Pairing-Friendly Curves with Discrete Logarithm Trapdoor Could be Useful

Pairing-friendly curves and elliptic curves with a trapdoo r for the discrete logarithm problem are versatile tools in t he design of cryptographic protocols. We show that curves having both properties simultaneously enable a non-interactive proto col for identitybased 3-party key distribution and deterministic identity -based signing with “short” signatures. All our protocols a re in the random oracle model.

[1]  Pascal Paillier,et al.  Trapdooring Discrete Logarithms on Elliptic Curves over Rings , 2000, ASIACRYPT.

[2]  Kenneth G. Paterson,et al.  ID-based Signatures from Pairings on Elliptic Curves , 2002, IACR Cryptol. ePrint Arch..

[3]  Siu-Ming Yiu,et al.  Efficient Forward and Provably Secure ID-Based Signcryption Scheme with Public Verifiability and Public Ciphertext Authenticity , 2003, ICISC.

[4]  Jung Hee Cheon,et al.  An Identity-Based Signature from Gap Diffie-Hellman Groups , 2003, Public Key Cryptography.

[5]  Matthew K. Franklin,et al.  Identity-Based Encryption from the Weil Pairing , 2001, CRYPTO.

[6]  Edlyn Teske,et al.  An Elliptic Curve Trapdoor System , 2004, Journal of Cryptology.

[7]  Hovav Shacham,et al.  Short Signatures from the Weil Pairing , 2001, J. Cryptol..

[8]  Daniel R. L. Brown,et al.  The Static Diffie-Hellman Problem , 2004, IACR Cryptology ePrint Archive.

[9]  Paulo S. L. M. Barreto,et al.  Efficient and Provably-Secure Identity-Based Signatures and Signcryption from Bilinear Maps , 2005, ASIACRYPT.

[10]  Jung Hee Cheon,et al.  Security Analysis of the Strong Diffie-Hellman Problem , 2006, EUROCRYPT.

[11]  Steven D. Galbraith,et al.  Hidden Pairings and Trapdoor DDH Groups , 2006, ANTS.

[12]  Dan Boneh,et al.  Short Signatures Without Random Oracles and the SDH Assumption in Bilinear Groups , 2008, Journal of Cryptology.

[13]  David Jao,et al.  Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem , 2009, Pairing.

[14]  Michael Scott,et al.  A Taxonomy of Pairing-Friendly Elliptic Curves , 2010, Journal of Cryptology.

[15]  Hyang-Sook Lee,et al.  Pairing-Friendly Curves with Minimal Security Loss by Cheon's Algorithm , 2011 .