Ring Signature and Identity-Based Ring Signature from Lattice Basis Delegation

In this paper, we propose a set of ring signature (RS) schemes and identity-based ring signature (IBRS) schemes using the lattice basis delegation technique due to [10,22]. The schemes are unforgeable and hold anonymity in the random oracle model. Using the method in [28,29], we also extend our constructions to obtain RS and IBRS schemes in the standard model. Our proposed ring signature schemes fit with ring trapdoor functions introduced by Brakerski and Kalai [31]. However, their work does not include ring signature in the random oracle model and identity-based ring signature schemes. For the lattice-based ring signature in the standard model, our construction is motivated by Boyen’s work [28] and results in shorter signatures than Brakeski-Kalai scheme. 1

[1]  Oded Regev,et al.  On lattices, learning with errors, random linear codes, and cryptography , 2009, JACM.

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

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

[4]  Kwangjo Kim,et al.  ID-Based Blind Signature and Ring Signature from Pairings , 2002, ASIACRYPT.

[5]  Xavier Boyen,et al.  Lattice Mixing and Vanishing Trapdoors A Framework for Fully Secure Short Signatures and more , 2010 .

[6]  Yael Tauman Kalai,et al.  How to Leak a Secret: Theory and Applications of Ring Signatures , 2001, Essays in Memory of Shimon Even.

[7]  Germán Sáez,et al.  Forking Lemmas for Ring Signature Schemes , 2003, INDOCRYPT.

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

[9]  Jonathan Katz,et al.  Ring Signatures: Stronger Definitions, and Constructions without Random Oracles , 2005, IACR Cryptol. ePrint Arch..

[10]  Craig Gentry,et al.  Practical Identity-Based Encryption Without Random Oracles , 2006, EUROCRYPT.

[11]  Clifford C. Cocks.  An Identity Based Encryption Scheme Based on Quadratic Residues , 2001, IMACC.

[12]  Jacques Stern,et al.  Threshold Ring Signatures and Applications to Ad-hoc Groups , 2002, CRYPTO.

[13]  Yael Tauman Kalai,et al.  A Framework for Efficient Signatures, Ring Signatures and Identity Based Encryption in the Standard Model , 2010, IACR Cryptol. ePrint Arch..

[14]  Chris Peikert,et al.  Bonsai Trees (or, Arboriculture in Lattice-Based Cryptography) , 2009, IACR Cryptol. ePrint Arch..

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

[16]  Masayuki Abe,et al.  1-out-of-n Signatures from a Variety of Keys , 2002, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[17]  Cynthia Dwork,et al.  A public-key cryptosystem with worst-case/average-case equivalence , 1997, STOC '97.

[18]  Joseph K. Liu,et al.  A Suite of Non-pairing ID-Based Threshold Ring Signature Schemes with Different Levels of Anonymity (Extended Abstract) , 2010, ProvSec.

[19]  David Cash,et al.  How to Delegate a Lattice Basis , 2009, IACR Cryptol. ePrint Arch..

[20]  Siu-Ming Yiu,et al.  Efficient Identity Based Ring Signature , 2005, ACNS.

[21]  Tsz Hon Yuen,et al.  Ring signatures without random oracles , 2006, ASIACCS '06.

[22]  Hovav Shacham,et al.  Efficient Ring Signatures Without Random Oracles , 2007, Public Key Cryptography.

[23]  Germán Sáez,et al.  New Identity-Based Ring Signature Schemes , 2004, ICICS.

[24]  Yi Mu,et al.  Revocable Ring Signature , 2007, Journal of Computer Science and Technology.

[25]  Tsz Hon Yuen,et al.  ID-Based Ring Signature Scheme Secure in the Standard Model , 2006, IWSEC.

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

[27]  Miklós Ajtai,et al.  Generating Hard Instances of the Short Basis Problem , 1999, ICALP.

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

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

[30]  Xavier Boyen,et al.  Identity-Based Encryption from Lattices in the Standard Model , 2009 .

[31]  Cécile Delerablée,et al.  Identity-Based Broadcast Encryption with Constant Size Ciphertexts and Private Keys , 2007, ASIACRYPT.