A weak key test for braid based cryptography

Designs, Codes, and Cryptography

Volumn 39, Issue 3, 2006, Pages 347-373

  Maffre, Samuel ^a  

^a UNIVERSITY OF LIMOGES   (France)

Author keywords

Braid groups; Conjugacy problem; Cryptanalysis; Random generator; Weak key test

Indexed keywords

ALGORITHMS; POLYNOMIALS; PROBLEM SOLVING; RANDOM PROCESSES;

BRAID GROUPS; CONJUGACY PROBLEM; CRYPTANALYSIS; RANDOM GENERATOR;

CRYPTOGRAPHY;

EID: 33645985154     PISSN: 09251022     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10623-005-5382-9     Document Type: Article

References (25)

1. Anshel I, Goldfeld D (1999). An algebraic method for public-key cryptography. Math Res Lett 6:287-291
2. Anshel I, Fischer B, Goldfeld D (2001). New key agreement protocols in braid group cryptography, RSA 2001, LNCS 2020, 1-15
3. Artin E (1947). Theory of braids. Anna Math 48:101-126
4. Cha JC, Ko KH, Lee SJ, Han JW, Cheon JH (2001). An efficient implementation of braid groups, Asiacrypt 2001, LNCS 2248, pp 144-156
5. Cheon JH, Jun B (2003). A polynomial rime algorithm for the braid Diffie-Hellman conjugacy problem. Crypto 2003
6. Dehornoy P (1997). A fast method for computing braids. Adv Math 125(2):200-235
7. Dehornoy P (2004). Braid-based cryptography. Contemp Math Amer Math Soc 360:5-33
8. Elrifai EA, Morton HR (1994). Algorithms for positive braids. Quart J Math Oxford 45(2):479-497
9. Epstein D, Cannon J, Holt D, Levy S, Patterson M, Thurston W (1992). Word processing in groups. Jones et Barlett Publishers, Boston, chapter 9
10. Franco N, Gonzalez-Meneses J (2003). Conjugacy problem for braid groups and Garside groups. J Algebra 266(1):112-132
11. Garber D, Kaplan S, Teicher M, Tsaban B, Vishne U (2002). Length-based conjugacy search in the Braid group. http://arXiv.org/abs/math.GR/0209267
12. Garside FA (1969). The braid group and other groups. Quart J Math Oxford 20-78, 235-254
13. Gebhardt V (2003). A new approach to the conjugacy problem in Garside groups to appear in J Algebra: http://arXiv.org/abs/math.GT/0306199
14. Hofheinz D, Steinwandt R (2003). A practical attack on some braid group cryptographic primitives, PKC 2003, LNCS 2567, pp 187-198
15. Hughes J (2002). A Linear Algebraic Attack on the AAFG1 Braid Group Cryptosystem, ACISP 2002, LNCS 2384, 02, pp 176-189
16. Hughes J (2000). Allen Tannenbaum, Length-based attacks for certain group based encryption rewriting systems, Inst. for Math, and its Applic. Minneapolis
17. Jacquemard A (1990). About the effective classification of conjugacy classes of braids. J Pure Appl Algebra 63(2):161-169
18. Ko KH, Choi DH, Cho MS, Lee JW (2002). New Signature Scheme Using Conjugacy Problem: http://eprint.iacr.org/2002/168/
19. Ko KH, Lee SJ, Cheon JH, Han JW, Kang JS, Park C (2000). New public-key cryptosystem using braid groups, Crypto 2000, LNCS 1880, pp 166-184
20. Lee SJ, Lee EK (2002). Potential weakness of the commutator key agreement protocol based on braid groups, Eurocrypt 2002, LNCS 2332, pp 14-28
21. Lee E, Park JH (2003). Cryptanalysis of the public-key encryption based on braid groups, Eurocrypt 2003, LNCS 2656
22. Maffre S (2005). Reduction of conjugacy problem in braid groups, using two Garside structures, WCC 2005, pp 214-224
23. Michel J (1999). A note on words in braid monoids. J Algebra 215:366-377
24. Sibert H (2003). Algorithmique des groupes de tresses, Ph.D. Lab. LMNO
25. Sibert H, Dehornoy P, Girault M (2003). Entity authentification schemes using braid word reduction, WCC 2003, pp 153-163