A Method to Eliminate Fruitless Cycles for Pollard's Rho Method by Splitting a Seed-point Table for a Random Walk

The most efficient method for solving ECDLP is the Pollard-Rho method, which is known to be more efficient in solving ECDLP by using skew Frobenius mapping and splitting a seed-point table to eliminate the fruitless cycles, but some fruitless cycles increase non-negligibly. In this paper, we propose...

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Bibliographic Details
Main Authors: Kanzawa, Shota, Miura, Hiromasa, Nogami, Yasuyuki, Kodera, Yuta, Kusaka, Takuya
Format: Conference Proceeding
Language:English
Subjects:
Barreto-Naehrig curve
Cryptography
ECDLP
Elliptic curve cryptography
Elliptic curves
Encryption
Foot
fruitless cycle
Internet of Things
Pollard's rho method
skew Frobenius mapping
Zirconium
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Summary:The most efficient method for solving ECDLP is the Pollard-Rho method, which is known to be more efficient in solving ECDLP by using skew Frobenius mapping and splitting a seed-point table to eliminate the fruitless cycles, but some fruitless cycles increase non-negligibly. In this paper, we propose a method to further reduce the number of fruitless cycles in the Pollard's rho method using skew Frobenius mapping. We also apply the proposed method to a 21-bit BN curve and confirm its effectiveness.
ISSN:2379-1896
DOI:10.1109/CANDAR57322.2022.00022