Fermat's Theorem

Fermat little theorem :

The public key ,private key  cryptography is based on prime number.

 

Fermat's little theorem states that if p is a prime number, then for any integer a, the number ap − a is an integer multiple of p. In the notation of modular arithmetic, this is expressed as. For example, if a = 2 and p = 7, then 27 = 128, and 128 − 2 = 126 = 7 × 18 is an integer multiple of 7

or we can say ,

ap-1≅ 1(modp)

or ap≅ a(modp)

 

Example:

P = an integer Prime number

a = an integer which is not multiple of P

Let a = 2 and P = 17

According to Fermat's little theorem 2 17 - 1 ≡ 1 mod(17) we got 65536 % 17 ≡ 1 that mean (65536-1) is an multiple of 17

Contributor's Info

Created:
0Comment