The RSA Group is Pseudo-Free
- Cite this paper as:
- Micciancio D. (2005) The RSA Group is Pseudo-Free. In: Cramer R. (eds) Advances in Cryptology – EUROCRYPT 2005. EUROCRYPT 2005. Lecture Notes in Computer Science, vol 3494. Springer, Berlin, Heidelberg
We prove, under the strong RSA assumption, that the group of invertible integers modulo the product of two safe primes is pseudo-free. More specifically, no polynomial time algorithm can output (with non negligible probability) an unsatisfiable system of equations over the free abelian group generated by the symbols g1,...,gn, together with a solution modulo the product of two randomly chosen safe primes when g1,...,gn are instantiated to randomly chosen quadratic residues. Ours is the first provably secure construction of pseudo-free abelian groups under a standard cryptographic assumption, and resolves a conjecture of Rivest (TCC 2004).