Efficient checking of computations in number theory

Abstract

We present efficient program checkers for two important number theory problems, integer GCD and modular exponentiation. The notion of program checkers was introduced by Manuel Blum as a new approach to the problem of program correctness. Our result regarding checking integer GCD answers an open problem posed by Blum; furthermore, the checker we give is a constant query checker. The other result paves the way for more robust cryptographic programs, as modular exponentiation is the basis for several cryptosystems, and introduces a new technique for writing checkers, the tester-checker. Taken together, these results lay the foundation for more reliable number-theoretic programs. Further details can found in [AHK].