ABSTRACT
Since the seminal result of Kilian, Oblivious Transfer (OT) has proven to be a fundamental primitive in cryptography. In such a scheme, a user is able to gain access to an element owned by a server, without learning more than this single element, and without the server learning which element the user has accessed. The NIST call for post-quantum encryption and signature schemes has revived the interest for cryptographic protocols based on post-quantum assumptions and the need for secure post-quantum OT schemes. In this paper, we show how to construct an OT scheme based on lattices, from a collision-resistant chameleon hash scheme (CH) and a CCA encryption scheme accepting a smooth projective hash function (SPHF). Note that our scheme does not rely on random oracles and provides UC security against adaptive corruptions assuming reliable erasures.
- Michel Abdalla, Fabrice Benhamouda, Olivier Blazy, Céline Chevalier, and David Pointcheval. 2013. SPHF-Friendly Non-interactive Commitments. In ASI-ACRYPT 2013, Part I (LNCS), Kazue Sako and Palash Sarkar (Eds.), Vol. 8269. Springer, Heidelberg, 214--234. Google ScholarDigital Library
- Martin R Albrecht, Rachel Player, and Sam Scott. 2015. On the concrete hardness of learning with errors. Journal of Mathematical Cryptology 9, 3 (2015), 169--203.Google ScholarCross Ref
- Fabrice Benhamouda, Olivier Blazy, Léo Ducas, and Willy Quach. 2018. Hash Proof Systems over Lattices Revisited. In PKC 2018, Part II (LNCS), Michel Abdalla and Ricardo Dahab (Eds.), Vol. 10770. Springer, Heidelberg, 644--674.Google ScholarCross Ref
- Olivier Blazy and Céline Chevalier. 2015. Generic Construction of UC-Secure Oblivious Transfer. In ACNS 15 (LNCS), Tal Malkin, Vladimir Kolesnikov, Allison Bishop Lewko, and Michalis Polychronakis (Eds.), Vol. 9092. Springer, Heidelberg, 65--86.Google Scholar
- Olivier Blazy, CÃľline Chevalier, and Quoc Huy Vu. 2019. Post-Quantum UC-Secure Oblivious Transfer in the Standard Model with Adaptive Corruptions. Cryptology ePrint Archive, Report 2019/707. https://eprint.iacr.org/2019/707.Google Scholar
- Ran Canetti. 2001. Universally Composable Security: A New Paradigm for Cryptographic Protocols. In 42nd FOCS. IEEE Computer Society Press, 136--145. Google ScholarDigital Library
- Ran Canetti, Shai Halevi, Jonathan Katz, Yehuda Lindell, and Philip D. MacKenzie. 2005. Universally Composable Password-Based Key Exchange. In EURO-CRYPT 2005 (LNCS), Ronald Cramer (Ed.), Vol. 3494. Springer, Heidelberg, 404--421. Google ScholarDigital Library
- David Cash, Dennis Hofheinz, Eike Kiltz, and Chris Peikert. 2010. Bonsai Trees, or How to Delegate a Lattice Basis. In EUROCRYPT 2010 (LNCS), Henri Gilbert (Ed.), Vol. 6110. Springer, Heidelberg, 523--552. Google ScholarDigital Library
- Ronald Cramer and Victor Shoup. 2002. Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure Public-Key Encryption. In EUROCRYPT 2002 (LNCS), Lars R. Knudsen (Ed.), Vol. 2332. Springer, Heidelberg, 45--64. Google ScholarDigital Library
- Bernardo David, Rafael Dowsley, and Anderson C. A. Nascimento. 2014. Universally Composable Oblivious Transfer Based on a Variant of LPN. In CANS 14 (LNCS), Dimitris Gritzalis, Aggelos Kiayias, and Ioannis G. Askoxylakis (Eds.), Vol. 8813. Springer, Heidelberg, 143--158. Google ScholarDigital Library
- Nicholas Genise and Daniele Micciancio. 2018. Faster Gaussian Sampling for Trapdoor Lattices with Arbitrary Modulus. In EUROCRYPT 2018, Part I (LNCS), Jesper Buus Nielsen and Vincent Rijmen (Eds.), Vol. 10820. Springer, Heidelberg, 174--203.Google ScholarCross Ref
- Rosario Gennaro and Yehuda Lindell. 2003. A Framework for Password-Based Authenticated Key Exchange. In EUROCRYPT 2003 (LNCS), Eli Biham (Ed.), Vol. 2656. Springer, Heidelberg, 524--543. http://eprint.iacr.org/2003/032.ps.gz. Google ScholarDigital Library
- Jonathan Katz and Vinod Vaikuntanathan. 2009. Smooth Projective Hashing and Password-Based Authenticated Key Exchange from Lattices. In ASIACRYPT 2009 (LNCS), Mitsuru Matsui (Ed.), Vol. 5912. Springer, Heidelberg, 636--652. Google ScholarDigital Library
- Joe Kilian. 1988. Founding Cryptography on Oblivious Transfer. In 20th ACM STOC. ACM Press, 20--31. Google ScholarDigital Library
- Daniele Micciancio and Chris Peikert. 2012. Trapdoors for Lattices: Simpler, Tighter, Faster, Smaller. In EUROCRYPT 2012 (LNCS), David Pointcheval and Thomas Johansson (Eds.), Vol. 7237. Springer, Heidelberg, 700--718. Google ScholarDigital Library
- Michael Naehrig, Erdem Alkim, Joppe Bos, Leo Ducas, Karen Easterbrook, Brian LaMacchia, Patrick Longa, Ilya Mironov, Valeria Nikolaenko, Christopher Peikert, Ananth Raghunathan, and Douglas Stebila. 2017. FrodoKEM. Technical Report. National Institute of Standards and Technology. available at https://csrc.nist.gov/projects/post-quantum-cryptography/round-1-submissions.Google Scholar
- Chris Peikert, Vinod Vaikuntanathan, and Brent Waters. 2008. A Framework for Efficient and Composable Oblivious Transfer. In CRYPTO 2008 (LNCS), David Wagner (Ed.), Vol. 5157. Springer, Heidelberg, 554--571. Google ScholarDigital Library
- Michael O. Rabin. 1981. How To Exchange Secrets with Oblivious Transfer. Technical Report TR81, Harvard University.Google Scholar
Index Terms
- Post-Quantum UC-Secure Oblivious Transfer in the Standard Model with Adaptive Corruptions
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