Efficient Password-Authenticated Key Exchange Based on RSA
In this paper, we propose an efficient password-authenticated key exchange (PAKE) based on RSA, called RSA-EPAKE. Unlike SNAPI using a prime pubic key e greater than an RSA modulus n, RSA-EPAKE uses the public key e of a 96-bit prime, where e = 2H(n, s) + 1 for some s. By the Prime Number Theorem, it is easy to find such an s. But the probability that an adversary finds n and s with \(\gcd(e, \phi(n)) \neq 1\) is less than 2− 80. Hence, in the same as SNAPI, RSA-EPAKE is also secure against e-residue attacks. The computational load on Alice (or Server) and Bob (or Client) in RSA-EPAKE is less than in the previous RSA-based PAKEs such as SNAPI, PEKEP ,CEKEP, and QR-EKE. In addition, the computational load on Bob in RSA-EPAKE is less than in PAKEs based on Diffie-Hellman key exchange (DHKE) with a 160-bit exponent. If we exclude perfect forward secrecy from consideration, the computational load on Alice is a little more than that in PAKEs based on DHKE with a 160-bit exponent. In this paper, we compare RSA-EPAKE with SNAPI, PEKEP, and CEKEP in computation and the number of rounds, and provide a formal security analysis of RSA-EPAKE under the RSA assumption in the random oracle model.
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