Group-based cryptography

Group-based cryptography is a use of groups to construct cryptographic primitives. A group is a very general algebraic object and most cryptographic schemes use groups in some way. In particular Diffie–Hellman key exchange uses finite cyclic groups. So the term group-based cryptography refers mostly to cryptographic protocols that use infinite nonabelian groups such as a braid group.

Examples

• Shpilrain–Zapata public-key protocols
• Magyarik–Wagner public key protocol
• Anshel–Anshel–Goldfeld key exchange
• Ko–Lee et al. key exchange protocol

See also

• Non-commutative cryptography

References

• V. Shpilrain and G. Zapata, Combinatorial group theory and public key cryptography, Appl. Algebra Eng. Commun. Comput. 17 (2006), no. 3-4, 291–302.
• A. G. Myasnikov, V. Shpilrain, and A. Ushakov, Group-based Cryptography. Advanced Courses in Mathematics – CRM Barcelona, Birkhauser Basel, 2008.
• M. R. Magyarik and N. R. Wagner, A Public Key Cryptosystem Based on the Word Problem. Advances in Cryptology—CRYPTO 1984, Lecture Notes in Computer Science 196, pp. 19–36. Springer, Berlin, 1985.
• I. Anshel, M. Anshel, and D. Goldfeld, An algebraic method for public-key cryptography, Math. Res. Lett. 6 (1999), pp. 287–291.
• K. H. Ko, S. J. Lee, J. H. Cheon, J. W. Han, J. Kang, and C. Park, New public-key cryptosystem using braid groups. Advances in Cryptology—CRYPTO 2000, Lecture Notes in Computer Science 1880, pp. 166–183. Springer, Berlin, 2000.

External links

• Cryptography and Braid Groups page