Open AccessPosted Content
Length-Based Attacks for Certain Group Based Encryption Rewriting Systems
James P. Hughes,Allen Tannenbaum +1 more
TL;DR: A probabilistic attack on public key cryptosystems based on the word/conjugacy problems for finitely presented groups of the type proposed recently by Anshel, Anshel and Goldfeld is described.
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Abstract: In this note, we describe a probabilistic attack on public ke y cryptosystems based on the word/conjugacy problems for finitely presented groups of the type proposed r ecently by Anshel, Anshel and Goldfeld. In such a scheme, one makes use of the property that in the given group the word problem has a polynomial time solution, while the conjugacy problem has no known polynomial solution. An example is the braid group from topology in which the word problem is solvable in polynomial time while the only known solutions to the conjugacy problem are exponential. The attack in this paper is based on having a canonical representative of each string relative to which a length function may be computed. Hence the term length attack. Such canonical representatives are known to exist for the braid group.
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Citations
[서평]「Applied Cryptography」
염흥렬
- 01 Apr 1997
TL;DR: The objective of this paper is to give a comprehensive introduction to applied cryptography with an engineer or computer scientist in mind on the knowledge needed to create practical systems which supports integrity, confidentiality, or authenticity.
2.1K
[기술해설]암호법(Cryptography)
조위덕
- 01 Jul 1987
TL;DR: This paper is basically a survey paper and it has studied the importance, features, advantages, and disadvantages and authenticated on the topic cryptography.
303
•Book
Non-Commutative Cryptography and Complexity of Group-Theoretic Problems
Alexei Myasnikov,Vladimir Shpilrain,Alexander Ushakov +2 more
- 09 Nov 2011
TL;DR: This book explores how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public-key cryptography and describes new interesting developments in the algorithmic theory of solvable groups.
184
•Posted Content
Length-based conjugacy search in the braid group
TL;DR: Experimental results suggest that anfeasible computational power is required for this method to solve the Generalized Conjugacy Search Problem when its parameters are as in existing protocols.
Length based attack and braid groups: cryptanalysis of Anshel-Anshel-Goldfeld key exchange protocol
Alex D. Myasnikov,Alexander Ushakov +1 more
- 16 Apr 2007
TL;DR: It is shown that accurately designed length based attack can successfully break a random instance of the simultaneous conjugacy search problem for certain parameter values and it is argued that the public/private information chosen uniformly random leads to weak keys.
References
[서평]「Applied Cryptography」
염흥렬
- 01 Apr 1997
TL;DR: The objective of this paper is to give a comprehensive introduction to applied cryptography with an engineer or computer scientist in mind on the knowledge needed to create practical systems which supports integrity, confidentiality, or authenticity.
2.1K
•Book
Using Algebraic Geometry
David A. Cox,John Little,Donal O'Shea +2 more
- 01 Jan 1998
TL;DR: The Berlekamp-Massey-Sakata Decoding Algorithm is used for solving Polynomial Equations and for computations in Local Rings.
Artin-Gruppen und Coxeter-Gruppen
Egbert Brieskorn,Kyoji Saito +1 more
TL;DR: The Coxeter-Gruppen as mentioned in this paper are a subset of the Gruppen of the Z6pfegruppe G, i.e., the groups with the most symmetrischen structure.
615
New Public-Key Cryptosystem Using Braid Groups
Ki Hyoung Ko,Sangjin Lee,Jung Hee Cheon,Jae Woo Han,Ju-Sung Kang,Choonsik Park +5 more
- 20 Aug 2000
TL;DR: The aim of this article is to show that the braid groups can serve as a good source to enrich cryptography and to propose and implement a new key agreement scheme and public key cryptosystem based on these primitives in thebraid groups.