Universally Composable Oblivious Transfer from Lossy Encryption and the McEliece Assumptions

Oblivious transfer (OT) is a primitive of great importance in two-party and multi-party computation. We introduce a general construction of universally composable (UC) oblivious transfer protocols based on lossy cryptosystems in the common reference string (CRS) model, yielding protocols under several assumptions. In order to achieve this, we show that for most known lossy encryption constructions it is possible to distinguish between lossy and injective public keys given the corresponding secret key, similarly to dual-mode encryption in messy mode. Furthermore, we adapt the techniques of our general construction to obtain the first UC secure OT protocol based on the McEliece assumptions, which are coding theory based assumptions that until now have resisted quantum attacks, thus introducing the first UC secure OT protocol based on coding assumptions. However, differently from previous results based on dual-mode encryption, our scheme does not require a trapdoor for opening lossy ciphertexts, relying instead on CRS manipulation and cut-and-choose techniques to construct the simulators. In both constructions we circumvent the need for universally composable string commitment schemes, which are required by previous black-box compilers.

[1]  Moni Naor,et al.  Efficient oblivious transfer protocols , 2001, SODA '01.

[2]  Iftach Haitner,et al.  Semi-honest to Malicious Oblivious Transfer - The Black-Box Way , 2008, TCC.

[3]  Yuval Ishai,et al.  Priced Oblivious Transfer: How to Sell Digital Goods , 2001, EUROCRYPT.

[4]  Josef Pieprzyk,et al.  Advances in Cryptology - ASIACRYPT 2008, 14th International Conference on the Theory and Application of Cryptology and Information Security, Melbourne, Australia, December 7-11, 2008. Proceedings , 2008, ASIACRYPT.

[5]  Silvio Micali,et al.  Non-Interactive Oblivious Transfer and Spplications , 1989, CRYPTO.

[6]  Moni Naor.  Advances in Cryptology - EUROCRYPT 2007, 26th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Barcelona, Spain, May 20-24, 2007, Proceedings , 2007, EUROCRYPT.

[7]  Michael Wiener,et al.  Advances in Cryptology — CRYPTO’ 99 , 1999 .

[8]  Yehuda Lindell,et al.  Black-box constructions for secure computation , 2006, STOC '06.

[9]  Robert J. McEliece,et al.  A public key cryptosystem based on algebraic coding theory , 1978 .

[10]  Alexander Russell,et al.  McEliece and Niederreiter Cryptosystems That Resist Quantum Fourier Sampling Attacks , 2011, CRYPTO.

[11]  Ran Canetti,et al.  Universal Composition with Joint State , 2003, CRYPTO.

[12]  Elisabeth Oswald,et al.  A Comprehensive Evaluation of Mutual Information Analysis Using a Fair Evaluation Framework , 2011, CRYPTO.

[13]  Vitaly Shmatikov,et al.  Efficient Two-Party Secure Computation on Committed Inputs , 2007, EUROCRYPT.

[14]  Juan A. Garay.  Efficient and Universally Composable Committed Oblivious Transfer and Applications , 2004, TCC.

[15]  Moti Yung,et al.  A New Randomness Extraction Paradigm for Hybrid Encryption , 2009, EUROCRYPT.

[16]  Oded Goldreich,et al.  A randomized protocol for signing contracts , 1985, CACM.

[17]  Elwyn R. Berlekamp,et al.  On the inherent intractability of certain coding problems (Corresp.) , 1978, IEEE Trans. Inf. Theory.

[18]  Martijn Stam.  Beyond Uniformity: Better Security/Efficiency Tradeoffs for Compression Functions , 2008, CRYPTO.

[19]  Jacques Stern,et al.  Advances in Cryptology — EUROCRYPT ’99 , 1999, Lecture Notes in Computer Science.

[20]  Matthew Green,et al.  Universally Composable Adaptive Oblivious Transfer , 2008, IACR Cryptol. ePrint Arch..

