TY - GEN
T1 - Analysis of a method to eliminate fruitless cycles for Pollard’s rho method with skew Frobenius mapping over a Barreto-Naehrig curve
AU - Miura, Hiromasa
AU - Matsumura, Rikuya
AU - Kusaka, Takuya
AU - Nogami, Yasuyuki
N1 - Funding Information:
ACKNOWLEDGMENT The authors thank the anonymous reviewers to improve this work. This work was supported by the JSPS KAKENHI Challenging Research (Pioneering) 19H05579.
Publisher Copyright:
© 2020 IEEE
PY - 2020/11
Y1 - 2020/11
N2 - Pollard’s rho method is one of the most efficient methods for solving elliptic curve discrete logarithm problem (ECDLP) in elliptic curve cryptography. Pollard’s rho method with skew Frobenius mapping can solve ECDLP over a Barreto-Naehrig (BN) curve efficiently. Pollard’s rho method may result in an unsolvable cycle called a fruitless cycle. When a random walk pass results in a fruitless cycle, the random walk pass must restart with a different starting point. However, an effective method for eliminating the fruitless cycle has been not proposed yet. This paper proposes a method for eliminating the fruitless cycle in Pollard’s rho method with skew Frobenius mapping. In addition, the authors apply the proposed method to a BN curve with 17-bit parameters and confirm the effectiveness.
AB - Pollard’s rho method is one of the most efficient methods for solving elliptic curve discrete logarithm problem (ECDLP) in elliptic curve cryptography. Pollard’s rho method with skew Frobenius mapping can solve ECDLP over a Barreto-Naehrig (BN) curve efficiently. Pollard’s rho method may result in an unsolvable cycle called a fruitless cycle. When a random walk pass results in a fruitless cycle, the random walk pass must restart with a different starting point. However, an effective method for eliminating the fruitless cycle has been not proposed yet. This paper proposes a method for eliminating the fruitless cycle in Pollard’s rho method with skew Frobenius mapping. In addition, the authors apply the proposed method to a BN curve with 17-bit parameters and confirm the effectiveness.
KW - Barreto-Naehrig curve
KW - ECDLP
KW - Fruitless cycle
KW - Pollard’s rho method
KW - Skew Frobenius mapping
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U2 - 10.1109/CANDAR51075.2020.00029
DO - 10.1109/CANDAR51075.2020.00029
M3 - Conference contribution
AN - SCOPUS:85104648880
T3 - Proceedings - 2020 8th International Symposium on Computing and Networking, CANDAR 2020
SP - 160
EP - 166
BT - Proceedings - 2020 8th International Symposium on Computing and Networking, CANDAR 2020
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 8th International Symposium on Computing and Networking, CANDAR 2020
Y2 - 24 November 2020 through 27 November 2020
ER -