Analysis of Block Recombination and Lazy Interpolation Methods and Their Applications to Saber

Date

2022-01-01

Author

Aksoy, Berkin
Cenk, Murat

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Since the beginning of the National Institute of Standards and Technology (NIST), The Post-Quantum Cryptog-raphy (PQC) Standardization Process, efficient implementations of lattice-based algorithms have been studied extensively. Lattice-based NIST PQC finalists use polynomial or matrix-vector multiplications on the ring with type Zq [x]/f(x). For convenient ring types, Number Theoretic Transform (NTT) can be used to perform multiplications as done in Crystals-KYBER among the finalists of the NIST PQC Standardization Process. On the other hand, if the $q$ value of the scheme is a power of 2, as in NTRU and Saber, which are among the other lattice-based finalists, NTT can not be used explicitly. Hence multiplications are performed by the combination of Toom-Cook and Karatsuba algorithms. Recently, a novel technique called lazy interpolation [IACR Transactions on Cryptographic Hardware and Embedded Systems 2020.2: 222-244 (2020)] has been introduced to increase the performance of Toom-Cook and Karatsuba algorithms. This paper shows that the block recombination method [IEEE Transactions on Computers 63(9): 2273-2287 (2014)] is equivalent to lazy interpolation and can be used efficiently on multiplication algorithms. On the practical side, we compare different hybrid multiplications algorithms, then implement the block recombination method for Saber. Performance results are given in cycle values on general-purpose Intel processors with C implementation. Our work speeds up key generation, encapsulation, and decapsulation parts of Saber than the previous C implementations in the literature with a rate of between 10% - 13%.

Subject Keywords

Block Recombination, Efficient Software Implementations, Lattice-Based Cryptography, Lazy Interpolation, Post-Quantum Cryptography, Saber

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85142779867&origin=inward
https://hdl.handle.net/11511/101658

DOI

https://doi.org/10.1109/iscturkey56345.2022.9931800

Conference Name

15th International Conference on Information Security and Cryptography, ISCTURKEY 2022

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Graduate School of Applied Mathematics, Conference / Seminar

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Citation Formats

B. Aksoy and M. Cenk, “Analysis of Block Recombination and Lazy Interpolation Methods and Their Applications to Saber,” presented at the 15th International Conference on Information Security and Cryptography, ISCTURKEY 2022, Ankara, Türkiye, 2022, Accessed: 00, 2023. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85142779867&origin=inward.