[21]  Yael Tauman Kalai.  Smooth Projective Hashing and Two-Message Oblivious Transfer , 2005, EUROCRYPT.

[22]  Mihir Bellare,et al.  Possibility and Impossibility Results for Encryption and Commitment Secure under Selective Opening , 2009, EUROCRYPT.

[23]  Ronald Cramer,et al.  Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure Public-Key Encryption , 2001, EUROCRYPT.

[24]  Tal Malkin,et al.  Simple, Black-Box Constructions of Adaptively Secure Protocols , 2009, TCC.

[25]  Tal Malkin.  Topics in Cryptology - CT-RSA 2008, The Cryptographers' Track at the RSA Conference 2008, San Francisco, CA, USA, April 8-11, 2008. Proceedings , 2008, CT-RSA.

[26]  Oded Regev,et al.  On lattices, learning with errors, random linear codes, and cryptography , 2005, STOC '05.

[27]  Anderson C. A. Nascimento,et al.  Efficient fully simulatable oblivious transfer from the McEliece assumptions , 2011, 2011 IEEE Information Theory Workshop.

[28]  Yehuda Lindell,et al.  Efficient Fully-Simulatable Oblivious Transfer , 2008, Chic. J. Theor. Comput. Sci..

[29]  Jeroen van de Graaf,et al.  Committed Oblivious Transfer and Private Multi-Party Computation , 1995, CRYPTO.

[30]  Aggelos Kiayias,et al.  Traitor Tracing with Constant Transmission Rate , 2002, EUROCRYPT.

[31]  Yehuda Lindell,et al.  Universally composable two-party and multi-party secure computation , 2002, STOC '02.

[32]  Kazukuni Kobara,et al.  Semantic security for the McEliece cryptosystem without random oracles , 2008, Des. Codes Cryptogr..

[33]  Silvio Micali,et al.  How to play ANY mental game , 1987, STOC.

[34]  Brent Waters,et al.  A Framework for Efficient and Composable Oblivious Transfer , 2008, CRYPTO.

[35]  Aggelos Kiayias,et al.  Self Protecting Pirates and Black-Box Traitor Tracing , 2001, CRYPTO.

[36]  Ivan Damgård,et al.  On the (Im)possibility of Basing Oblivious Transfer and Bit Commitment on Weakened Security Assumptions , 1998, EUROCRYPT.

[37]  Dan Boneh,et al.  Advances in Cryptology - CRYPTO 2003 , 2003, Lecture Notes in Computer Science.

[38]  Rafail Ostrovsky,et al.  Lossy Encryption: Constructions from General Assumptions and Efficient Selective Opening Chosen Ciphertext Security , 2011, ASIACRYPT.

[39]  John P. Steinberger,et al.  The preimage security of double-block-length compression functions , 2011, IACR Cryptol. ePrint Arch..

[40]  Joe Kilian,et al.  Founding crytpography on oblivious transfer , 1988, STOC '88.

[41]  Shlomo Shamai,et al.  Information Theoretic Security , 2009, Found. Trends Commun. Inf. Theory.

[42]  Ran Canetti,et al.  Universally composable security: a new paradigm for cryptographic protocols , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[43]  Brent Waters,et al.  Lossy trapdoor functions and their applications , 2008, SIAM J. Comput..

[44]  Ran Canetti,et al.  Universally Composable Commitments , 2001, CRYPTO.

[45]  Ronald Cramer,et al.  Advances in Cryptology - EUROCRYPT 2005, 24th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Aarhus, Denmark, May 22-26, 2005, Proceedings , 2005, EUROCRYPT.

[46]  Jean-Charles Faugère,et al.  A Distinguisher for High-Rate McEliece Cryptosystems , 2011, IEEE Transactions on Information Theory.

[47]  Ivan Damgård,et al.  Essentially Optimal Universally Composable Oblivious Transfer , 2009, ICISC.

[48]  Anderson C. A. Nascimento,et al.  Oblivious Transfer Based on the McEliece Assumptions , 2008, ICITS.