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Undergraduate topics in computer science

Lattice-Based Cryptography and NTRU

Duncan A. Buell

Published Jan 1, 2021• 2 citations
Publisher
DOI
10.1007/978-3-030-73492-3_15

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This paper provides an explanation of NTRU, a post quantum encryption scheme, while also providing a gentle introduction to cryptography. NTRU is a very efficient lattice based cryptosystem that appears to be safe against attacks by quantum computers. NTRU's efficiency suggests that it is a strong candidate as an alternative to RSA, ElGamal, and ECC for the post quantum world. The paper begins with an introduction to cryptography and security proofs for cryptographic schemes before explaining the NTRU cryptosystem and culminating with a proof that the original presentation of NTRU is not IND-CPA secure. We will conclude by mentioning padding schemes to NTRU that are provably IND-CCA2 secure in the random oracle model. The paper is designed to be accessible to anyone with minimal background in abstract algebra and number theory - no previous knowledge of cryptography is assumed. Given the author's lack of familiarity with the subject, this paper aims to be an expository work rather than to provide new insights to the subject matter.
The safety and security of various cryptosystems are related to the hardness of the integer factorization problem and discrete logarithm problem, most cryptosystems will be rendered vulnerable to attack and outdated as quantum computers become more advanced.This study examines lattice-based cryptography (the NTRU cryptosystem), compares the suggested variation to other cryptosystems by simulation and presents the execution time for key generation, encryption, and decryption procedures, as well as to highlight the benefits and drawbacks of the proposed cryptosystem.A variant of the NTRU cryptosystem is developed with the purpose of improving the cryptosystem's security by allowing it to withstand attacks in both classical and quantum computing.The simulation revealed that the existing NTRU cryptosystem has a better time complexity compared to the proposed NTRU cryptosystem.The existing NTRU cryptosystem has a time complexity of O(n 2 ) while the proposed variant has O(n 3 ).Though had a better capacity of handling large data because of the introduction of lattice multiplication.