Cryptology ePrint Archive: Report 2018/995

Preprocess-then-NTT Technique and Its Applications to KYBER and NEWHOPE

Shuai Zhou and Haiyang Xue and Daode Zhang and Kunpeng Wang and Xianhui Lu and Bao Li and Jingnan He

Abstract: The Number Theoretic Transform (NTT) provides efficient algorithm for multiplying large degree polynomials. It is commonly used in cryptographic schemes that are based on the hardness of the Ring Learning With Errors problem (RLWE), which is a popular basis for post-quantum key exchange, encryption and digital signature. To apply NTT, modulus q should satisfy that q = 1 mod 2n, RLWE-based schemes have to choose an oversized modulus, which leads to excessive bandwidth. In this work, we present “Preprocess-then-NTT (PtNTT)” technique which weakens the limitation of modulus q, i.e., we only require q = 1 mod n or q = 1 mod n/2. Based on this technique, we provide new parameter settings for KYBER and NEWHOPE (two NIST candidates). In these new schemes, we can reduce public key size and ciphertext size at a cost of very little efficiency loss.

Category / Keywords: NTT, Preprocess-then-NTT, Kyber, NewHope, Ring LWE, Module LWE

Original Publication (in the same form): Inscrypt 2018

Date: received 16 Oct 2018, last revised 24 Oct 2018

Contact author: zhoushuai at iie ac cn

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Version: 20181024:070327 (All versions of this report)

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