A New Cryptosystem Based on Positive Braids

The braid group is an important non commutative group, at the same time, it is an important tool in quantum field theory with better topological structure, and often used as a res-earch carrier for anti-quantum cryptographic algorithms. This paper proposed a difficult problem on a positive braid semi-group, and proved that the difficulty is not lower than the conju-gate search problem. Based on this new difficult problem, we pr-opose a new cryptosystem, which include a key exchange protocol and a public key encryption algorithm. Since our cryptosystem is implemented on a semi-group, it effectively avoids the analysis of attack algorithms on the cluster and makes our algorithm more secure.

[1]  Volker Gebhardt,et al.  Conjugacy Search in Braid Groups , 2006, Applicable Algebra in Engineering, Communication and Computing.

[2]  Sean Clark,et al.  Quantum Supergroups V. Braid Group Action , 2014, 1409.0448.

[3]  Iris Anshel,et al.  New Key Agreement Protocols in Braid Group Cryptography , 2001, CT-RSA.

[4]  Patrick Dehornoy Braid-based cryptography , 2004 .

[5]  Jung Hee Cheon,et al.  A Polynomial Time Algorithm for the Braid Diffie-Hellman Conjugacy Problem , 2003, CRYPTO.

[6]  Sangjin Lee,et al.  Potential Weaknesses of the Commutator Key Agreement Protocol Based on Braid Groups , 2002, EUROCRYPT.

[7]  F. A. Garside,et al.  THE BRAID GROUP AND OTHER GROUPS , 1969 .

[8]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[9]  Alexander Ushakov,et al.  Length Based Attack and Braid Groups: Cryptanalysis of Anshel-Anshel-Goldfeld Key Exchange Protocol , 2007, Public Key Cryptography.

[10]  Allen R. Tannenbaum,et al.  Length-Based Attacks for Certain Group Based Encryption Rewriting Systems , 2003, IACR Cryptol. ePrint Arch..

[11]  Alexei G. Myasnikov,et al.  A Practical Attack on a Braid Group Based Cryptographic Protocol , 2005, CRYPTO.

[12]  Christof Zalka,et al.  Shor's discrete logarithm quantum algorithm for elliptic curves , 2003, Quantum Inf. Comput..

[13]  D. Goldfeld,et al.  An algebraic method for public-key cryptography , 1999 .

[14]  Eonkyung Lee,et al.  Cryptanalysis of the Public-Key Encryption Based on Braid Groups , 2003, EUROCRYPT.

[15]  Giacomo Micheli,et al.  A Practical Cryptanalysis of WalnutDSA , 2017, IACR Cryptol. ePrint Arch..

[16]  Stepan Yu. Orevkov,et al.  Automorphism group of the commutator subgroup of the braid group , 2015, 1506.05517.

[17]  Derek Atkins,et al.  WALNUTDSA: A QUANTUM-RESISTANT DIGITAL SIGNATURE ALGORITHM , 2017 .

[18]  Giacomo Micheli,et al.  A Practical Cryptanalysis of WalnutDSA , 2017, IACR Cryptol. ePrint Arch..