G - 16th workshop on Elliptic Curve Cryptography

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Problems in ρ-method • Problem1: RW function F(G d ) outputs same points in DB for G d • Problem2: RW function F(G d ) does not output next points • These problems also exist in RW function F(G) G d Since the number of points does not increase we can not find a collision collision!! G k1 25 Copyright 2012 FUJITSU LABORATORIES Ltd.
Causes of Problems • Since RW function randomly generates points, a collision is occurred in points generated by G d • Problem1: a collision occurred in distinguished elements generated by G d • Problem2: a collision occurred in undistinguished elements generated by G d • This collision is called fruitless cycle G d We can not find a collision collision!! G collision!! k1 26 Copyright 2012 FUJITSU LABORATORIES Ltd.
Page 1 and 2: Project Report on Solving Discrete
Page 3 and 4: Pairing-based Cryptosystems • New
Page 5 and 6: Implication to pairing-based crypto
Page 7 and 8: Motivation of Our Project • Recor
Page 9 and 10: Cheon’s Algorithm • Input: G, G
Page 11 and 12: Baby-step Giant-step Method • Fin
Page 13 and 14: Kozaki-Kutsuma-Matsuo’s method
Page 15 and 16: Our Approach: Bucket-sorting 0x0000
Page 17 and 18: 1 PC is used 16 Copyright 2012 FUJI
Page 19 and 20: Estimations: BSGS method r DB Gener
Page 21 and 22: -method on Step1 • Step1 of Cheon
Page 23 and 24: Applying ρ-method on Step 1 (cont
Page 25: Distinguished element technique •
Page 29 and 30: Target Elliptic Curve Parameters
Page 31 and 32: Comparison with BSGS method Require
Page 33 and 34: Difficulties of solving 160-bit ECD
Page 35 and 36: Problem in Parallelization • Prob
Page 37 and 38: Construction of the solving system
Page 39 and 40: Our System for Solving ECDLPwAI •
Page 41 and 42: Chapter 4 r -bit 160-bit Chapter 4
Page 43 and 44: If we can use super computer K …
Page 45 and 46: 160-bit curve case log 2 d 80 # of
Page 47 and 48: Feedback to protocol with static DH
Page 49 and 50: Summary of Our Project Yao-Yoshida
Page 51 and 52: 50 Copyright 2012 FUJITSU LABORATOR
Page 53 and 54: References [WAIS10] T. Izu, M. Take

G - 16th workshop on Elliptic Curve Cryptography

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