User:Kailashtg

This is an example to show how R.S.A algorithm worls:

1) given p=11, q=13, m=2 2) n=p*q=11*13=143 3) phi(n)=(p-1)*(q-1)=10*12=120 4) choose e=11 ,a prime number 5)d=e^-1 mod phi(n)  =11^-1 mod 120

Euclid's Algorithm to find GCD

--- Q            | A1 A2 A3 |  B1 B2 B3  |  B1=A1-QA1, B2=A2-QA2, B3=A3-QA3 --- A3/B3=Q= -    | 1  0 120 |  0  1  11  | --- 120/11=  10   | 0  1  11 |  1  -1 10  | --- 11/10=     1   | 1  -1 10 | 0   11  1  | ---    d=23

6) c=(m^e)mod n   = (2^11)mod 143    = (2^1 mod 143)(2^2 mod 143)(2^4 mod 143)(2^4 mod 143)    = (2*4*16*16)mod 143  c = 46

7) m=(c^d) mod n   = (46^11) mod 143    = (46^1 mod 143)(46^2 mod 143)(46^4 mod 143)(46^4 mod 143)      =(46*114*126*126) mod 143    m=2

8) hence m=2 in original message.

By Kailash Gajara