This has been discussed extensively for Internet security reasons, and the Photuris folks decided to use a common modulus (actually, several with different lengths.) I think they chose a strong prime (form p = 2q+1, q prime), specifically to avoid small-prime attacks, though they may have decided that that was no longer necessary.

I assume from the last sentence that you know that the use of strong primes is no longer advantageous but I will just reiterate it here for the good of those writing code which implements strong primes: Strong primes are no longer of any benefit for cryptographic applications. The elliptic curve method of factoring takes no longer to factor a "strong" prime than it does for any other general number. You may *SLIGHTLY* hinder progress if an attacker sieves first, but as you should have done so when you created the primes in the first place it won`t be a problem because there wont be any small factors. Implementing strong primes won`t make your code any less secure, it will just take longer to create the keys and won`t gain you any security, all te big boys are using elliptic curve factoring methods now so you really have nothing to gain. Datacomms Technologies web authoring and data security Paul Bradley, Paul@fatmans.demon.co.uk Http://www.fatmans.demon.co.uk/crypt/ "Don`t forget to mount a scratch monkey" -----BEGIN PGP PUBLIC KEY BLOCK----- Version: 2.6.3ia mQCNAjH9j+cAAAEEAMBvREiQR0ot9dFCO0TiSCSunAYLv2g1Bc6I3bz8FzKXNH53 6mieJf/W4rD+CxJpT0q9RQaaoRtkHJLwbjfK2il3D7mEahMAyqvF/xRJNqkXfhM3 sRJM0Jh43l+W0M5vwokbEbk25/bxWWGspTsLD3YHbzKnG6pOcL5OPIRbv66xAAUR tCdQYXVsIEJyYWRsZXkgPHBhdWxAZmF0bWFucy5kZW1vbi5jby51az6JAJUDBRAy NwfvNkCBjDT0xHEBATQPA/9TORmN/UjNecj03q4anpvdyCLiez5sKuNbnYK50RiP Jj4QpWWvST3smyQ0A86DrZY/re056MXwQmARESx0rFZxdnD0oORICl5r8dJLIy3b j8rbA5olXwZwKz73/X5s13v/pvHYX4cIsbVK8NHXqh5llSKt6TBAuGgkIGF29z5k C4kAlQMFEDI3B9mdtf/umVkv7QEBcRYD/1FBteLqsUmr81euxqqnnrpLlyHb58B/ 9sdATuua4uSjX46hXDZ264YozspNrzSB4NEdrmXOWVX3fiE0ga6XkSSkIeF23V90 En37Z0BdbFzgF00FRYTFyTq8eezQrdg/+rBPUsZUmG5wpq3e12FKHQsX01i+1mB2 YmqqwCV5e95eiQCVAgUQMh8uSb5OPIRbv66xAQEqJwP/fxQyiCasjFcbDpsFfsYp put5cCC/9pOx6X3DlbKShPMpUOS+A9HsTEmJQN8Iawv1nSwPdtc2cR/GhW6ilVjW LSloGdMVLabm9pGpZZMkRaZlXFUkOv7VhfgsUiL+vIDryBCAwUZCzQiWycjt/cPi mUqFH41Z7NkyO8ZFdi5GGX0= =CMZA -----END PGP PUBLIC KEY BLOCK-----