Toward Quantum-Resistant Strong Designated Verifier Signature from Isogenies

This paper proposes a strong designated verifier signature (SDVS) based on a recently proposed mathematical problem. It consists in searching for an isogeny between super singular elliptic curves. The problem is hypothetically strong against a quantum computer. This makes our proposal the first SDVS scheme that may be secure against a quantum computer.

[1]  David Jao,et al.  Constructing elliptic curve isogenies in quantum subexponential time , 2010, J. Math. Cryptol..

[2]  Anton Stolbunov,et al.  Constructing public-key cryptographic schemes based on class group action on a set of isogenous elliptic curves , 2010, Adv. Math. Commun..

[3]  Yi Mu,et al.  Short Designated Verifier Signature Scheme and Its Identity-based Variant , 2008, Int. J. Netw. Secur..

[4]  Markus Jakobsson,et al.  Designated Verifier Proofs and Their Applications , 1996, EUROCRYPT.

[5]  Guomin Yang,et al.  Efficient Strong Designated Verifier Signature Schemes without Random Oracles or Delegatability , 2009, IACR Cryptol. ePrint Arch..

[6]  Olivier Markowitch,et al.  An Efficient Strong Designated Verifier Signature Scheme , 2003, ICISC.

[7]  Richard J. Lipton,et al.  Quantum Cryptanalysis of Hidden Linear Functions (Extended Abstract) , 1995, CRYPTO.

[8]  David Jao,et al.  Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies , 2011, J. Math. Cryptol..

[9]  Alexander Rostovtsev,et al.  Public-Key Cryptosystem Based on Isogenies , 2006, IACR Cryptol. ePrint Arch..

[10]  R. Stephenson A and V , 1962, The British journal of ophthalmology.

[11]  Guomin Yang,et al.  Efficient strong designated verifier signature schemes without random oracle or with non-delegatability , 2011, International Journal of Information Security.

[12]  Fabien Laguillaumie,et al.  Designated Verifier Signatures: Anonymity and Efficient Construction from Any Bilinear Map , 2004, SCN.