org.bouncycastle.math.raw.Mod Maven / Gradle / Ivy
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The Long Term Stable (LTS) Bouncy Castle Crypto package is a Java implementation of cryptographic algorithms. This jar contains the JCA/JCE provider and low-level API for the BC LTS version 2.73.7 for Java 8 and later.
package org.bouncycastle.math.raw;
import java.util.Random;
import org.bouncycastle.util.Integers;
/*
* Modular inversion as implemented in this class is based on the paper "Fast constant-time gcd
* computation and modular inversion" by Daniel J. Bernstein and Bo-Yin Yang.
*/
public abstract class Mod
{
private static final int M30 = 0x3FFFFFFF;
private static final long M32L = 0xFFFFFFFFL;
public static void checkedModOddInverse(int[] m, int[] x, int[] z)
{
if (0 == modOddInverse(m, x, z))
{
throw new ArithmeticException("Inverse does not exist.");
}
}
public static void checkedModOddInverseVar(int[] m, int[] x, int[] z)
{
if (!modOddInverseVar(m, x, z))
{
throw new ArithmeticException("Inverse does not exist.");
}
}
public static int inverse32(int d)
{
// assert (d & 1) == 1;
// int x = d + (((d + 1) & 4) << 1); // d.x == 1 mod 2**4
int x = d; // d.x == 1 mod 2**3
x *= 2 - d * x; // d.x == 1 mod 2**6
x *= 2 - d * x; // d.x == 1 mod 2**12
x *= 2 - d * x; // d.x == 1 mod 2**24
x *= 2 - d * x; // d.x == 1 mod 2**48
// assert d * x == 1;
return x;
}
public static int modOddInverse(int[] m, int[] x, int[] z)
{
int len32 = m.length;
// assert len32 > 0;
// assert (m[0] & 1) != 0;
// assert m[len32 - 1] != 0;
int bits = (len32 << 5) - Integers.numberOfLeadingZeros(m[len32 - 1]);
int len30 = (bits + 29) / 30;
int[] t = new int[4];
int[] D = new int[len30];
int[] E = new int[len30];
int[] F = new int[len30];
int[] G = new int[len30];
int[] M = new int[len30];
E[0] = 1;
encode30(bits, x, 0, G, 0);
encode30(bits, m, 0, M, 0);
System.arraycopy(M, 0, F, 0, len30);
int delta = 0;
int m0Inv32 = inverse32(M[0]);
int maxDivsteps = getMaximumDivsteps(bits);
for (int divSteps = 0; divSteps < maxDivsteps; divSteps += 30)
{
delta = divsteps30(delta, F[0], G[0], t);
updateDE30(len30, D, E, t, m0Inv32, M);
updateFG30(len30, F, G, t);
}
int signF = F[len30 - 1] >> 31;
cnegate30(len30, signF, F);
/*
* D is in the range (-2.M, M). First, conditionally add M if D is negative, to bring it
* into the range (-M, M). Then normalize by conditionally negating (according to signF)
* and/or then adding M, to bring it into the range [0, M).
*/
cnormalize30(len30, signF, D, M);
decode30(bits, D, 0, z, 0);
// assert 0 != Nat.lessThan(len32, z, m);
return equalTo(len30, F, 1) & equalTo(len30, G, 0);
}
public static boolean modOddInverseVar(int[] m, int[] x, int[] z)
{
int len32 = m.length;
// assert len32 > 0;
// assert (m[0] & 1) != 0;
// assert m[len32 - 1] != 0;
int bits = (len32 << 5) - Integers.numberOfLeadingZeros(m[len32 - 1]);
int len30 = (bits + 29) / 30;
int[] t = new int[4];
int[] D = new int[len30];
int[] E = new int[len30];
int[] F = new int[len30];
int[] G = new int[len30];
int[] M = new int[len30];
E[0] = 1;
encode30(bits, x, 0, G, 0);
encode30(bits, m, 0, M, 0);
System.arraycopy(M, 0, F, 0, len30);
int clz = Math.max(0, bits - 1 - Nat.getBitLength(len32, x));
int eta = -1 - clz;
int lenDE = len30, lenFG = len30;
int m0Inv32 = inverse32(M[0]);
int maxDivsteps = getMaximumDivsteps(bits) - clz;
int divsteps = 0;
while (!equalToVar(lenFG, G, 0))
{
if (divsteps >= maxDivsteps)
{
return false;
}
divsteps += 30;
eta = divsteps30Var(eta, F[0], G[0], t);
updateDE30(lenDE, D, E, t, m0Inv32, M);
updateFG30(lenFG, F, G, t);
lenFG = trimFG30(lenFG, F, G);
}
int signF = F[lenFG - 1] >> 31;
/*
* D is in the range (-2.M, M). First, conditionally add M if D is negative, to bring it
* into the range (-M, M). Then normalize by conditionally negating (according to signF)
* and/or then adding M, to bring it into the range [0, M).
