Forward-Secure Linkable Ring Signatures from Bilinear Maps

We present the first linkable ring signature scheme with both unconditional anonymity and forward-secure key update: a powerful tool which has direct applications in elegantly addressing a number of simultaneous constraints in remote electronic voting. We propose a comprehensive security model, and construct a scheme based on the hardness of finding discrete logarithms, and (for forward security) inverting bilinear or multilinear maps of moderate degree to match the time granularity of forward security. We prove efficient security reductions—which, of independent interest, apply to, and are much tighter than, linkable ring signatures without forward security, thereby vastly improving the provable security of these legacy schemes. If efficient multilinear maps should ever admit a secure realisation, our contribution would elegantly address a number of problems heretofore unsolved in the important application of (multi-election) practical Internet voting. Even if multilinear maps are never obtained, our minimal two-epoch construction instantiated from bilinear maps can be combinatorially boosted to synthesise a polynomial time granularity, which would be sufficient for Internet voting and more.

[1]  Xavier Boyen,et al.  Forward-Secure Linkable Ring Signatures , 2018, ACISP.

[2]  Ben Adida,et al.  Helios: Web-based Open-Audit Voting , 2008, USENIX Security Symposium.

[3]  Mark Zhandry,et al.  Adaptively Secure Broadcast Encryption with Small System Parameters , 2014, IACR Cryptol. ePrint Arch..

[4]  Torben P. Pedersen.  Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing , 1991, CRYPTO.

[5]  Craig Gentry,et al.  Graph-Induced Multilinear Maps from Lattices , 2015, TCC.

[6]  Ronald Cramer,et al.  Recovering Short Generators of Principal Ideals in Cyclotomic Rings , 2016, EUROCRYPT.

[7]  Dan Boneh,et al.  Immunizing Multilinear Maps Against Zeroizing Attacks , 2014, IACR Cryptol. ePrint Arch..

[8]  Jacques Stern,et al.  Security Proofs for Signature Schemes , 1996, EUROCRYPT.

[9]  Joseph K. Liu,et al.  Linkable Ring Signature with Unconditional Anonymity , 2014, IEEE Transactions on Knowledge and Data Engineering.

[10]  David Chaum,et al.  Group Signatures , 1991, EUROCRYPT.

[11]  Panayiotis Tsanakas,et al.  From Helios to Zeus , 2013, EVT/WOTE.

[12]  J. Cheon,et al.  An algorithm for NTRU problems and cryptanalysis of the GGH multilinear map without a low-level encoding of zero , 2016, LMS J. Comput. Math..

[13]  Jung Hee Cheon,et al.  Cryptanalysis of the Multilinear Map over the Integers , 2014, EUROCRYPT.

[14]  Martin R. Albrecht,et al.  A Subfield Lattice Attack on Overstretched NTRU Assumptions - Cryptanalysis of Some FHE and Graded Encoding Schemes , 2016, CRYPTO.

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

[16]  Joseph K. Liu,et al.  Linkable Spontaneous Anonymous Group Signature for Ad Hoc Groups (Extended Abstract) , 2004, ACISP.

[17]  Eric Miles,et al.  Annihilation Attacks for Multilinear Maps: Cryptanalysis of Indistinguishability Obfuscation over GGH13 , 2016, CRYPTO.

[18]  Koutarou Suzuki,et al.  Traceable Ring Signature , 2007, Public Key Cryptography.

[19]  Jeroen van de Graaf,et al.  Improving Helios with Everlasting Privacy Towards the Public , 2012, EVT/WOTE.

[20]  Ron Steinfeld,et al.  GGHLite: More Efficient Multilinear Maps from Ideal Lattices , 2014, IACR Cryptol. ePrint Arch..

[21]  Craig Gentry,et al.  Candidate Multilinear Maps from Ideal Lattices , 2013, EUROCRYPT.

[22]  Yupu Hu,et al.  Cryptanalysis of GGH Map , 2016, EUROCRYPT.

[23]  Omer Paneth,et al.  On the Equivalence of Obfuscation and Multilinear Maps , 2015, IACR Cryptol. ePrint Arch..

[24]  Jean-Sébastien Coron,et al.  Practical Multilinear Maps over the Integers , 2013, CRYPTO.

[25]  Dan Boneh,et al.  Applications of Multilinear Forms to Cryptography , 2002, IACR Cryptol. ePrint Arch..