BYTE
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
Experimantal Analysis of Cheon's Algorithm Against Pairing-Friendly Curves
AINA '11 Proceedings of the 2011 IEEE International Conference on Advanced Information Networking and Applications
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
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
Remarks on Cheon's algorithms for pairing-related problems
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Solving a discrete logarithm problem with auxiliary input on a 160-bit elliptic curve
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
| Hi-index | 0.00 |
The discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find a positive integer α from elements G, αG, αdG in an additive cyclic group generated by G of prime order r and a positive integer d dividing r ---1. In 2011, Sakemi et al. implemented Cheon's algorithm for solving DLPwAI, and solved a DLPwAI in a group with 128-bit order r in about 131 hours with a single core on an elliptic curve defined over a prime finite field which is used in the TinyTate library for embedded cryptographic devices. However, since their implementation was based on Shanks' Baby-step Giant-step (BSGS) algorithm as a sub-algorithm, it required a large amount of memory (246 GByte) so that it was concluded that applying other DLPwAIs with larger parameter is infeasible. In this paper, we implemented Cheon's algorithm based on Pollard's ρ-algorithm in order to reduce the required memory. As a result, we have succeeded solving the same DLPwAI in about 136 hours by a single core with less memory (0.5 MByte).