*/
int signD = D[lenDE - 1] >> 31;
if (signD < 0)
{
signD = add30(lenDE, D, M);
}
if (signF < 0)
{
signD = negate30(lenDE, D);
signF = negate30(lenFG, F);
}
// assert 0 == signF;
if (!equalToVar(lenFG, F, 1))
{
return false;
}
if (signD < 0)
{
signD = add30(lenDE, D, M);
}
// assert 0 == signD;
decode30(bits, D, 0, z, 0);
// assert !Nat.gte(len32, z, m);
return true;
}
public static int modOddIsCoprime(int[] m, int[] x)
{
int len32 = m.length;
// assert len32 > 0;
// assert (m[0] & 1) != 0;
// assert m[len32 - 1] != 0;
int bits = (len32 << 5) - Integers.numberOfLeadingZeros(m[len32 - 1]);
int len30 = (bits + 29) / 30;
int[] t = new int[4];
int[] F = new int[len30];
int[] G = new int[len30];
int[] M = new int[len30];
encode30(bits, x, 0, G, 0);
encode30(bits, m, 0, M, 0);
System.arraycopy(M, 0, F, 0, len30);
int delta = 0;
int maxDivsteps = getMaximumDivsteps(bits);
for (int divSteps = 0; divSteps < maxDivsteps; divSteps += 30)
{
delta = divsteps30(delta, F[0], G[0], t);
updateFG30(len30, F, G, t);
}
int signF = F[len30 - 1] >> 31;
cnegate30(len30, signF, F);
return equalTo(len30, F, 1) & equalTo(len30, G, 0);
}
public static boolean modOddIsCoprimeVar(int[] m, int[] x)
{
int len32 = m.length;
// assert len32 > 0;
// assert (m[0] & 1) != 0;
// assert m[len32 - 1] != 0;
int bits = (len32 << 5) - Integers.numberOfLeadingZeros(m[len32 - 1]);
int len30 = (bits + 29) / 30;
int[] t = new int[4];
int[] F = new int[len30];
int[] G = new int[len30];
int[] M = new int[len30];
encode30(bits, x, 0, G, 0);
encode30(bits, m, 0, M, 0);
System.arraycopy(M, 0, F, 0, len30);
int clz = Math.max(0, bits - 1 - Nat.getBitLength(len32, x));
int eta = -1 - clz;
int lenFG = len30;
int maxDivsteps = getMaximumDivsteps(bits) - clz;
int divsteps = 0;
while (!equalToVar(lenFG, G, 0))
{
if (divsteps >= maxDivsteps)
{
return false;
}
divsteps += 30;
eta = divsteps30Var(eta, F[0], G[0], t);
updateFG30(lenFG, F, G, t);
lenFG = trimFG30(lenFG, F, G);
}
int signF = F[lenFG - 1] >> 31;
if (signF < 0)
{
signF = negate30(lenFG, F);
}
// assert 0 == signF;
return equalToVar(lenFG, F, 1);
}
public static int[] random(int[] p)
{
int len = p.length;
Random rand = new Random();
int[] s = Nat.create(len);
int m = p[len - 1];
m |= m >>> 1;
m |= m >>> 2;
m |= m >>> 4;
m |= m >>> 8;
m |= m >>> 16;
do
{
for (int i = 0; i != len; i++)
{
s[i] = rand.nextInt();
}
s[len - 1] &= m;
}
while (Nat.gte(len, s, p));
return s;
}
private static int add30(int len30, int[] D, int[] M)
{
// assert len30 > 0;
// assert D.length >= len30;
// assert M.length >= len30;
int c = 0, last = len30 - 1;
for (int i = 0; i < last; ++i)
{
c += D[i] + M[i];
D[i] = c & M30; c >>= 30;
}
c += D[last] + M[last];
D[last] = c; c >>= 30;
return c;
}
