« A trick for using DIP at NetScreen firewall | Main | MAC and HMAC »

March 06, 2005

RSA Encryption and Digital Signature

It offers encryption and authentication (digital signature), developed in 1977 by Ron Rivest, Adi Shamir and Adleman and it works asymetric and generate public and private key by itself.thus encryption and authentication take place without any sharing of private keys: each person uses only another’s public key or their own private key.


rsa.jpg


For generate public and private keys it takes two larg prime numbers p and q , they should not equal and with a size of at least 1024 bits.
Let's take a look to its algorithm :
n define as follow :
n = p · q
phi define as follow :
φ = (p – 1) · (q – 1)
e is a number greater than 1 and less than φ as follow :
1< e < φ
d define as follow :
(d.e)/φ=1

d is private key and n,e are public key so it's difficult to obtain the private key d from the public key (n, e).
for example when our plaintext = 707
The encrypted data is c = m^e (mod n) :
ciphertext = 707^425(mod 3431) = 2142
then the plaintext is easily retrieved using m = c^d(mod n)
plaintext = 2142^1769(mod 3431) = 707

RSA group 2003 Picture

Posted by Mehrdad at March 6, 2005 10:20 AM