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 \(q \equiv 1 \mod 2n\), 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 \(q \equiv 1 \mod n\) or \(q \equiv 1 \mod n/2\). 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.
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- 1.
Kyber was constructed under the Module Learning With Errors (MLWE) assumption, which is a module version of the RLWE assumption.
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Acknowledgments
We thank the anonymous Inscrypt’2018 reviewers for their helpful comments. This work was supported by the National Basic Research Program of China (973 project, No.2014CB340603), the National Cryptography Development Fund MMJJ20170116 and the National Natural Science Foundation of China (No. 61572495, No.61602473, No.61772515, No.61672030, No.61272040).
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Zhou, S. et al. (2019). Preprocess-then-NTT Technique and Its Applications to Kyber and NewHope. In: Guo, F., Huang, X., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2018. Lecture Notes in Computer Science(), vol 11449. Springer, Cham. https://doi.org/10.1007/978-3-030-14234-6_7
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