private static void cnegate30(int len30, int cond, int[] D)
{
// assert len30 > 0;
// assert D.length >= len30;
int c = 0, last = len30 - 1;
for (int i = 0; i < last; ++i)
{
c += (D[i] ^ cond) - cond;
D[i] = c & M30; c >>= 30;
}
c += (D[last] ^ cond) - cond;
D[last] = c;
}
private static void cnormalize30(int len30, int condNegate, int[] D, int[] M)
{
// assert len30 > 0;
// assert D.length >= len30;
// assert M.length >= len30;
int last = len30 - 1;
{
int c = 0, condAdd = D[last] >> 31;
for (int i = 0; i < last; ++i)
{
int di = D[i] + (M[i] & condAdd);
di = (di ^ condNegate) - condNegate;
c += di; D[i] = c & M30; c >>= 30;
}
{
int di = D[last] + (M[last] & condAdd);
di = (di ^ condNegate) - condNegate;
c += di; D[last] = c;
}
}
{
int c = 0, condAdd = D[last] >> 31;
for (int i = 0; i < last; ++i)
{
int di = D[i] + (M[i] & condAdd);
c += di; D[i] = c & M30; c >>= 30;
}
{
int di = D[last] + (M[last] & condAdd);
c += di; D[last] = c;
}
// assert c >> 30 == 0;
}
}
private static void decode30(int bits, int[] x, int xOff, int[] z, int zOff)
{
// assert bits > 0;
// assert x != z;
int avail = 0;
long data = 0L;
while (bits > 0)
{
while (avail < Math.min(32, bits))
{
data |= (long)x[xOff++] << avail;
avail += 30;
}
z[zOff++] = (int)data; data >>>= 32;
avail -= 32;
bits -= 32;
}
}
private static int divsteps30(int delta, int f0, int g0, int[] t)
{
int u = 1 << 30, v = 0, q = 0, r = 1 << 30;
int f = f0, g = g0;
for (int i = 0; i < 30; ++i)
{
// assert (f & 1) == 1;
// assert ((u >> (30 - i)) * f0 + (v >> (30 - i)) * g0) == f << i;
// assert ((q >> (30 - i)) * f0 + (r >> (30 - i)) * g0) == g << i;
int c1 = delta >> 31;
int c2 = -(g & 1);
int x = f ^ c1;
int y = u ^ c1;
int z = v ^ c1;
g -= x & c2;
q -= y & c2;
r -= z & c2;
c2 &= ~c1;
delta = (delta ^ c2) - (c2 - 1);
f += g & c2;
u += q & c2;
v += r & c2;
g >>= 1;
q >>= 1;
r >>= 1;
}
t[0] = u;
t[1] = v;
t[2] = q;
t[3] = r;
return delta;
}
private static int divsteps30Var(int eta, int f0, int g0, int[] t)
{
int u = 1, v = 0, q = 0, r = 1;
int f = f0, g = g0, m, w, x, y, z;
int i = 30, limit, zeros;
for (;;)
{
// Use a sentinel bit to count zeros only up to i.
zeros = Integers.numberOfTrailingZeros(g | (-1 << i));
g >>= zeros;
u <<= zeros;
v <<= zeros;
eta -= zeros;
i -= zeros;
if (i <= 0)
{
break;
}
// assert (f & 1) == 1;
// assert (g & 1) == 1;
// assert (u * f0 + v * g0) == f << (30 - i);
// assert (q * f0 + r * g0) == g << (30 - i);
if (eta < 0)
{
eta = -eta;
x = f; f = g; g = -x;
y = u; u = q; q = -y;
z = v; v = r; r = -z;
// Handle up to 6 divsteps at once, subject to eta and i.
limit = (eta + 1) > i ? i : (eta + 1);
m = (-1 >>> (32 - limit)) & 63;
w = (f * g * (f * f - 2)) & m;
}
else
{
// Handle up to 4 divsteps at once, subject to eta and i.
