A Practical Implementation of Identity-Based Encryption Over NTRU Lattices

An identity-based encryption scheme enables the efficient distribution of keys in a multi-user system. Such schemes are particularly attractive in resource constrained environments where critical resources such as processing power, memory and bandwidth are severely limited. This research examines the first pragmatic lattice-based IBE scheme presented by Ducas, Lyubashevsky and Prest in 2014 and brings it into the realm of practicality for use on small devices. This is the first standalone ANSI C implementation of all the software elements of the scheme with improved performance. User Key Extraction demonstrates a 180% speed increase and Encrypt and Decrypt demonstrate increases of over 500% and 1200% respectively for 80-bit security on an Intel Core i7-6700 CPU at 4.0 GHz, with similar accelerations for 192-bit security, compared with Prest’s NTL proof-of-concept implementation on an Intel Core i5-3210M CPU at 2.5 GHz. In addition, we provide a range of suggestions to further enhance performance.

[1]  Chris Peikert,et al.  An Efficient and Parallel Gaussian Sampler for Lattices , 2010, CRYPTO.

[2]  Léo Ducas,et al.  Efficient Identity-Based Encryption over NTRU Lattices , 2014, ASIACRYPT.

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

[4]  Markku-Juhani O. Saarinen Arithmetic coding and blinding countermeasures for lattice signatures , 2018, Journal of Cryptographic Engineering.

[5]  Léo Ducas,et al.  Lattice Signatures and Bimodal Gaussians , 2013, IACR Cryptol. ePrint Arch..

[6]  Dan Boneh,et al.  Efficient Lattice (H)IBE in the Standard Model , 2010, EUROCRYPT.

[7]  Shota Yamada,et al.  Adaptively Secure Identity-Based Encryption from Lattices with Asymptotically Shorter Public Parameters , 2016, EUROCRYPT.

[8]  Andrew Chi-Chih Yao,et al.  The complexity of nonuniform random number generation , 1976 .

[9]  Adi Shamir,et al.  Identity-Based Cryptosystems and Signature Schemes , 1984, CRYPTO.

[10]  Nicolas Gama,et al.  Predicting Lattice Reduction , 2008, EUROCRYPT.

[11]  Matthew K. Franklin,et al.  Identity-Based Encryption from the Weil Pairing , 2001, CRYPTO.

[12]  Craig Gentry,et al.  Trapdoors for hard lattices and new cryptographic constructions , 2008, IACR Cryptol. ePrint Arch..

[13]  Johannes A. Buchmann,et al.  Discrete Ziggurat: A Time-Memory Trade-off for Sampling from a Gaussian Distribution over the Integers , 2013, IACR Cryptol. ePrint Arch..

[14]  Cynthia Dwork,et al.  A public-key cryptosystem with worst-case/average-case equivalence , 1997, STOC '97.

[15]  Masao Kasahara,et al.  ID based Cryptosystems with Pairing on Elliptic Curve , 2003, IACR Cryptol. ePrint Arch..

[16]  Ron Steinfeld,et al.  Making NTRU as Secure as Worst-Case Problems over Ideal Lattices , 2011, EUROCRYPT.

[17]  Tim Güneysu,et al.  An Investigation of Sources of Randomness Within Discrete Gaussian Sampling , 2017, IACR Cryptol. ePrint Arch..

[18]  Yan Gu,et al.  A Performance Analysis of Identity-Based Encryption Schemes , 2011, INTRUST.

[19]  Clifford C. Cocks An Identity Based Encryption Scheme Based on Quadratic Residues , 2001, IMACC.

[20]  Feng-Hao Liu,et al.  Bi-Deniable Inner Product Encryption from LWE , 2015, IACR Cryptol. ePrint Arch..

[21]  Nicolas Gama,et al.  An Homomorphic LWE based E-voting Scheme , 2015 .

[22]  Tim Güneysu,et al.  Towards lightweight Identity-Based Encryption for the post-quantum-secure Internet of Things , 2017, 2017 18th International Symposium on Quality Electronic Design (ISQED).

[23]  David Pointcheval,et al.  The Whole is Less Than the Sum of Its Parts: Constructing More Efficient Lattice-Based AKEs , 2016, SCN.

[24]  Feng-Hao Liu,et al.  Compact Identity Based Encryption from LWE , 2016 .

[25]  László Babai,et al.  On Lovász’ lattice reduction and the nearest lattice point problem , 1986, Comb..

[26]  Vadim Lyubashevsky,et al.  Lattice Signatures Without Trapdoors , 2012, IACR Cryptol. ePrint Arch..

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

[28]  Chris Peikert,et al.  On Ideal Lattices and Learning with Errors over Rings , 2010, JACM.

[29]  Vadim Lyubashevsky,et al.  Quadratic Time, Linear Space Algorithms for Gram-Schmidt Orthogonalization and Gaussian Sampling in Structured Lattices , 2015, EUROCRYPT.