On the Number of Arithmetic Operations in NTT-based Polynomial Multiplication in Kyber and Dilithium Cryptosystems

Date

2021-01-01

Author

Ilter, Murat Burhan
Kocak, Nese
Uslu, Erkan
Yayla, Oğuz
Yuca, Nergiz

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

89
views

0
downloads

National Institute of Standards and Technology (NIST) initiated a post-quantum standardization process in 2016, and as of July 2020, Round 3 candidates were announced. Among these candidates, Crystals-Kyber and Crystals-Dilithium are the most promising lattice-based key encapsulation mechanism (KEM) and signature algorithm that rely on the module learning with errors (Module-LWE) problem. In general, polynomial multiplication is one of the most time-consuming operations in Module-LWE based cryptosystems. There are several polynomial multiplication methods for multiplying two polynomials effectively. One of the most efficient methods is Number Theoretic Transform (NTT). This paper analyzes the number of arithmetic operations occupied in NTT multiplication for Kyber and Dilithium cryptosystems. The general formula on the number of multiplications and additions used in NTT operation for the lattice-based algorithms which have a ring structure similar to Kyber and Dilithium is given for q < 2(w-1) where w is the word size and q is the modulus. Also, cycle counts of arithmetic operations of Kyber and Dilithium are calculated on reference implementations to determine the relationship between our formulations and cycle counts.

Subject Keywords

Post-quantum cryptography, lattice-based cryptography, polynomial multiplication, number theoretic transform, Crystals-Kyber, Crystals-Dilithium

URI

https://hdl.handle.net/11511/100330

DOI

https://doi.org/10.1109/sin54109.2021.9699310

Conference Name

14th International Conference on Security of Information and Networks (SIN)

Collections

Graduate School of Applied Mathematics, Conference / Seminar

Suggestions

OpenMETU
Core

On some cryptographic properties of Rijndael Kavut, S; Yucel, MD (2001-01-01) We examine diffusion properties of Rijndael which has been selected by US National Institute of Standards and Technology (NIST) for the proposed Advanced Encryption Standard (AES). Since the s-box of Rijndael applies a nonlinear transformation operating on each byte of the intermediate cipher result independently, its characteristics have significant effects on the strength of the entire system. The characteristics of Rijndael's s-box are investigated for the criteria of avalanche, strict avalanche, bit ind...
Analyzes of Block Recombination and Lazy Interpolation Methods and Their Applications to Saber Aksoy, Berkin; Cenk, Murat; Department of Cryptography (2022-2-28) Since the beginning of the National Institute of Standards and Technology (NIST), The Post-Quantum Cryptography (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 {Z}_{q}[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 S...
Analysis of Block Recombination and Lazy Interpolation Methods and Their Applications to Saber Aksoy, Berkin; Cenk, Murat (2022-01-01) 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 Standa...
On statistical analysis of synchronous stream ciphers Sönmez Turan, Meltem; Doğanaksoy, Ali; Department of Cryptography (2008) Synchronous stream ciphers constitute an important class of symmetric ciphers. After the call of the eSTREAM project in 2004, 34 stream ciphers with different design approaches were proposed. In this thesis, we aim to provide a general framework to analyze stream ciphers statistically. Firstly, we consider stream ciphers as pseudo random number generators and study the quality of their output. We propose three randomness tests based on one dimensional random walks. Moreover, we theoretically and experimenta...
Radix-3 NTT-Based Polynomial Multiplication for Lattice-Based Cryptography Hassan, Chenar Abdulla; Yayla, Oğuz; Department of Cryptography (2022-5-31) The lattice-based cryptography is considered as a strong candidate amongst many other proposed quantum-safe schemes for the currently deployed asymmetric cryptosystems that do not seem to stay secure when quantum computers come into play. Lattice-based algorithms possesses a time consuming operation of polynomial multiplication. As it is relatively the highest time consuming operation in lattice-based cryptosystems, one can obtain fast polynomial multiplication by using number theoretic transform (NTT). In ...

Citation Formats

M. B. Ilter, N. Kocak, E. Uslu, O. Yayla, and N. Yuca, “On the Number of Arithmetic Operations in NTT-based Polynomial Multiplication in Kyber and Dilithium Cryptosystems,” presented at the 14th International Conference on Security of Information and Networks (SIN), ELECTR NETWORK, 2021, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/100330.