Group-based cryptography explained

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 non-abelian 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

• Book: A.G. . Myasnikov . V. . Shpilrain . A. . Ushakov . [{{GBurl|mEa3BAAAQBAJ|pg=PR7}} Group-based Cryptography ]. Birkhauser . Advanced Courses in Mathematics – CRM Barcelona . 2008 . 9783764388270 .
• Book: A.G. . Myasnikov . V. . Shpilrain . A. . Ushakov . Non-commutative cryptography and complexity of group-theoretic problems . Amer. Math. Soc. Surveys and Monographs . 2011 . 9780821853603 .
• Book: M.R. . Magyarik . N.R. . Wagner . A Public Key Cryptosystem Based on the Word Problem . https://doi.org/10.1007/3-540-39568-7_3 . Advances in Cryptology—CRYPTO 1984 . Springer . 10.1007/3-540-39568-7_3 . Lecture Notes in Computer Science . 196 . 1985 . 978-3-540-39568-3 . 19–36 .
• I. . Anshel . M. . Anshel . D. . Goldfeld . An algebraic method for public-key cryptography . Math. Res. Lett. . 6 . 3. 287–291 . 1999 . 10.4310/MRL.1999.v6.n3.a3. 10.1.1.25.8355.
• Book: K.H. . Ko . S.J. . Lee . J.H. . Cheon . J.W. . Han . J. . Kang . C. . Park . New public-key cryptosystem using braid groups . https://link.springer.com/chapter/10.1007/3-540-44598-6_10 . 10.1007/3-540-44598-6_10 . 10.1.1.85.5306 . Advances in Cryptology—CRYPTO 2000 . Springer . Lecture Notes in Computer Science . 1880 . 2000 . 978-3-540-44598-2 . 166–183 .
• V. . Shpilrain . G. . Zapata . Combinatorial group theory and public key cryptography . Appl. Algebra Eng. Commun. Comput. . 17 . 3–4 . 291–302 . 2006 . 10.1007/s00200-006-0006-9 . 10.1.1.100.888 . math/0410068 . 2251819 .

Further reading

• Paul, Kamakhya; Goswami, Pinkimani; Singh, Madan Mohan. (2022). "ALGEBRAIC BRAID GROUP PUBLIC KEY CRYPTOGRAPHY", Jnanabha, Vol. 52(2) (2022), 218-223. ISSN 0304-9892 (Print) ISSN 2455-7463 (Online)

External links

• Cryptography and Braid Groups page (archived version 7/17/2017)