The padding scheme for RSA signatures

The RSA scheme is used to sign messages; however, in order to avoid forgeries, a message can be padded with a fixed string of data P. De Jonge and Chaum showed in 1985 that forgeries can be constructed if the size of P (measured in bytes) is less than the size of N/3, where N is the RSA modulus. Girault and Misarsky then showed in 1997 that forgeries can be constructed if the size of P is less than the size of N/2. In 2001, Brier, Clavier, Coron and Naccache showed that forgeries can still be constructed when the size of P is less than two thirds the size of N. In this paper, we demonstrate that this padding scheme is always insecure; however, the complexity of actually finding a forgery is O(N). We then focus specifically on the next unsettled case, where P is less than 3/4 the size of N and show that finding a forgery is equivalent to solving a set of diophantine equations. While we are not able to solve these equations, this work may lead to a break-through by means of algebraic number theory techniques

Divisibility, Smoothness and Cryptographic Applications

This paper deals with products of moderate-size primes, familiarly known as smooth numbers. Smooth numbers play a crucial role in information theory, signal processing and cryptography. We present various properties of smooth numbers relating to their enumeration, distribution and occurrence in various integer sequences. We then turn our attention to cryptographic applications in which smooth numbers play a pivotal role