On the Notion of Pseudo-Free Groups

We explore the notion of a pseudo-free group, first introduced by Hohenberger [Hoh03], and provide an alternative stronger definition. We show that if Z∗ n is a pseudo-free abelian group (as we conjecture), then Z∗ n also satisfies the Strong RSA Assumption [FO97,CS00,BP97]. Being a “pseudo-free abelian group” may be the strongest natural cryptographic assumption one can make about a group such as Z∗ n. More generally, we show that a pseudo-free group satisfies several standard cryptographic assumptions, such as the difficulty of computing discrete logarithms.

• Type: Conference
• Year: 2004
• Where: TCC
• Authors: Ronald L. Rivest
• Keywords: Cryptographic Assumptions, Cryptography, Pseudo-free Abelian Group, Pseudo-free Group, TCC 2004