + x over GF(2^255-19) */
/* t1 = ax + az
* t2 = ax - az */
private static final void mont_prep(long10 t1, long10 t2, long10 ax, long10 az) {
add(t1, ax, az);
sub(t2, ax, az);
}
/* A = P + Q where
* X(A) = ax/az
* X(P) = (t1+t2)/(t1-t2)
* X(Q) = (t3+t4)/(t3-t4)
* X(P-Q) = dx
* clobbers t1 and t2, preserves t3 and t4 */
private static final void mont_add(long10 t1, long10 t2, long10 t3, long10 t4,long10 ax, long10 az, long10 dx) {
mul(ax, t2, t3);
mul(az, t1, t4);
add(t1, ax, az);
sub(t2, ax, az);
sqr(ax, t1);
sqr(t1, t2);
mul(az, t1, dx);
}
/* B = 2 * Q where
* X(B) = bx/bz
* X(Q) = (t3+t4)/(t3-t4)
* clobbers t1 and t2, preserves t3 and t4 */
private static final void mont_dbl(long10 t1, long10 t2, long10 t3, long10 t4,long10 bx, long10 bz) {
sqr(t1, t3);
sqr(t2, t4);
mul(bx, t1, t2);
sub(t2, t1, t2);
mul_small(bz, t2, 121665);
add(t1, t1, bz);
mul(bz, t1, t2);
}
/* Y^2 = X^3 + 486662 X^2 + X
* t is a temporary */
private static final void x_to_y2(long10 t, long10 y2, long10 x) {
sqr(t, x);
mul_small(y2, x, 486662);
add(t, t, y2);
t._0++;
mul(y2, t, x);
}
/* P = kG and s = sign(P)/k */
private static final void core(byte[] Px, byte[] s, byte[] k, byte[] Gx) {
long10
dx=new long10(),
t1=new long10(),
t2=new long10(),
t3=new long10(),
t4=new long10();
long10[]
x=new long10[]{new long10(),new long10()},
z=new long10[]{new long10(),new long10()};
int i, j;
/* unpack the base */
if (Gx!=null)
unpack(dx, Gx);
else
set(dx, 9);
/* 0G = point-at-infinity */
set(x[0], 1);
set(z[0], 0);
/* 1G = G */
cpy(x[1], dx);
set(z[1], 1);
for (i = 32; i--!=0; ) {
if (i==0) {
i=0;
}
for (j = 8; j--!=0; ) {
/* swap arguments depending on bit */
int bit1 = (k[i] & 0xFF) >> j & 1;
int bit0 = ~(k[i] & 0xFF) >> j & 1;
long10 ax = x[bit0];
long10 az = z[bit0];
long10 bx = x[bit1];
long10 bz = z[bit1];
/* a' = a + b */
/* b' = 2 b */
mont_prep(t1, t2, ax, az);
mont_prep(t3, t4, bx, bz);
mont_add(t1, t2, t3, t4, ax, az, dx);
mont_dbl(t1, t2, t3, t4, bx, bz);
}
}
recip(t1, z[0], 0);
mul(dx, x[0], t1);
pack(dx, Px);
/* calculate s such that s abs(P) = G .. assumes G is std base point */
if (s!=null) {
x_to_y2(t2, t1, dx); /* t1 = Py^2 */
recip(t3, z[1], 0); /* where Q=P+G ... */
mul(t2, x[1], t3); /* t2 = Qx */
add(t2, t2, dx); /* t2 = Qx + Px */
t2._0 += 9 + 486662; /* t2 = Qx + Px + Gx + 486662 */
dx._0 -= 9; /* dx = Px - Gx */
sqr(t3, dx); /* t3 = (Px - Gx)^2 */
mul(dx, t2, t3); /* dx = t2 (Px - Gx)^2 */
sub(dx, dx, t1); /* dx = t2 (Px - Gx)^2 - Py^2 */
dx._0 -= 39420360; /* dx = t2 (Px - Gx)^2 - Py^2 - Gy^2 */
mul(t1, dx, BASE_R2Y); /* t1 = -Py */
if (is_negative(t1)!=0) /* sign is 1, so just copy */
cpy32(s, k);
else /* sign is -1, so negate */
mula_small(s, ORDER_TIMES_8, 0, k, 32, -1);
/* reduce s mod q
* (is this needed? do it just in case, it's fast anyway) */
//divmod((dstptr) t1, s, 32, order25519, 32);
/* take reciprocal of s mod q */
byte[] temp1=new byte[32];
byte[] temp2=new byte[64];
byte[] temp3=new byte[64];
cpy32(temp1, ORDER);
cpy32(s, egcd32(temp2, temp3, s, temp1));
if ((s[31] & 0x80)!=0)
mula_small(s, s, 0, ORDER, 32, 1);
}
}
/* smallest multiple of the order that's >= 2^255 */
private static final byte[] ORDER_TIMES_8 = {
(byte)104, (byte)159, (byte)174, (byte)231,
(byte)210, (byte)24, (byte)147, (byte)192,
(byte)178, (byte)230, (byte)188, (byte)23,
(byte)245, (byte)206, (byte)247, (byte)166,
(byte)0, (byte)0, (byte)0, (byte)0,
(byte)0, (byte)0, (byte)0, (byte)0,
(byte)0, (byte)0, (byte)0, (byte)0,
(byte)0, (byte)0, (byte)0, (byte)128
};
/* constants 2Gy and 1/(2Gy) */
private static final long10 BASE_2Y = new long10(
39999547, 18689728, 59995525, 1648697, 57546132,
24010086, 19059592, 5425144, 63499247, 16420658
);
private static final long10 BASE_R2Y = new long10(
5744, 8160848, 4790893, 13779497, 35730846,
12541209, 49101323, 30047407, 40071253, 6226132
);
}