A strategy for finding roots of multivariate polynomials with new applications in attacking RSA variants

We describe a strategy for finding small modular and integer roots of multivariate polynomials using lattice-based Coppersmith techniques. Applying our strategy, we obtain new polynomial-time attacks on two RSA variants. First, we attack the Qiao-Lam scheme that uses a Chinese Remaindering decryption process with a small difference in the private exponents. Second, we attack the so-called Common Prime RSA variant, where the RSA primes are constructed in a way that circumvents the Wiener attack