Identity-based Signatures from Lattices: Simpler, Faster, Shorter

Identity-based signature is an important technique for lig ht-weight authentication. Re- cently, many efforts have been made to construct identity-based signatures over lattice assumptions since they would remain secure in future quantum age. In this paper we present a new identity- based signature scheme from lattice problems. This scheme is more efficient than other lattice-based identity-based signature schemes in terms of both computation and communication complexities. We prove its security in the random oracle model under short integer solution assumption that is as hard as approximating several worst-case lattice problems. We also extend the scheme to an identity-based message recovery signature scheme that has better performance.

[1]  Vadim Lyubashevsky,et al.  Lattice Signatures Without Trapdoors , 2012, IACR Cryptol. ePrint Arch..

[2]  Krste Asanovic,et al.  Energy-aware lossless data compression , 2006, TOCS.

[3]  Oded Regev,et al.  Lattice-Based Cryptography , 2006, CRYPTO.

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

[5]  Tatsuaki Okamoto,et al.  A Signature Scheme with Message Recovery as Secure as Discrete Logarithm , 1999, ASIACRYPT.

[6]  Liusheng Huang,et al.  Efficient hierarchical identity-based signatures from lattices , 2013, Int. J. Electron. Secur. Digit. Forensics.

[7]  Fagen Li,et al.  Efficient and strongly unforgeable identity-based signature scheme from lattices in the standard model , 2013, Secur. Commun. Networks.

[8]  Rainer A. Rueppel,et al.  Message Recovery for Signature Schemes Based on the Discrete Logarithm Problem , 1994, EUROCRYPT.

[9]  Dan Boneh,et al.  Efficient Lattice (H)IBE in the Standard Model , 2010, EUROCRYPT.

[10]  Markus Rückert,et al.  Strongly Unforgeable Signatures and Hierarchical Identity-Based Signatures from Lattices without Random Oracles , 2010, PQCrypto.

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

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

[13]  Craig Gentry,et al.  Trapdoors for hard lattices and new cryptographic constructions , 2008, IACR Cryptol. ePrint Arch..

[14]  Liusheng Huang,et al.  A New Hierarchical Identity-based Signature Scheme From Lattices In The Standard Model , 2012, Int. J. Netw. Secur..

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

[16]  Chris Peikert,et al.  Generating Shorter Bases for Hard Random Lattices , 2009, Theory of Computing Systems.

[17]  Adi Shamir,et al.  Identity-Based Cryptosystems and Signature Schemes , 1984, CRYPTO.

[18]  Rainer A. Rueppel,et al.  A new signature scheme based on the DSA giving message recovery , 1993, CCS '93.

[19]  Yi Mu,et al.  Identity-Based Partial Message Recovery Signatures (or How to Shorten ID-Based Signatures) , 2005, Financial Cryptography.

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

[21]  Florian Hess,et al.  Efficient Identity Based Signature Schemes Based on Pairings , 2002, Selected Areas in Cryptography.

[22]  Miklós Ajtai,et al.  Generating Hard Instances of Lattice Problems , 1996, Electron. Colloquium Comput. Complex..

[23]  Dan Boneh,et al.  Lattice Basis Delegation in Fixed Dimension and Shorter-Ciphertext Hierarchical IBE , 2010, CRYPTO.

[24]  Kenneth G. Paterson,et al.  Efficient Identity-Based Signatures Secure in the Standard Model , 2006, ACISP.

[25]  Liusheng Huang,et al.  Efficient Identity-Based Signature from Lattices , 2014, SEC.

[26]  David Cash,et al.  Bonsai Trees, or How to Delegate a Lattice Basis , 2010, EUROCRYPT.

[27]  Daniele Micciancio,et al.  Worst-case to average-case reductions based on Gaussian measures , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[28]  Mihir Bellare,et al.  Multi-signatures in the plain public-Key model and a general forking lemma , 2006, CCS '06.