TY - GEN

T1 - Solving a discrete logarithm problem with auxiliary input on a 160-bit elliptic curve

AU - Sakemi, Yumi

AU - Hanaoka, Goichiro

AU - Izu, Tetsuya

AU - Takenaka, Masahiko

AU - Yasuda, Masaya

N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2012

Y1 - 2012

N2 - A discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find α from G, αG, α dG 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.

AB - A discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find α from G, αG, α dG 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.

UR - http://www.scopus.com/inward/record.url?scp=84861691788&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861691788&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-30057-8_35

DO - 10.1007/978-3-642-30057-8_35

M3 - Conference contribution

AN - SCOPUS:84861691788

SN - 9783642300561

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 595

EP - 608

BT - Public Key Cryptography, PKC 2012 - 15th International Conference on Practice and Theory in Public Key Cryptography, Proceedings

T2 - 15th International Conference on Practice and Theory in Public Key Cryptography, PKC 2012

Y2 - 21 May 2012 through 23 May 2012

ER -