Random oracles are practical: a paradigm for designing efficient protocols
CCS '93 Proceedings of the 1st ACM conference on Computer and communications security
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Open Key Exchange: How to Defeat Dictionary Attacks Without Encrypting Public Keys
Proceedings of the 5th International Workshop on Security Protocols
Password Authenticated Key Exchange Based on RSA for Imbalanced Wireless Networks
ISC '02 Proceedings of the 5th International Conference on Information Security
Encrypted Key Exchange: Password-Based Protocols SecureAgainst Dictionary Attacks
SP '92 Proceedings of the 1992 IEEE Symposium on Security and Privacy
Number theoretic attacks on secure password schemes
SP '97 Proceedings of the 1997 IEEE Symposium on Security and Privacy
Number Theory: An Introduction via the Distribution of Primes
Number Theory: An Introduction via the Distribution of Primes
The exact security of digital signatures-how to sign with RSA and Rabin
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Authenticated key exchange secure against dictionary attacks
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Efficient password-authenticated key exchange based on RSA
CT-RSA'07 Proceedings of the 7th Cryptographers' track at the RSA conference on Topics in Cryptology
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The RSA-based Password-Authenticated Key Exchange (PAKE) protocols have been proposed to realize both mutual authentication and generation of secure session keys where a client is sharing his/her password only with a server and the latter should generate its RSA public/private key pair (e, n), (d, n) every time due to the lack of PKI (Public-Key Infrastructures). One of the ways to avoid a special kind of off-line (so called e-residue) attacks in the RSA-based PAKE protocols is to deploy a challenge/response method by which a client verifies the relative primality of e and φ(n) interactively with a server. However, this kind of RSA-based PAKE protocols did not give any proof of the underlying challenge/response method and therefore could not specify the exact complexity of their protocols since there exists another security parameter, needed in the challenge/response method. In this paper, we first present an RSA-based PAKE (RSA-PAKE) protocol that can deploy two different challenge/response methods (denoted by Challenge/Response Method1 and Challenge/Response Method2). The main contributions of this work include: (1) Based on the number theory, we prove that the Challenge/Response Method1 and the Challenge/Response Method2 are secure against e-residue attacks for any odd prime e; (2) With the security parameter for the on-line attacks, we show that the RSA-PAKE protocol is provably secure in the random oracle model where all of the off-line attacks are not more efficient than on-line dictionary attacks; and (3) By considering the Hamming weight of e and its complexity in the RSA-PAKE protocol, we search for primes to be recommended for a practical use. We also compare the RSA-PAKE protocol with the previous ones mainly in terms of computation and communication complexities.