Publication

Efficient Modular Arithmetic

2021

Abstract

In Chapter 8, Efficient Modular Arithmetic, Joppe W. Bos, Thorsten Kleinjung and Dan Page discuss how to realise efficient modular arithmetic in practice on a range of platforms. They cover generic modular multiplication routines such as the popular Montgomery multiplication as well as special routines for primes of a specific shape. Moreover, especially fast methods are outlined that might produce errors with a very small probability. Such faster 'sloppy reduction' techniques are especially beneficial in cryptanalytic settings. Bos, Kleinjung and Page have all been involved in various cryptographic and cryptanalytic record-setting software implementations. In Chapter 8 they explain how to select the most efficient modular arithmetic routines for the cryptologic implementation task at hand.

Official source

https://infoscience.epfl.ch/entities/publication/82fe958e-9896-4003-94af-ba0e7781398a

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2021

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/82fe958e-9896-4003-94af-ba0e7781398a

About this result

Related concepts (31)

Modular exponentiation

Modular exponentiation is exponentiation performed over a modulus. It is useful in computer science, especially in the field of public-key cryptography, where it is used in both Diffie-Hellman Key Exchange and RSA public/private keys. Modular exponentiation is the remainder when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus); that is, c = be mod m. From the definition of division, it follows that 0 ≤ c < m.

Number theory

Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers).

Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801. A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00.