[Caml-list] primality test for Big_int ?

[Caml-list] primality test for Big_int ?

[Francesco Abbate]

Hello everyone,

I was implementing a modular GCD algorithm for polynomial with big_int coefficients when I've discovered that there isn't any primality test in the Nums library.

Someone can help me about this question ?

If possible I would avoid to implement a primality test by myself because
- I have to study the Rabin-Miller test
- I have to implement it in C to obtain a good speed (maybe ?)

-- 
Francesco Abbate <france.abbate@tiscalinet.it>

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Re: [Caml-list] primality test for Big_int ?

[Xavier Leroy]

> I was implementing a modular GCD algorithm for polynomial with
> big_int coefficients when I've discovered that there isn't any
> primality test in the Nums library.
> 
> Someone can help me about this question ?

The Cryptokit library (http://pauillac.inria.fr/~xleroy/software.html)
contains an implementation of probabilistic primality testing,
as part of RSA key generation.  

The function is called "is_pseudoprime" and it's not exported, but it
shouldn't be hard to extract it from the sources.  It operates on type
"nat", so you'll have to stick a "Big_int.nat_of_big_int" conversion
on input.

The algorithm used is that of PGP 2.6: Fermat tests against 8 small
primes.  While not as sophisticated as Miller-Rabin, this test seems
good enough for PGP, so it's good enough for me :-)

> If possible I would avoid to implement a primality test by myself because
> - I have to study the Rabin-Miller test
> - I have to implement it in C to obtain a good speed (maybe ?)

No need for C: Caml code working at the "nat" level (hand-allocated
big natural integers) is plenty fast enough.

- Xavier Leroy

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Re: [Caml-list] primality test for Big_int ?

[Yamagata Yoriyuki]

I think Numerix contains the Rabin-Miller test as an example.

http://pauillac.inria.fr/~quercia/

cryptokit also includes an implementation of Rabin-Miller, but IIRC, it
does not work with arbitrary integers.

http://pauillac.inria.fr/~xleroy/software.html

--
Yamagata Yoriyuki

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