Improved Modular Inversion over GF(p)

The Modular Inversion Hidden Number Problem

We study a class of problems called Modular Inverse Hidden Number Problems (MIHNPs). The basic problem in this class is the following: Given many pairs 〈 xi, msbk ( (α+ xi) −1 mod p )〉 for random xi ∈ Zp the problem is to find α ∈ Zp (here msbk(x) refers to the k most significant bits of x). We describe an algorithm for this problem when k > (log2 p)/3 and conjecture that the problem is hard wh...

The CREW PRAM Complexity of Modular Inversion

On the modular inversion hidden number problem

We give a rigorous deterministic polynomial time algorithm for the modular inversion hidden number problem introduced by D. Boneh, S. Halevi and N. A. Howgrave-Graham in 2001. For our algorithm we need to be given about 2/3 of the bits of the output, which matches one of the heuristic algorithms of D. Boneh, S. Halevi and N. A. Howgrave-Graham and answers one of their open questions. However th...

Using an RSA Accelerator for Modular Inversion

We present a very simple new algorithm for modular inversion. Modular inversion can be done by the extended Euclidean algorithm. We substitute the extended Euclidean algorithm by a standard (non-extended) Euclidean algorithm that works on integers of approximately double the length of the modulus. This substitution can be very useful on smart card coprocessors, since in some cases computations ...

Notably improved DMPS data inversion