# Fast Modular Reduction

@article{Hasenplaugh2007FastMR, title={Fast Modular Reduction}, author={William Hasenplaugh and Gunnar Gaubatz and Vinodh Gopal}, journal={18th IEEE Symposium on Computer Arithmetic (ARITH '07)}, year={2007}, pages={225-229} }

It is widely acknowledged that efficient modular multiplication is a key to high-performance implementation of public-key cryptography, be it classical RSA, Diffie-Hellman, or (hyper-) elliptic curve algorithms. In the recent decade, practitioners have relied mainly on two popular methods: Montgomery Multiplication and regular long-integer multiplication in combination with Barrett's modular reduction technique. In this paper, we propose a modification to Barrett's algorithm that leads to a… Expand

#### 39 Citations

Fast modular reduction for large-integer multiplication for cryptosystem application

- Mathematics, Computer Science
- 2012 Second International Conference on Digital Information and Communication Technology and it's Applications (DICTAP)
- 2012

This paper proposes a revision to the Modified Barrett algorithm based on the properties of Mersenne and Quasi-Mersenne primes, and describes four distinct sets of moduli which are responsible for converting the single-precision multiplication prevalent in many of today's techniques into an addition operation and a few simple shift operations. Expand

Partially Interleaved Modular Karatsuba-Ofman Multiplication

- Mathematics
- 2015

Summary We describe a method of performing modular multiplication that has various applications in the field of modern cryptography and coding theory. The proposed algorithm, which combines the… Expand

Fast Modular Reduction for Large-Integer Multiplication

- Computer Science
- 2012

The work contained in this thesis is a representation of the successful attempt to speed-up the modular reduction as an independent step of modular multiplication, which is the central operation in… Expand

Hardware Implementation of Barrett Reduction Exploiting Constant Multiplication

- Computer Science
- 2019

This thesis studies the influence using constant multipliers has on four different Barrett reduction variants targeting the Virtex-7 and creates a hybrid constant multiplier circuit based on Karatsuba multiplication which uses smaller FloPoCo-generated base multipliers. Expand

Arithmetic Considerations for Isogeny-Based Cryptography

- Computer Science, Mathematics
- IEEE Transactions on Computers
- 2019

In this paper we investigate various arithmetic techniques which can be used to potentially enhance the performance in the supersingular isogeny Diffie-Hellman (SIDH) key-exchange protocol which is… Expand

Fast Arithmetic Modulo 2^x p^y ± 1

- Mathematics, Computer Science
- 2017 IEEE 24th Symposium on Computer Arithmetic (ARITH)
- 2017

An overview of techniques to compute arithmetic modulo 2x py ± 1 and shows that in the SIDH setting, where arithmetic over a quadratic extension field is required, the approaches based on Montgomery multiplication are to be preferred. Expand

A High-Performance Low-Power Barrett Modular Multiplier for Cryptosystems

- Computer Science
- 2021 IEEE/ACM International Symposium on Low Power Electronics and Design (ISLPED)
- 2021

This paper presents a fast architecture for Barrett modular multiplication that eliminates costly multiplications while concurrently avoiding large-bitwidth additions by replacing the integer multiplications in each iteration with carry-save compressions and using Booth coding plus operation rescheduling to increase parallelism. Expand

An application of Miller Moreno groups to establishment protocol Non commutative cryptography

- Computer Science
- 2020 Fourth World Conference on Smart Trends in Systems, Security and Sustainability (WorldS4)
- 2020

An algorithm of generating (designing) of common key for a non-commutative group with two mutually commuting subgroups has been constructed by us. Expand

Justification of Montgomery Modular Reduction

- Computer Science
- 2012

one of the most known and widely used methods in Cryptography is the method suggested by Peter Montgomery; this method is based on the changing of the original reduction modulo by some other… Expand

Gpu and asic acceleration of elliptic curve scalar point multiplication

- Mathematics
- 2012

As public information is increasingly communicated across public networks such as the internet, the use of public key cryptography to provide security services such as authentication, data integrity,… Expand

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