???? 5- Find an inverse of a modulo m for the following pairsa. a = your day of birth, m = 43Ib.a 29, m = your month of birth=

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Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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5- Find an inverse of a modulo m for the following pairs
a. a = your day of birth, m = 43
I
b.
a 29, m = your month of birth
=

Expert Solution

Step 1: Modular inverse

In modular arithmetic, there is no division operation. Hence, modular inverse is done instead.

The modular inverse of A (mod C) is A^^-1
(A * A^^-1) ≡ 1 (mod C) or equivalently (A * A^^-1) mod C = 1
Only the numbers coprime to C (numbers that share no prime factors with C) have a modular inverse (mod C)

There are three main methods to find the multiplicative modular inverse.

The naive method
The extended Euclidean algorithm
The Fermat's little theorem

The first step to finding the multiplicative modular inverse exists, need to check if a and m are coprime, i.e., if gcd(a,m) = 1.

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