Entity authentication schemes using braid word reduction

Artin's braid groups currently provide a promising background for cryptographical applications, since the first cryptosystems using braids were introduced in [I. Anshel, M. Anshel, D. Goldfeld, An algebraic method for public-key cryptography, Math. Res. Lett. 6 (1999) 287–291, I. Anshel, M. Anshel, B. Fisher, D. Goldfeld, New key agreement schemes in braid group cryptography, RSA 2001, K.H. Ko, S.J. Lee, J.H. Cheon, J.W. Han, J.S. Kang, C. Park, New public-key cryptosystem using braid groups, Crypto 2000, pp. 166–184] (see also [V.M. Sidelnikov, M.A. Cherepnev, V.Y. Yashcenko, Systems of open distribution of keys on the basis of noncommutative semigroups, Ross. Acad. Nauk Dokl. 332-5 (1993); English translation: Russian Acad. Sci. Dokl. Math. 48-2 (1194) 384–386]). A variety of key agreement protocols based on braids have been described, but few authentication or signature schemes have been proposed so far. We introduce three authentication schemes based on braids, two of them being zero-knowledge interactive proofs of knowledge. Then we discuss their possible implementations, involving normal forms or an alternative braid algorithm, called handle reduction, which can achieve good efficiency under specific requirements.