Authenticated Key Exchange Protocols Based on Factoring Assumption

Abstract

This paper investigates authenticated key exchange protocols over signed quadratic residues group $\mathbb{QR}_N^+$ , which is originally used for encryption schemes. The key technical tool developed by Hofheinz et al. is that in group $\mathbb{QR}_N^+$ the strong Diffie-Hellman (SDH) problem is implied by the factoring assumption. To apply group $\mathbb{QR}_N^+$ to authenticated key exchange protocols in the enhanced Canetti-Krawczyk (eCK) model, we extend Hofheinz et al.'s technique and introduce a new proof approach called k'—'th power. The k'—'th power proof approach is almost generic, i.e., applying it to many, if not all, existing authenticated Diffie-Hellman key exchange protocols in eCK model under gap assumption immediately produces protocols in eCK model under factoring assumption if they work over $\mathbb{QR}_N^+$ . As one application of k'—'th power approach, we show that FS protocol, in which k is a constant, is provably secure in eCK model under factoring assumption if it works over $\mathbb{QR}_N^+$ . Our technique also applies to other protocols, e.g., UP,HMQV and its variants, in which k is a non-constant, but at the cost of degrading a factor in the reduction.