Crypto Wiki

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.


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


  • 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.

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