CRYPTOGRAPHY Gayathri V.R. Kunapuli

OUTLINE History of Cryptography Need for cryptography Private Key Cryptosystems Public Key Cryptosystems Comparison between Public and Private Key Cryptosystems PEM Future Work

History of Cryptography[2] Ceaser Ciphers Transposition Cipher Substitution Cipher Vigene`re Cipher Enigma Machine

Need for Cryptography[1] Authentication of the Communicating Principals Authenticated message carries a Digital Signature

Private Key Cryptosystems[1,2] Also called Symmetric Cryptography Encryption algorithm E turns plain text message M into a cipher text C C=E(M) Decrypt C by using decryption algorithm D which is an inverse function of E M=D(C)

Private Key Cryptosystems cont[1,2] Algorithm decomposed into Function(public) and Key(secret) Encrypted using the key K e and decrypted using the key K d M=D Kd (E Ke (M)) A function and a variable number of keys constitute a class of algorithms indexed by the keys.

Cont… The encryption function is -One-to-one injective mapping -One way function The secrecy rests on the keys rather than on algorithms. The key should be of sufficient length in bits.

DES(Jan,1977)[1,2] Encryption consists of 3 stages of Transposition and 16 stages of Substitution of bits. Easy to implement on VLSI The 56-bit length key was found insufficient and easy to break Repetitions in cipher text give clues to eavesdroppers Spurious data can be injected

Contd… Private Key systems require [n*(n-1)]/2 keys for ‘n’ principals in a system The conversation key must be agreed upon beforehand Management of the keys is a function of the Key Distribution Server(KDS)

Public Key Cryptographic Systems (Need)[1] Also called as the Asymmetric Cryptography To avoid the need to transmit secret keys and To reduce the key requirement to 2n, the public key systems are used

Public Key Cryptosystems Cont Introduced by Diffie and Hellman Each principal keeps a set of encryption keys (Ke & Kd) Encryption algorithm E is public and so is the key Ke Decryption algorithm D and decryption key Kd is kept private Data sent to a principal is encrypted using that corresponding Ke E and D can be made public if Ke and Kd are chosen such that it is impossible to infer Kd from Ke.

RSA(Aug,1977)[1,2,5] The algorithms E and D are inverses Plain text messages are limited to a size is limited to ‘k’ Integer k is chosen such that 2 k < N N =p * q where p & q are LARGE prime numbers Kp (public encyrption key) and Ks (private decryption key) are derived from p & q

Contd The robustness of RSA algorithm relies on the computational complexity in factoring a large number upon which the keys are based. The authenticity of the sender can also be verified.

Comparison between the cryptosystems[1] Private Key DES is computationally efficient Public Key RSA is computationally expensive Possible best use is RSA for short/important data and DES for long or less critical

PEM[1,5] Provides mechanism for the mail users to specify the cryptographic algorithm and parameters to be used for mail messages. Essential data fields in PEM are ◦ DEK ◦ IK ◦ MIC

Extended Works[4] To prevent the Denial-of-Decryption To reduce the time taken for the authentication of the digital signatures Self Generated Certificate Public Key Cryptography

References 1. Chow, Randy; Johnson, Theodore; Distributed Operating Systems & Algorithms, Aiden A.Bruen,Mario A.Forcinito ; Cryptography, I nformation theory and Error-correction, of cryptography 4. Self generated certificate public key cryptography and certificateless signature/Encryption scheme in the standard model ASIACCS’07, March 20-22, 2007, Singapore. 5. les/Hebert.html (April 2007)