## Cryptology ePrint Archive: Report 2011/537

Lattice Signatures Without Trapdoors

Vadim Lyubashevsky

Abstract: We provide an alternative method for constructing lattice-based digital signatures which does not use the hash-and-sign'' methodology of Gentry, Peikert, and Vaikuntanathan (STOC 2008). Our resulting signature scheme is secure, in the random oracle model, based on the worst-case hardness of the $\tilde{O}(n^{1.5})-SIVP$ problem in general lattices. The secret key, public key, and the signature size of our scheme are smaller than in all previous instantiations of the hash-and-sign signature, and our signing algorithm is also much simpler, requiring just a few matrix-vector multiplications and rejection samplings. We then also show that by slightly changing the parameters, one can get even more efficient signatures that are based on the hardness of the Learning With Errors problem. Our construction naturally transfers to the ring setting, where the size of the public and secret keys can be significantly shrunk, which results in the most practical to-date provably secure signature scheme based on lattices.

Category / Keywords: public-key cryptography / Lattice-Based Cryptography,Digital Signatures, Knapsacks, Learning With Errors

Publication Info: Full version of paper appearing at Eurocrypt 2012

Date: received 1 Oct 2011, last revised 18 Oct 2017

Contact author: vadim lyubash at gmail com

Available format(s): PDF | BibTeX Citation

Note: Small mistakes corrected: Added sqrt(m) to the statement of Lemma 3.7. Changed >0 to >1 in item 3 of Lemma 4.4.

Short URL: ia.cr/2011/537

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