Factoring Products of Braids via Garside Normal Form

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Authors

Colleges, School and Institutes

External organisations

  • Royal Holloway, University of London

Abstract

Braid groups are infinite non-abelian groups naturally arising from geometric braids. For two decades they have been proposed for cryptographic use. In braid group cryptography public braids often contain secret braids as factors and it is hoped that rewriting the product of braid words hides individual factors. We provide experimental evidence that this is in general not the case and argue that under certain conditions parts of the Garside normal form of factors can be found in the Garside normal form of their product. This observation can be exploited to decompose products of braids of the form ABC when only B is known. Our decomposition algorithm yields a universal forgery attack on WalnutDSA™, which is one of the 20 proposed signature schemes that are being considered by NIST for standardization of quantum-resistant public-key cryptography. Our attack on WalnutDSA™ can universally forge signatures within seconds for both the 128-bit and 256-bit security level, given one random message-signature pair. The attack worked on 99.8% and 100% of signatures for the 128-bit and 256-bit security levels in our experiments. Furthermore, we show that the decomposition algorithm can be used to solve instances of the conjugacy search problem and decomposition search problem in braid groups. These problems are at the heart of other cryptographic schemes based on braid groups.

Details

Original languageEnglish
Title of host publicationPublic-Key Cryptography – PKC 2019 - 22nd IACR International Conference on Practice and Theory of Public-Key Cryptography, Proceedings
Subtitle of host publication22nd IACR International Conference on Practice and Theory of Public-Key Cryptography, Beijing, China, April 14-17, 2019, Proceedings, Part II
EditorsKazue Sako, Dongdai Lin
Publication statusE-pub ahead of print - 6 Apr 2019
Event2nd IACR International Conference on Practice and Theory of Public-Key Cryptography (PKC 2019) - Beijing, China
Duration: 14 Apr 201917 Apr 2019

Publication series

NameLecture Notes in Computer Science
Volume11443 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference2nd IACR International Conference on Practice and Theory of Public-Key Cryptography (PKC 2019)
CountryChina
CityBeijing
Period14/04/1917/04/19