> I've posted an answer on SE, but will give a short summary of what I think
> solves the problem here.
> Please contact the author to make sure my proposed fix solves the problem.
>
We benchmarked this, and we found there's about a non-trivial speedup using
the square of a random value. Below is the updated code.
We need to retain the Jacobi tests because of possible testing using small
moduli. That is, landing on p and q may not be that remote in some
scenarios.
*****
Here are the representative benchmarks. They ratios are consistent with and
without OpenMP, on a host or in a VM, etc.
Purely Random:
$ ./rw-test.exe
5000 signings performed in 22530 milliseconds
Random squaring:
$ ./rw-test.exe
5000 signings performed in 13580 milliseconds
*****
+void InvertibleRWFunction::GenerateBlindingValue(RandomNumberGenerator&
rng, Integer& r, Integer& rInv) const
+{
+ ModularArithmetic modn(m_n);
+ bool stop = false;
+
+ while(!stop)
+ {
+ // Jacobi is O(m*log(n)); ModInv is O(n^2). Perform the Jacobi's
first
+ r.Randomize(rng, Integer::One(), m_n - Integer::One());
+ r = modn.Square(r);
+
+ int jp, jq;
+ #pragma omp parallel sections
+ {
+ #pragma omp section
+ jp = Jacobi(r % m_p, m_p);
+ #pragma omp section
+ jq = Jacobi(r % m_q, m_q);
+ }
+
+ if ((jp != -1) && (jq != -1))
+ {
+ rInv = modn.MultiplicativeInverse(r);
+ if(rInv.NotZero())
+ stop = true;
+ }
+ }
+ }
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