Integer Modular Multiplication With Barrett Reduction and Its Variants for Homomorphic Encryption Applications: A Comprehensive Review and an Empirical Study
Sign Up to like & getrecommendations! Published in 2024 at "IEEE Access"
DOI: 10.1109/access.2024.3473901
Abstract: Modular arithmetic calculations, such as modular addition and multiplication, are fundamental building blocks to Post-Quantum Cryptography (PQC) and Homomorphic Encryption (HE) systems. While modular addition has straightforward hardware implementations, integer modular multiplication is more challenging… read more here.
Keywords: multiplication; modular multiplication; integer modular; multiplication barrett ... See more keywords
Optimized Modular Multiplication for Supersingular Isogeny Diffie-Hellman
Sign Up to like & getrecommendations! Published in 2019 at "IEEE Transactions on Computers"
DOI: 10.1109/tc.2019.2899847
Abstract: Recent progress in quantum physics shows that quantum computers may be a reality in the not too distant future. Post-quantum cryptography (PQC) refers to cryptographic schemes that are based on hard problems which are believed… read more here.
Keywords: diffie hellman; supersingular isogeny; isogeny diffie; modular multiplication ... See more keywords
FLALM: A Flexible Low Area-Latency Montgomery Modular Multiplication on FPGA
Sign Up to like & getrecommendations! Published in 2025 at "IEEE Transactions on Computers"
DOI: 10.1109/tc.2024.3457739
Abstract: Montgomery Modular Multiplication (MMM) is widely used in many public key cryptography systems. This paper presents a Flexible Low Area-Latency MMM (FLALM) implementation, which supports Generic Montgomery Modular Multiplication (GMM) and Square Montgomery Modular Multiplication… read more here.
Keywords: montgomery modular; modular multiplication; area latency;
Efficient High-Radix GF(p) Montgomery Modular Multiplication Via Deep Use Of Multipliers
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Circuits and Systems II: Express Briefs"
DOI: 10.1109/tcsii.2022.3197314
Abstract: High-radix Montgomery Modular Multiplication (MMM) is flexible and consumes fewer cycles, but turns inefficient especially when it comes to low-bit calculation. In this brief, we propose a high-radix MMM algorithm, called Separated Iterative Digit-Digit Modular… read more here.
Keywords: radix montgomery; radix; high radix; montgomery modular ... See more keywords
Improved Modular Multiplication Algorithms Using Solely IEEE 754 Binary Floating-Point Operations
Sign Up to like & getrecommendations! Published in 2025 at "IEEE Transactions on Emerging Topics in Computing"
DOI: 10.1109/tetc.2025.3582551
Abstract: In this paper, we propose three modular multiplication algorithms that use only the IEEE 754 binary floating-point operations. Several previous studies have used floating-point operations to perform modular multiplication. However, they considered only positive integers… read more here.
Keywords: multiplication; modular multiplication; floating point; point operations ... See more keywords
Design of a High-Performance Iterative Barrett Modular Multiplier for Crypto Systems
Sign Up to like & getrecommendations! Published in 2024 at "IEEE Transactions on Very Large Scale Integration (VLSI) Systems"
DOI: 10.1109/tvlsi.2024.3368002
Abstract: Modular multiplication (MM) is a fundamental operation in many cryptographic and arithmetic applications. In this article, we present an improved Barrett modular multiplication (BMM) algorithm and its hardware-efficient implementation. The proposed algorithm leverages parallel computation… read more here.
Keywords: modular multiplication; barrett; performance; barrett modular ... See more keywords