Network Security and Cryptography by Sarhan M. Musa

Author:Sarhan M. Musa
Language: eng
Format: epub, mobi
ISBN: 9781942270836
Publisher: Mercury Learning and Information
Published: 2018-02-09T05:00:00+00:00

7.4.1 Main Components

Determination of Keys

Encryption Algorithm

Decryption Algorithm

7.4.1.1 Determination of Keys

A User (Say User “A”) computes its private key and public key as follows:

Choose two large prime numbers p and q. (The larger the prime numbers, the more difficult it would be to break the cipher.)

Compute n = pq

Compute Φ (n) = (p – 1) (q – 1)

Choose an integer e such that e is less than Φ(n) and relatively prime to Φ(n), that is, GCD (e, Φ(n)) = 1. Note that e will always be odd, since Φ(n) is even.

Compute integer d as the multiplicative inverse of e mod Φ(n)

D = e – 1 (mod Φ(n))

Thus, e and d form multiplicative inverses of each other (mod Φ(n)).

• The pair (e, n) forms the Public Key of the user “A,” which is made public and distributed to other users in the cryptosystem.

• The pair (d, n) forms the Private Key of the user “A,” which “A keeps secret; it is not known to anyone except “A”.

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