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Group-based cryptography

{{Short description|Application of group theory to 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 non-abelian groups such as a braid group.

Examples

See also

References

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  • {{cite book |first1=A.G. |last1=Myasnikov |first2=V. |last2=Shpilrain |first3=A. |last3=Ushakov |title=Group-based Cryptography |publisher=Birkhauser |series=Advanced Courses in Mathematics – CRM Barcelona |date=2008 |isbn=9783764388270 |url={{GBurl|mEa3BAAAQBAJ|pg=PR7}} }}
  • {{cite book |first1=A.G. |last1=Myasnikov |first2=V. |last2=Shpilrain |first3=A. |last3=Ushakov |title=Non-commutative cryptography and complexity of group-theoretic problems |publisher= |series=Amer. Math. Soc. Surveys and Monographs |date=2011 |isbn=9780821853603 }}
  • {{cite book |first1=M.R. |last1=Magyarik |first2=N.R. |last2=Wagner |chapter=A Public Key Cryptosystem Based on the Word Problem |chapter-url=https://doi.org/10.1007/3-540-39568-7_3 |title=Advances in Cryptology—CRYPTO 1984 |publisher=Springer |doi=10.1007/3-540-39568-7_3 |series=Lecture Notes in Computer Science |volume=196 |date=1985 |isbn=978-3-540-39568-3 |pages=19–36 |url=}}
  • {{cite journal |first1=I. |last1=Anshel |first2=M. |last2=Anshel |first3=D. |last3=Goldfeld |title=An algebraic method for public-key cryptography |journal=Math. Res. Lett. |volume=6 |issue= 3|pages=287–291 |date=1999 |doi= 10.4310/MRL.1999.v6.n3.a3|url=https://www.intlpress.com/site/pub/files/_fulltext/journals/mrl/1999/0006/0003/MRL-1999-0006-0003-a003.pdf |citeseerx=10.1.1.25.8355}}
  • {{cite book |first1=K.H. |last1=Ko |first2=S.J. |last2=Lee |first3=J.H. |last3=Cheon |first4=J.W. |last4=Han |first5=J. |last5=Kang |first6=C. |last6=Park |chapter=New public-key cryptosystem using braid groups |chapter-url=https://link.springer.com/chapter/10.1007/3-540-44598-6_10 |doi=10.1007/3-540-44598-6_10 |citeseerx=10.1.1.85.5306 |title=Advances in Cryptology—CRYPTO 2000 |publisher=Springer |series=Lecture Notes in Computer Science |volume=1880 |date=2000 |isbn=978-3-540-44598-2 |pages=166–183 |url=}}
  • {{cite journal |first1=V. |last1=Shpilrain |first2=G. |last2=Zapata |title=Combinatorial group theory and public key cryptography |journal=Appl. Algebra Eng. Commun. Comput. |volume=17 |issue=3–4 |pages=291–302 |date=2006 |doi=10.1007/s00200-006-0006-9 |citeseerx=10.1.1.100.888 |arxiv=math/0410068 |s2cid=2251819 |url=}}

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Further reading

  • Paul, Kamakhya; Goswami, Pinkimani; Singh, Madan Mohan. (2022). [https://docs.vijnanaparishadofindia.org/jnanabha/jnanabha_volume_52_v2_2022/52_2_p26-218-223.pdf "ALGEBRAIC BRAID GROUP PUBLIC KEY CRYPTOGRAPHY"], [http://www.vijnanaparishadofindia.org/jnanabha Jnanabha], Vol. 52(2) (2022), 218-223. ISSN 0304-9892 (Print) ISSN 2455-7463 (Online)

External links

  • [https://web.archive.org/web/20170717103854/http://kodu.ut.ee/~lipmaa/crypto/link/public/braid/ Cryptography and Braid Groups page] (archived version 7/17/2017)

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Category:Theory of cryptography

Category:Braid groups

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