Recovering Private Keys Generated with Weak PRNGs

Pierre-Alain Fouque (1, 2) , Mehdi Tibouchi (3) , Jean-Christophe Zapalowicz (4)

1 UR - Université de Rennes
2 IUF - Institut universitaire de France
3 NTT Secure Platform Laboratories [Tokyo]
4 CELTIQUE - Software certification with semantic analysis

Suppose that the private key of discrete logarithm-based or factoring-based public-key primitive is obtained by concatenating the outputs of a linear congruential generator. How seriously is the scheme weakened as a result? While linear congruential generators are cryptographically very weak "pseudorandom" number generators, the answer to that question is not immediately obvious, since an adversary in such a setting does not get to examine the outputs of the congruential generator directly, but can only obtain an implicit hint about them—namely the public key. In this paper, we take a closer look at that problem, and show that, in most cases, an attack does exist to retrieve the key much faster than with a naive exhaustive search on the seed of the generator.

Domaines: Cryptographie et sécurité [cs.CR]

Pierre-Alain Fouque, Mehdi Tibouchi, Jean-Christophe Zapalowicz. Recovering Private Keys Generated with Weak PRNGs. Cryptography and Coding - 14th {IMA} International Conference, Dec 2013, Oxford, United Kingdom. pp.158 - 172, ⟨10.1007/978-3-642-45239-0_10⟩. ⟨hal-01094296⟩