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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.
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package org.bouncycastle.pqc.crypto.falcon;
class SamplerZ
{
FPREngine fpr;
SamplerZ()
{
this.fpr = new FPREngine();
}
int sample(SamplerCtx ctx, FalconFPR mu, FalconFPR iSigma)
{
return sampler(ctx, mu, iSigma);
}
/*
* Sample an integer value along a half-gaussian distribution centered
* on zero and standard deviation 1.8205, with a precision of 72 bits.
*/
int gaussian0_sampler(FalconRNG p)
{
int[] dist = {
10745844, 3068844, 3741698,
5559083, 1580863, 8248194,
2260429, 13669192, 2736639,
708981, 4421575, 10046180,
169348, 7122675, 4136815,
30538, 13063405, 7650655,
4132, 14505003, 7826148,
417, 16768101, 11363290,
31, 8444042, 8086568,
1, 12844466, 265321,
0, 1232676, 13644283,
0, 38047, 9111839,
0, 870, 6138264,
0, 14, 12545723,
0, 0, 3104126,
0, 0, 28824,
0, 0, 198,
0, 0, 1
};
int v0, v1, v2, hi;
long lo;
int u;
int z;
/*
* Get a random 72-bit value, into three 24-bit limbs v0..v2.
*/
lo = p.prng_get_u64();
hi = (p.prng_get_u8() & 0xff);
v0 = (int)lo & 0xFFFFFF;
v1 = (int)(lo >>> 24) & 0xFFFFFF;
v2 = (int)(lo >>> 48) | (hi << 16);
/*
* Sampled value is z, such that v0..v2 is lower than the first
* z elements of the table.
*/
z = 0;
for (u = 0; u < dist.length; u += 3)
{
int w0, w1, w2, cc;
w0 = dist[u + 2];
w1 = dist[u + 1];
w2 = dist[u + 0];
cc = (v0 - w0) >>> 31;
cc = (v1 - w1 - cc) >>> 31;
cc = (v2 - w2 - cc) >>> 31;
z += (int)cc;
}
return z;
}
/*
* Sample a bit with probability exp(-x) for some x >= 0.
*/
int BerExp(FalconRNG p, FalconFPR x, FalconFPR ccs)
{
int s, i;
FalconFPR r;
int sw, w;
long z;
/*
* Reduce x modulo log(2): x = s*log(2) + r, with s an integer,
* and 0 <= r < log(2). Since x >= 0, we can use fpr_trunc().
*/
s = (int)fpr.fpr_trunc(fpr.fpr_mul(x, fpr.fpr_inv_log2));
r = fpr.fpr_sub(x, fpr.fpr_mul(fpr.fpr_of(s), fpr.fpr_log2));
/*
* It may happen (quite rarely) that s >= 64; if sigma = 1.2
* (the minimum value for sigma), r = 0 and b = 1, then we get
* s >= 64 if the half-Gaussian produced a z >= 13, which happens
* with probability about 0.000000000230383991, which is
* approximatively equal to 2^(-32). In any case, if s >= 64,
* then BerExp will be non-zero with probability less than
* 2^(-64), so we can simply saturate s at 63.
*/
sw = s;
sw ^= (sw ^ 63) & -((63 - sw) >>> 31);
s = sw;
/*
* Compute exp(-r); we know that 0 <= r < log(2) at this point, so
* we can use fpr_expm_p63(), which yields a result scaled to 2^63.
* We scale it up to 2^64, then right-shift it by s bits because
* we really want exp(-x) = 2^(-s)*exp(-r).
*
* The "-1" operation makes sure that the value fits on 64 bits
* (i.e. if r = 0, we may get 2^64, and we prefer 2^64-1 in that
* case). The bias is negligible since fpr_expm_p63() only computes
* with 51 bits of precision or so.
*/
z = ((fpr.fpr_expm_p63(r, ccs) << 1) - 1) >>> s;
/*
* Sample a bit with probability exp(-x). Since x = s*log(2) + r,
* exp(-x) = 2^-s * exp(-r), we compare lazily exp(-x) with the
* PRNG output to limit its consumption, the sign of the difference
* yields the expected result.
*/
i = 64;
do
{
i -= 8;
w = (p.prng_get_u8() & 0xff) - ((int)(z >>> i) & 0xFF);
}
while (w == 0 && i > 0);
return (w >>> 31);
}
/*
* The sampler produces a random integer that follows a discrete Gaussian
* distribution, centered on mu, and with standard deviation sigma. The
* provided parameter isigma is equal to 1/sigma.
*
* The value of sigma MUST lie between 1 and 2 (i.e. isigma lies between
* 0.5 and 1); in Falcon, sigma should always be between 1.2 and 1.9.
*/
int sampler(SamplerCtx ctx, FalconFPR mu, FalconFPR isigma)
{
SamplerCtx spc;
int s;
FalconFPR r, dss, ccs;
spc = ctx;
/*
* Center is mu. We compute mu = s + r where s is an integer
* and 0 <= r < 1.
*/
s = (int)fpr.fpr_floor(mu);
r = fpr.fpr_sub(mu, fpr.fpr_of(s));
/*
* dss = 1/(2*sigma^2) = 0.5*(isigma^2).
*/
dss = fpr.fpr_half(fpr.fpr_sqr(isigma));
/*
* ccs = sigma_min / sigma = sigma_min * isigma.
*/
ccs = fpr.fpr_mul(isigma, spc.sigma_min);
/*
* We now need to sample on center r.
*/
for (; ; )
{
int z0, z, b;
FalconFPR x;
/*
* Sample z for a Gaussian distribution. Then get a
* random bit b to turn the sampling into a bimodal
* distribution: if b = 1, we use z+1, otherwise we
* use -z. We thus have two situations:
*
* - b = 1: z >= 1 and sampled against a Gaussian
* centered on 1.
* - b = 0: z <= 0 and sampled against a Gaussian
* centered on 0.
*/
z0 = gaussian0_sampler(spc.p);
b = (spc.p.prng_get_u8() & 0xff) & 1;
z = b + ((b << 1) - 1) * z0;
/*
* Rejection sampling. We want a Gaussian centered on r;
* but we sampled against a Gaussian centered on b (0 or
* 1). But we know that z is always in the range where
* our sampling distribution is greater than the Gaussian
* distribution, so rejection works.
*
* We got z with distribution:
* G(z) = exp(-((z-b)^2)/(2*sigma0^2))
* We target distribution:
* S(z) = exp(-((z-r)^2)/(2*sigma^2))
* Rejection sampling works by keeping the value z with
* probability S(z)/G(z), and starting again otherwise.
* This requires S(z) <= G(z), which is the case here.
* Thus, we simply need to keep our z with probability:
* P = exp(-x)
* where:
* x = ((z-r)^2)/(2*sigma^2) - ((z-b)^2)/(2*sigma0^2)
*
* Here, we scale up the Bernouilli distribution, which
* makes rejection more probable, but makes rejection
* rate sufficiently decorrelated from the Gaussian
* center and standard deviation that the whole sampler
* can be said to be constant-time.
*/
x = fpr.fpr_mul(fpr.fpr_sqr(fpr.fpr_sub(fpr.fpr_of(z), r)), dss);
x = fpr.fpr_sub(x, fpr.fpr_mul(fpr.fpr_of(z0 * z0), fpr.fpr_inv_2sqrsigma0));
if (BerExp(spc.p, x, ccs) != 0)
{
/*
* Rejection sampling was centered on r, but the
* actual center is mu = s + r.
*/
return s + z;
}
}
}
}
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