Braid-based cryptography

Short Description
Braid-based cryptography appeared recently: its birthdate can be traced back to … to give a sketchy description of braid-based cryptography, including a …

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Content
Contemporary Mathematics
Braid-based cryptography
Patrick DEHORNOY
Abstract. We survey some of the recently developed cryptographic schemes
involving Artin’s braid groups, as well as the attacks against these schemes.
We also point out some hints for future work.
Contents:
1. Background on braids
1.1. Braid groups
1.2. The greedy normal form
1.3. Implementation of braids
2. Braid-based schemes
2.1. Key exchange
2.2. Enciphering-deciphering
2.3. Authentication
2.4. Signature
3. Attacks against the braid schemes
3.1. Solutions to the Conjugacy Problem
3.2. Attacks based on length
3.3. Attacks based on linear representations
3.4. Are these attacks dangerous?
4. Clues for further research
4.1. Key generation
4.2. Random drawing and security proofs
4.3. Using braid words and braid reduction
4.4. Hash functions
4.3. Resorting to other braid problems
5. Conclusion
Braid-based cryptography appeared recently: its birthdate can be traced back to
the pioneering papers [3] and [42] published by Anshel, Anshel & Goldfeld in 1999
and by Ko, Lee, Cheon, Han, Kang and Park in 2000. The subject has met with
2000 Mathematics Subject Classification. 20F36, 94A60, 94A62, 68P25.
Key words and phrases. braid group, normal form, handle reduction, word problem, conjugacy
problem.
The author thanks Herv’…