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

• Magyarik-Wagner public key protocol
• Anshel-Anshel-Goldfeld key exchange
• Ko-Lee et. al Key exchange protocol

References

• 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.