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Volume 61, 2024The 9th International Symposium on Current Progress in Mathematics and Sciences 2023 (The 9th ISCPMS 2023) in conjunction with AUA Academic Conference on the Application of Artificial Intelligences and Data Sciences in a Modern Science for a Better Life
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|10 January 2024
Polynomial equation in algebraic attack on NTRU-HPS and NTRU-HRSS
Department of Mathematics, Faculty of Mathematics and Natural Sciences (FMIPA), Universitas Indonesia, Depok 16424, Indonesia
* Corresponding author: email@example.com
NTRU is a lattice-based public-key cryptosystem designed by Jeffrey Hoffstein, Jill Pipher, and Joseph H. Silverman in 1996. NTRU published on Algorithmic Number Theory Symposium (ANTS) in 1998. The ANTS’98 NTRU became the IEEE standard for public key cryptographic techniques based on hard problems over lattices in 2008. NTRU was later redeveloped by NTRU Inc. since 2018 and became one of the finalists in round 3 of the PQC (Post-Quantum Cryptography) standardization process organized by NIST in 2020. There are two types of NTRU algorithms proposed by NTRU Inc., which are classified based on parameter determination, NTRU-HPS (Hoffstein, Pipher, Silverman) and NTRU-HRSS (Hulsing, Rijnveld, Schanck, Schwabe). Algebraic attacks on ANTS’98 NTRU had previously been carried out in 2009 and 2012. In this paper, algebraic attack is performed on the renewed NTRU submitted to the third round of NIST PQC standardization in 2020. This study aims to obtain system of polynomial equations representing plaintext bits of NTRU-HPS and NTRU-HRSS which can be used to find the private key in the next study. As a result, some polynomial equations with unknown variables were obtained.
Key words: Algebraic attack / NTRU-HPS / NTRU-HRSS
© The Authors, published by EDP Sciences, 2024
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