A simple and fast probabilistic algorithm for computing square roots modulo a prime number
IEEE Transactions on Information Theory
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
The Relationship Between Breaking the Diffie--Hellman Protocol and Computing Discrete Logarithms
SIAM Journal on Computing
Towards the Equivalence of Breaking the Diffie-Hellman Protocol and Computing Discrete Algorithms
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Assumptions Related to Discrete Logarithms: Why Subtleties Make a Real Difference
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Equitable Key Escrow with Limited Time Span (or, How to Enforce Time Expiration Cryptographically)
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Anonymous Fingerprinting with Direct Non-repudiation
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Efficient designated confirmer signature from bilinear pairings
Proceedings of the 2008 ACM symposium on Information, computer and communications security
A new signature scheme without random oracles from bilinear pairings
VIETCRYPT'06 Proceedings of the First international conference on Cryptology in Vietnam
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The Computational Square-Root Exponent Problem (CSREP), which is a problem to compute a value whose discrete logarithm is a square root of the discrete logarithm of a given value, was proposed in the literature to show the reduction between the discrete logarithm problem and the factoring problem. The CSREP was also used to construct certain cryptography systems. In this paper, we analyze the complexity of the CSREP, and show that under proper conditions the CSREP is polynomial-time equivalent to the Computational Diffie-Hellman Problem (CDHP). We also demonstrate that in group G with certain prime order p, the DLP, CDHP and CSREP may be polynomial time equivalent with respect to the computational reduction for the first time in the literature.