Modulo

Summary

In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another (called the modulus of the operation). Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor. For example, the expression "5 mod 2" would evaluate to 1, because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0, because 9 divided by 3 has a quotient of 3 and a remainder of 0; there is nothing to subtract from 9 after multiplying 3 times 3. Although typically performed with a and n both being integers, many computing systems now allow other types of numeric operands. The range of values for an integer modulo operation of n is 0 to n − 1 inclusive (a mod 1 is always 0; a mod 0 is undefined, possibly resulting in a division by zero error in some programming languages). See Modular arithmetic f

Official source

https://en.wikipedia.org/wiki/Modulo

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Related publications (3)

Experiments with the Markoff Surface

Matthew De Courcy-Ireland, Sandy Lee

We confirm, for the primes up to 3000, the conjecture of Bourgain-Gamburd-Sarnak and Baragar on strong approximation for the Markoff surface modulo primes. For primes congruent to 3 modulo 4, we find data suggesting that some natural graphs constructed from this equation are asymptotically Ramanujan. For primes congruent to 1 modulo 4, the data suggest a weaker spectral gap. In both cases, there is close agreement with the Kesten-McKay law for the density of states for random 3-regular graphs. We also study the connectedness of other level sets . In the degenerate case of the Cayley cubic, we give a complete description of the orbits.

TAYLOR & FRANCIS INC2020

Passive-Only Key Recovery Attacks on RC4

Serge Vaudenay, Martin Vuagnoux

We present several weaknesses in the key scheduling algorithm of RC4 when the secret key contains an initialization vector - a cryptographic scheme typically used by the WEP and WPA protocols to protect IEEE 802.11 wireless communications. First, we show how the previously discovered key recovery attacks can be improved by reducing the dependency between the secret key bytes. Then, we describe two new weaknesses related to the modulo operation of the key scheduling algorithm. Finally, we describe a passive-only attack able to significantly improve the key recovery process on WEP with a data complexity of 215 eavesdropped packets.

Springer2007

Method to manage the load of peripheral elements within a multicore system

Federico Angiolini, David Atienza Alonso, Giovanni De Micheli

The aim of the present invention is to propose a method to provide reliability, power management and load balancing support for multicore systems based on Networks- on-Chip (NoCs) as well as a way to efficiently implement architectural support for this method by introducing complex packet handling mechanisms achieved by modifying the basic network interfaces attached to the cores of multicore computation systems. The present invention provides also a solution in interrupt-based support in NoCs for multicore computation systems against transient failures or other system-level issues while the system is executing a certain application. It also proposes policies to leverage the proposed hardware extensions. This aim is achieved thanks to a method to manage the load of peripheral elements within a multicore system, said multicore system comprising several processing cores accessing peripheral elements through a Network on Chip (NoC), each processing unit and peripheral element attached to a Network Interface in charge of formatting and driving the packets sent to or received from the Network on Chip, wherein, while considering at least two peripheral elements having a similar function, the Network Interface dedicated to a first peripheral element reroutes the incoming packets to a second Network Interface dedicated to a second peripheral element.

2008

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