A Construction of Cramer-Shoup Like Encryption Protocols Based on the Anshel-Anshel-Goldfeld Key Exchange Protocol

We propose a secure encryption protocol on non-abelian groups. We follow the line of the construction of the Cramer-Shoup encryption protocol, which is proved to be indistinguishable against adaptive chosen ciphertext attack (IND-CCA, for short) by refining the ElGamal encryption protocol. In our protocol, the Anshel-Anshel-Goldfeld key exchange protocol plays the role of the Diffie-Hellman key exchange protocol in the Cramer-Shoup protocol. We then prove that the proposed protocol is indistinguishable against adaptive chosen ciphertext attacks in a slightly restricted sense, what we call the IND-rCCA security. The security notion of IND-rCCA is weaker than that of IND-CCA in a sense that the adversary's query is somewhat restricted in the security game.

[1]  Choonsik Park,et al.  New Public Key Cryptosystem Using Finite Non Abelian Groups , 2001, CRYPTO.

[2]  Tatsuaki Okamoto,et al.  How to Enhance the Security of Public-Key Encryption at Minimum Cost , 1999, Public Key Cryptography.

[3]  Jung Hee Cheon,et al.  New Public-Key Cryptosystem Using Braid Groups , 2000, CRYPTO.

[4]  Taher ElGamal,et al.  A public key cyryptosystem and signature scheme based on discrete logarithms , 1985 .

[5]  Spyros S. Magliveras,et al.  A Public Key Cryptosystem Based on Non-abelian Finite Groups , 2008, Journal of Cryptology.

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

[7]  Raghu Teja,et al.  A non-Abelian factorization problem and an associated cryptosystem , 2011, IACR Cryptol. ePrint Arch..

[8]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[9]  Ronald Cramer,et al.  Design and Analysis of Practical Public-Key Encryption Schemes Secure against Adaptive Chosen Ciphertext Attack , 2003, SIAM J. Comput..

[10]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[11]  Mianxiong Dong,et al.  Noncommutative Lightweight Signcryption for Wireless Sensor Networks , 2013, Int. J. Distributed Sens. Networks.

[12]  Jing Li,et al.  Novel Constructions of Cramer-Shoup Like Cryptosystems Based on Index Exchangeable Family , 2016, AsiaCCS.

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

[14]  Vladimir Shpilrain,et al.  Thompson's Group and Public Key Cryptography , 2005, ACNS.

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

[16]  Ayan Mahalanobis,et al.  A Simple Generalization of the ElGamal Cryptosystem to Non-Abelian Groups II , 2006, IACR Cryptol. ePrint Arch..

[17]  Zhenfu Cao,et al.  New public key cryptosystems based on non-Abelian factorization problems , 2013, Secur. Commun. Networks.