Oblivious Transfer from Weakly Random Self-Reducible Public-Key Cryptosystem

We define a new notion of Weakly Random-Self-Reducibile cryptosystems and show how it can be used to implement secure Oblivious Transfer. We also show that two recent Post-quantum cryptosystems (based on Learning With Errors and Approximate Integer GCD) can be viewed as Weakly Random-Self-Reducible.

[1]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[2]  Taher ElGamal,et al.  A public key cyryptosystem and signature scheme based on discrete logarithms , 1985 .

[3]  Richard Berger,et al.  A Provably Secure Oblivious Transfer Protocol , 1985, EUROCRYPT.

[4]  Claude Crépeau,et al.  Equivalence Between Two Flavours of Oblivious Transfers , 1987, CRYPTO.

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

[6]  Craig Gentry,et al.  A Simple BGN-Type Cryptosystem from LWE , 2010, EUROCRYPT.

[7]  Vinod Vaikuntanathan,et al.  Fully Homomorphic Encryption from Ring-LWE and Security for Key Dependent Messages , 2011, CRYPTO.

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

[9]  E. Kushilevitz.  Foundations of Cryptography Foundations of Cryptography , 2014 .

[10]  Vinod Vaikuntanathan,et al.  Noninteractive Statistical Zero-Knowledge Proofs for Lattice Problems , 2008, CRYPTO.

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

[12]  J. Loxton,et al.  Number Theory and Cryptography , 1990 .

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

[14]  Craig Gentry,et al.  Fully Homomorphic Encryption without Squashing Using Depth-3 Arithmetic Circuits , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[15]  Omer Reingold,et al.  Statistically Hiding Commitments and Statistical Zero-Knowledge Arguments from Any One-Way Function , 2009, SIAM J. Comput..

[16]  Joseph H. Silverman,et al.  NTRU: A Ring-Based Public Key Cryptosystem , 1998, ANTS.

[17]  Craig Gentry,et al.  Fully homomorphic encryption using ideal lattices , 2009, STOC '09.

[18]  Oded Goldreich.  Foundations of Cryptography: Index , 2001 .

[19]  Craig Gentry,et al.  Fully Homomorphic Encryption over the Integers , 2010, EUROCRYPT.

[20]  Anderson C. A. Nascimento,et al.  Oblivious Transfer Based on the McEliece Assumptions , 2012 .

[21]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

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

[23]  Kazukuni Kobara,et al.  Coding-Based Oblivious Transfer , 2008, MMICS.

[24]  Leonid A. Levin,et al.  A Pseudorandom Generator from any One-way Function , 1999, SIAM J. Comput..

[25]  Moni Naor,et al.  Bit commitment using pseudorandomness , 1989, Journal of Cryptology.

[26]  Silvio Micali,et al.  A secure protocol for the oblivious transfer (extended abstract) , 2004, Journal of Cryptology.

[27]  Claude Cripeaut.  Equivalence Between Two Flavours of Oblivious Transfers , 1988 .

[28]  Gilles Brassard,et al.  Zero-Knowledge Simulation of Boolean Circuits , 1986, CRYPTO.

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

[30]  Silvio Micali,et al.  Probabilistic Encryption , 1984, J. Comput. Syst. Sci..

[31]  Pascal Paillier,et al.  Public-Key Cryptosystems Based on Composite Degree Residuosity Classes , 1999, EUROCRYPT.

[32]  Claude Crépeau,et al.  Quantum Oblivious Transfer , 1994 .

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

[34]  Vinod Vaikuntanathan,et al.  Efficient Fully Homomorphic Encryption from (Standard) LWE , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[35]  Michael O. Rabin,et al.  How To Exchange Secrets with Oblivious Transfer , 2005, IACR Cryptol. ePrint Arch..

[36]  Gilles Brassard,et al.  All-or-Nothing Disclosure of Secrets , 1986, CRYPTO.

[37]  Nick Howgrave-Graham,et al.  Approximate Integer Common Divisors , 2001, CaLC.