Partly motivated by the possibility of quantum computation eventually breaking the security of cryptography based on abelian groups, such as elliptic curves, there are proposals to use non-abelian braid groups for purposes of cryptography (“post-quantum cryptography”).
An early proposal was to use the Conjugacy Search Problem in braid groups as a computationally hard problem for cryptography. This approach, though, was eventually found not to be viable.
Original articles:
Iris Anshel, M. Anshel and D. Goldfeld, An algebraic method for public-keycryptography, Math. Research Letters 6 (1999), 287–291 (pdf)
K.H. Ko, S.J. Lee, J.H. Cheon , J.W. Han, J. Kang, C. Park , New Public-Key Cryptosystem Using Braid Groups, In: M. Bellare (ed.) Advances in Cryptology — CRYPTO 2000 Lecture Notes in Computer Science, vol 1880. Springer 2000 (doi:10.1007/3-540-44598-6_10)
Review:
Karl Mahlburg, An Overview of Braid Group Encryption, 2004 (pdf)
Parvez Anandam, Introduction to Braid Group Cryptography, 2006 (pdf)
David Garber, Braid Group Cryptography, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore (arXiv:0711.3941, doi:10.1142/9789814291415_0006)
Cryptowiki, Cryptosystems based on braid groups
A followup proposal was to use the problem of reversing E-multiplication in braid groups, thought to remedy the previous problems.
Original article:
Review:
But other problems were found with this approach, rendering it non-viable.
Original article:
Review:
The basic idea is still felt to be promising:
Xiaoming Chen, Weiqing You, Meng Jiao, Kejun Zhang, Shuang Qing, Zhiqiang Wang, A New Cryptosystem Based on Positive Braids (arXiv:1910.04346)
Garry P. Dacillo, Ronnel R. Atole, Braided Ribbon Group -based Asymmetric Cryptography, Solid State Technology Vol. 63 No. 2s (2020) (JSST:5573)
But further attacks are being discussed:
As are further ways around these:
Last revised on May 25, 2021 at 14:55:14. See the history of this page for a list of all contributions to it.