limit = (eta + 1) > i ? i : (eta + 1);
m = (-1 >>> (32 - limit)) & 15;
w = f + (((f + 1) & 4) << 1);
w = (-w * g) & m;
}
g += f * w;
q += u * w;
r += v * w;
// assert (g & m) == 0;
}
t[0] = u;
t[1] = v;
t[2] = q;
t[3] = r;
return eta;
}
private static void encode30(int bits, int[] x, int xOff, int[] z, int zOff)
{
// assert bits > 0;
// assert x != z;
int avail = 0;
long data = 0L;
while (bits > 0)
{
if (avail < Math.min(30, bits))
{
data |= (x[xOff++] & M32L) << avail;
avail += 32;
}
z[zOff++] = (int)data & M30; data >>>= 30;
avail -= 30;
bits -= 30;
}
}
private static int equalTo(int len, int[] x, int y)
{
int d = x[0] ^ y;
for (int i = 1; i < len; ++i)
{
d |= x[i];
}
d = (d >>> 1) | (d & 1);
return (d - 1) >> 31;
}
private static boolean equalToVar(int len, int[] x, int y)
{
int d = x[0] ^ y;
if (d != 0)
return false;
for (int i = 1; i < len; ++i)
{
d |= x[i];
}
return d == 0;
}
private static int getMaximumDivsteps(int bits)
{
return (49 * bits + (bits < 46 ? 80 : 47)) / 17;
}
private static int negate30(int len30, int[] D)
{
// assert len30 > 0;
// assert D.length >= len30;
int c = 0, last = len30 - 1;
for (int i = 0; i < last; ++i)
{
c -= D[i];
D[i] = c & M30; c >>= 30;
}
c -= D[last];
D[last] = c; c >>= 30;
return c;
}
private static int trimFG30(int len30, int[] F, int[] G)
{
// assert len30 > 0;
// assert F.length >= len30;
// assert G.length >= len30;
int fn = F[len30 - 1];
int gn = G[len30 - 1];
int cond = (len30 - 2) >> 31;
cond |= fn ^ (fn >> 31);
cond |= gn ^ (gn >> 31);
if (cond == 0)
{
F[len30 - 2] |= fn << 30;
G[len30 - 2] |= gn << 30;
--len30;
}
return len30;
}
private static void updateDE30(int len30, int[] D, int[] E, int[] t, int m0Inv32, int[] M)
{
// assert len30 > 0;
// assert D.length >= len30;
// assert E.length >= len30;
// assert M.length >= len30;
// assert m0Inv32 * M[0] == 1;
final int u = t[0], v = t[1], q = t[2], r = t[3];
int di, ei, i, md, me, mi, sd, se;
long cd, ce;
/*
* We accept D (E) in the range (-2.M, M) and conceptually add the modulus to the input
* value if it is initially negative. Instead of adding it explicitly, we add u and/or v (q
* and/or r) to md (me).
*/
sd = D[len30 - 1] >> 31;
se = E[len30 - 1] >> 31;
md = (u & sd) + (v & se);
me = (q & sd) + (r & se);
mi = M[0];
di = D[0];
ei = E[0];
cd = (long)u * di + (long)v * ei;
ce = (long)q * di + (long)r * ei;
/*
* Subtract from md/me an extra term in the range [0, 2^30) such that the low 30 bits of the
* intermediate D/E values will be 0, allowing clean division by 2^30. The final D/E are
* thus in the range (-2.M, M), consistent with the input constraint.
*/
md -= (m0Inv32 * (int)cd + md) & M30;
me -= (m0Inv32 * (int)ce + me) & M30;
cd += (long)mi * md;
ce += (long)mi * me;
// assert ((int)cd & M30) == 0;
// assert ((int)ce & M30) == 0;
cd >>= 30;
ce >>= 30;
for (i = 1; i < len30; ++i)
{
mi = M[i];
di = D[i];
ei = E[i];
cd += (long)u * di + (long)v * ei + (long)mi * md;
ce += (long)q * di + (long)r * ei + (long)mi * me;
D[i - 1] = (int)cd & M30; cd >>= 30;
E[i - 1] = (int)ce & M30; ce >>= 30;
}
D[len30 - 1] = (int)cd;
E[len30 - 1] = (int)ce;
}
private static void updateFG30(int len30, int[] F, int[] G, int[] t)
{
// assert len30 > 0;
// assert F.length >= len30;
// assert G.length >= len30;
final int u = t[0], v = t[1], q = t[2], r = t[3];
int fi, gi, i;
long cf, cg;
fi = F[0];
gi = G[0];
cf = (long)u * fi + (long)v * gi;
cg = (long)q * fi + (long)r * gi;
// assert ((int)cf & M30) == 0;
// assert ((int)cg & M30) == 0;
cf >>= 30;
cg >>= 30;
for (i = 1; i < len30; ++i)
{
fi = F[i];
gi = G[i];
cf += (long)u * fi + (long)v * gi;
cg += (long)q * fi + (long)r * gi;
F[i - 1] = (int)cf & M30; cf >>= 30;
G[i - 1] = (int)cg & M30; cg >>= 30;
}
F[len30 - 1] = (int)cf;
G[len30 - 1] = (int)cg;
}
}
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