Pseudorandom Functions from LWE: RKA Security and Application

Pseudorandom Functions (PRF) is a basic primitive in cryptography. In this paper, we study related key attacks (RKA) with which the adversary is able to choose function \(\phi \) and observe the behavior of the PRF under the modified secret key \(\phi (k)\). We focus on the PRF from the Learning with Errors (LWE) assumption by Banerjee and Peikert in CRYPTO 2014. We prove that the PRF is secure against unique-input key shift attacks and restricted affine attacks. After that, we use this RKA-secure PRF to construct a robustly reusable fuzzy extractor, which enjoys higher efficiency and better error correction rate.

[1]  Silvio Micali,et al.  How to construct random functions , 1986, JACM.

[2]  Yunhua Wen,et al.  Robustly Reusable Fuzzy Extractor from Standard Assumptions , 2018, IACR Cryptol. ePrint Arch..

[3]  Abhishek Banerjee,et al.  New and Improved Key-Homomorphic Pseudorandom Functions , 2014, CRYPTO.

[4]  Rafail Ostrovsky,et al.  Secure Remote Authentication Using Biometric Data , 2005, EUROCRYPT.

[5]  Moni Naor,et al.  Synthesizers and Their Application to the Parallel Construction of Pseudo-Random Functions , 1999, J. Comput. Syst. Sci..

[6]  Kevin Lewi,et al.  Improved Constructions of PRFs Secure Against Related-Key Attacks , 2014, ACNS.

[7]  Joseph Bonneau,et al.  Cache-Collision Timing Attacks Against AES , 2006, CHES.

[8]  Dawu Gu,et al.  Generic Constructions of Robustly Reusable Fuzzy Extractor , 2019, IACR Cryptol. ePrint Arch..

[9]  David Cash,et al.  Cryptography Secure Against Related-Key Attacks and Tampering , 2011, IACR Cryptol. ePrint Arch..

[10]  Dan Boneh,et al.  Key Homomorphic PRFs and Their Applications , 2013, CRYPTO.

[11]  Jonathan Katz,et al.  Efficient, Reusable Fuzzy Extractors from LWE , 2017, CSCML.

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

[13]  Rafail Ostrovsky,et al.  Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data , 2004, SIAM J. Comput..

[14]  Richard J. Lipton,et al.  On the Importance of Checking Cryptographic Protocols for Faults (Extended Abstract) , 1997, EUROCRYPT.

[15]  David Cash,et al.  Pseudorandom Functions and Permutations Provably Secure against Related-Key Attacks , 2010, CRYPTO.

[16]  Oded Regev,et al.  The Learning with Errors Problem (Invited Survey) , 2010, 2010 IEEE 25th Annual Conference on Computational Complexity.