A New Zero Knowledge Identification Scheme based on Weil Pairing

identification schemes have been proposed in which security are based on the intractability of factoring or DLP (Discrete Logarithm Problem). In 2009, Massoud et.al gave identification scheme whose security was based on solving ECDLP (Elliptic Curve Discrete Logarithm Problem). The security of this scheme is improved in order to propose a more secure and efficient scheme. The security of proposed scheme is based on expressing torsion point of elliptic curve into linear combination of basis points. This is more complicated than solving ECDLP and thus provides a higher level of security. Also proposed scheme is more efficient with respect to encryption and decryption since it requires only minimal operations in both algorithms.

[1]  Jean-Jacques Quisquater,et al.  A Practical Zero-Knowledge Protocol Fitted to Security Microprocessor Minimizing Both Transmission and Memory , 1988, EUROCRYPT.

[2]  Amos Fiat,et al.  Zero-knowledge proofs of identity , 1987, Journal of Cryptology.

[3]  Taher El Gamal.  A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, IEEE Trans. Inf. Theory.

[4]  Avishek Adhikari,et al.  Introduction to Mathematical Cryptography , 2014 .

[5]  N. Koblitz.  Elliptic curve cryptosystems , 1987 .

[6]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[7]  Marco Furini,et al.  International Journal of Computer and Applications , 2010 .

[8]  Amos Fiat,et al.  How to Prove Yourself: Practical Solutions to Identification and Signature Problems , 1986, CRYPTO.

[9]  Silvio Micali,et al.  The Knowledge Complexity of Interactive Proof Systems , 1989, SIAM J. Comput..

[10]  T. Elgamal.  A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, CRYPTO 1984.

[11]  Massoud Hadian Dehkordi,et al.  Zero-knowledge identification scheme based on Weil pairing , 2009 .

[12]  Ian F. Blake,et al.  Elliptic curves in cryptography , 1999 .

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

[14]  Victor S. Miller,et al.  Use of Elliptic Curves in Cryptography , 1985, CRYPTO.

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