# modular arithmetic

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## modular arithmetic

n.
A form of integer arithmetic in which all integers having the same remainder when divided by a given natural number (called the modulus) are considered equivalent: Clocks use modular arithmetic with modulus 12, so 4 hours after 9 o'clock is 1 o'clock.
Translations
arithmétique modulaire
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My favourite sessions were Modular Arithmetic and Continued Fractions.
Another 23 papers cover arithmetic units, domain specific designs, verification and correctness proofs, modular arithmetic, floating-point error analysis, functional approximation, and arithmetic in cryptography.
To add security to messages, steps are added to the key, and in more complicated ciphers, the key can consist of multiple steps involving key phrases, modular arithmetic, and so on.
Among the topics are divisibility and modular arithmetic, the evolution of codemaking and codebreaking until the computer era, block cryptosystems and the data encryption standard, some number theory and algorithms, public key cryptography, and elliptic curve cryptography.
Since ancient time, number theory has been an important study subject and modular arithmetic has also been widely used in cryptography.
The chip also features a 1088-bit Modular Arithmetic Processor (MAP) for public-key cryptography, and an eDES hardware engine.
On the other hand the authors outline the basics of complex numbers and modular arithmetic.
In the early 1800s, while creating a branch of Mathematics called Modular Arithmetic, the great mathematician Carl Fredrich Gauss produced a method to find the date of Easter Sunday.
Both processors accelerate a variety of IPSec and SSL/TLS protocols, including DES, Triple DES, AES (with 128, 192, and 256-bit key lengths), and ARC4 encryption; MD5, SHA-1 hashing and authentication; RSA, DSA, SSL, IKE, and Diffie-Hellman public key support; 3,072-bit modular arithmetic and exponentiation, plus true Random Number Generation (RNG).
Rather than utilizing 32-bit integers or 64-bit floating point, key exchange heavily depends on extended precision modular arithmetic using 512-, 1024, or even 2048-bit integers.
The topics include divisibility and order in the integers, prime numbers and the factorization into primes, modular arithmetic and divisibility tests, the arithmetic of fractions, properties of the multiplication of fractions, and the decimal expansion of a fraction.
Incorporating feedback received by the authors since publication of the 2001 second edition, the third edition contains expanded material on logic, including a new section on the formal proof of the validity of arguments in propositional logic, and a new chapter covering elementary number theory and congruences, allowing deeper exploration of some of the groups arising in modular arithmetic and examination of the so-called public key encryption scheme that underpins much of the secure transmission of data on the internet.

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