Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
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
102
views
0
downloads
Cite This
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
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
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.