Improving the parallelized Pollard lambda search on anomalous binary curves
Mathematics of Computation
On random walks for Pollard's Rho method
Mathematics of Computation
Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Identity-Based Encryption from the Weil Pairing
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Speeding Up Pollard's Rho Method for Computing Discrete Logarithms
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
Solving DLP with auxiliary input over an elliptic curve used in TinyTate library
WISTP'11 Proceedings of the 5th IFIP WG 11.2 international conference on Information security theory and practice: security and privacy of mobile devices in wireless communication
Collusion resistant broadcast encryption with short ciphertexts and private keys
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Hierarchical identity based encryption with constant size ciphertext
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Using equivalence classes to accelerate solving the discrete logarithm problem in a short interval
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Security analysis of the strong diffie-hellman problem
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Practical identity-based encryption without random oracles
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Solving a DLP with auxiliary input with the ρ-algorithm
WISA'11 Proceedings of the 12th international conference on Information Security Applications
Remarks on Cheon's algorithms for pairing-related problems
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
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A discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find α from G , αG , α d G in an additive cyclic group generated by an element G of prime order r , and a positive integer d satisfying d |(r −1). The infeasibility of this problem assures the security of some cryptographic schemes. In 2006, Cheon proposed a novel algorithm for solving DLPwAI (Cheon's algorithm). This paper reports our experimental results of Cheon's algorithm by implementing it with some speeding-up techniques. In fact, we have succeeded to solve DLPwAI on a pairing-friendly elliptic curve of 160-bit order in 1314 core days. Implications of our experiments on cryptographic schemes are also discussed.