Mojtaba Bahramian, Elham Hajirezaei

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Identity-Based Encryption is a public key cryptosystem that uses the receiver identifier information such as email address, IP address, name and etc, to compute a public and a private key in a cryptosystem and encrypt a message. A message receiver can obtain the secret key corresponding with his privacy information from Private Key Generator and he can decrypt the ciphertext. In this paper, we review Boneh-Franklin’s scheme and use bilinear map and Weil pairing’s properties to propose an identity-based cryptography scheme based on isogeny of elliptic curves.


Identity-based encryption; elliptic curves; isogeny of elliptic curves.

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D. Boneh, M. Franklin, Identity-Based Encryption from the Weil Pairing, Proceedings of CRYPTO 2001, LNCS 2139, Springer-Verlag, 2001, 213-229.

A. Childs, D. Jao, V. Soukharev, Constructing elliptic curve isogenies in quantum subexponential time, J. Math. Cryptol. 8134 (2014), no. 1, 1-29.

S. D. Galbraith, Constructing isogenies between elliptic curves over finite fields, LMS J. Comput. Math. 2 (1999) 118-138.

S. D. Galbraith, A. Stolbunov, Improved algorithm for the isogeny problem for ordinary elliptic curves, Appl. Algebra Engrg. Comm. Comput. 24 (2013), no. 2, 107-131.

N. Koblitz, Elliptic curve cryptosystems, Mathematics of computation, 48(177), (1987), 203-209.

D. Kohel, Endomorphism rings of elliptic curves over finite fields, PhD Thesis, University of California at Berkeley, 1996.

A. J. Menezes, S. A. Vanstone, Elliptic curve cryptosystems and their implementation. Journal of Cryptology, 6(4): (1993), 209-224.

V. S. Miller, Use of elliptic curves in cryptography, In Advances in Cryptology CRYPTO85 Proceedings, Springer (1986), 417-426.

A. Sahai, B. Waters, Fuzzy Identity Based Encryption, IACR ePrint Archive, Report 2004/086. (

A. Shamir, Identity-based Cryptosystems and Signature Schemes, Proceedings of CRYPTO ’84, LNCS 196, Springer-Verlag (1984), 47-53.

J. H. Silverman, The arithmetic of elliptic curves, Vol. 106 of Graduate Texts in Mathematics, Springer-Verlag, New York, 1986.

A. Stolbunov, Constructing public-key cryptographic schemes based on class group action on a set of isogenous elliptic curves, Adv. Math. Commun. 4 (2010), no. 2, 215-235.

J. Tate, Endomorphisms of abelian varieties over finite fields, Invent. Math 2 (1966) 134-144.

L.C. Washington, Elliptic Curves, Number Theory and Cryptography, CRC press, 2nd edition, 2008.

L.C. Washington, Elliptic Curves, Number Theory and Cryptography, CRC Press, 2nd edition, 2008.



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