RSA and ELGAMAL Algorithms ppt, Slides of Cryptography and System Security

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IMPLEMENTATION OF

RSA AND ELGAMAL

ALGORITHMS

COUNSELLOR - G.REKHA MADAM

CO-ORDINATOR - S.NARASIMHA REDDY SIR

M.SRIRAM B16CS 3 CSE-

Cryptography  (^) Study of techniques for secure communication in the presence of third parties.  (^) It enables us to store sensitive information or transmit it across networks so that it cannot be read by anyone except the intended recipient.  (^) Types of Cryptography- Private Key Cryptography Public Key Cryptography

RSA Algorithm  (^) RSA stands for Rivest Shamir Adleman.  (^) It was the first practical implementation of public key encryption.  (^) The idea of RSA is based on integer prime factorization.

Example Destination(Client)

1. Let p=47 and q=
2. n=47*59=
3. phi=(47-1)*(59-1)=
4. Choose e=17 because gcd(17,2668)=
5. d=157 since (17*157)mod 2668= 6.Public key={17,2773} Private Key={157,2773} 9.Decryption:: C= M=587^157 (mod 2773)= Source(Server) 7.Let Message M=HI=31 ,M<n
6. Encryption:: C=M^e (mod n) C=31^7 (mod 2773)=

ELGAMAL Algorithm  (^) It was described by Taher Elgamal in 1985.  (^) It can be defined over any Cyclic Group G.  (^) Its security mainly depends on computing discrete logarithms.

Continued  (^) 6.Let M be the message , 0<M<p-  (^) 7.Encryption::  (^) Choose a random number k ,1<k<p-  (^) Compute c1=g^k (mod p) c2=M.A^k (mod p)  (^) 8. Decryption::  (^) M=c2.Inverse(c1^a) (mod p)  (^) Let M=  (^) SOURCE Let k= c1=2^4(mod 11)= c2=7.8^4(mod 11)=  (^) DESTINATION M=6.Inverse(5^3)(mod 11) =6.3(mod 11)=18mod = (Inverse(5^3) mod 11 Inverse(125)mod 11 ->125*3 mod 11=1)

APPLICATIONS  (^) Client Server Architecture  (^) Online chatting  (^) Digital Signature DIFFERENCES 1.RSA gives same ciphertext for repeated same plaintext. 2.ELGAMAL gives different ciphertext for repeated same plaintext.

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