G - 16th workshop on Elliptic Curve Cryptography

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Target <strong>Elliptic</strong> <strong>Curve</strong> Parameters •Target: TinyTate library [TinyTate07] •Pairing-based cryptographic library for embedded devices • Parameters •E/GF(p256): y 2 = x 3 + x (Supersingular) •p256 = 3778160688 9598235856 7455764726 5839472148 1625071533 3029839574 7614203820 7746163 (256-bit) •#E = 3778160688 9598235856 7455764726 5839472148 1625071533 3029839574 7614203820 7746164 (256-bit) •r = 1701411885 3107163264 4604909702 696927233 (128-bit) •d = 1268213655 0675316736 (64-bit) ← Ideal for adversaries •d1 = 3662760472 (32-bit) •d2 = 3561198752 (32-bit) 15 Copyright 2012 FUJITSU LABORATORIES Ltd.
1 PC is used 16 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: Our Approach: Bucket-sorting 0x0000
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 and 26: Distinguished element technique •
Page 27 and 28: Causes of Problems • Since RW fun
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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