Authors: Tikaram Sanyashi ; Sreyans Nahata ; Rushang Dhanesha and Bernard Menezes

Affiliation: Indian Institute of Technology Bombay, Powai, Mumbai and India

ISBN: 978-989-758-319-3

Keyword(s): Learning with Errors, Linear Programming, Integer Linear Programming, Galbraith’s Binary LWE.

Related Ontology Subjects/Areas/Topics: Applied Cryptography ; Cryptographic Techniques and Key Management ; Data Engineering ; Data Integrity ; Databases and Data Security ; Information and Systems Security

Abstract: Unlike many widely used cryptosytems, Learning with Errors (LWE) - based cryptosystems are known to be invulnerable to quantum computers. Galbraith’s Binary LWE (GB-LWE) was proposed to reduce the large key size of the original LWE scheme by over two orders of magnitude. In GB-LWE, recovering the plaintext from the ciphertext involves solving for the binary vector x in the equation xA = b (A, a 640×256 binary matrix and b, a 256 element integer vector are knowns). Previously, lattice-based attacks on binary matrices larger than 400 × 256 were found to be infeasible. Linear programming was proposed and shown to handle significantly larger matrices but its success rate for 640 × 256 matrices was found to be negligible. Our strategy involves identification of regimes L, M and H within the output (based on LP relaxation) where the mis-prediction rates are low, medium or high respectively. Bits in the output vector are guessed and removed to create and solve a reduced instance. We report e xtensive experimental results on prediction accuracy and success probability as a function of number of bits removed in L, M and H. We identify trade-offs between lower execution time and greater probability of success. Our success probability is much higher than previous efforts and its execution time of 1 day with 150 cores is a partial response to the challenge posed in (Galbraith, 2013) to solve a random 640 × 256 instance using “current computing facilities in less than a year”. (More)

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Paper citation in several formats:
Sanyashi, T.; Nahata, S.; Dhanesha, R. and Menezes, B. (2018). Learning Plaintext in Galbraith’s LWE Cryptosystem.In Proceedings of the 15th International Joint Conference on e-Business and Telecommunications - Volume 2 SECRYPT: SECRYPT, ISBN 978-989-758-319-3, pages 559-565. DOI: 10.5220/0006909407250731

author={Tikaram Sanyashi. and Sreyans Nahata. and Rushang Dhanesha. and Bernard Menezes.},
title={Learning Plaintext in Galbraith’s LWE Cryptosystem},
booktitle={Proceedings of the 15th International Joint Conference on e-Business and Telecommunications - Volume 2 SECRYPT: SECRYPT,},


JO - Proceedings of the 15th International Joint Conference on e-Business and Telecommunications - Volume 2 SECRYPT: SECRYPT,
TI - Learning Plaintext in Galbraith’s LWE Cryptosystem
SN - 978-989-758-319-3
AU - Sanyashi, T.
AU - Nahata, S.
AU - Dhanesha, R.
AU - Menezes, B.
PY - 2018
SP - 559
EP - 565
DO - 10.5220/0006909407250731

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