Diffie-Hellman Diffie-Hellman is a public key distribution scheme First public-key type scheme, proposed in 1976. W Diffie, M E Hellman, \New directions in Cryptography\, IEEE Trans. Information

Public-Key Applications can classify uses into 3 categories: – encryption/decryption (provide secrecy) – digital signatures (provide authentication) – key exchange (of session keys)

A. J. Menezes, P. C. van Oorschot and S. A. Vanstone. Handbook of Applied Cryptography, CRC Press, 1997. Bruce Schneier. Applied Cryptography, Second Edition: Protocols, Algorthms, and Source Code in C (cloth) John Wiley & Sons, Inc.) 1996 Douglas R. Stinson, Cryptography (Theory and Practice), CRC Press 1995 Resources

Security Attack: Any action that compromises the security of information. Security Mechanism: A mechanism that is designed to detect, prevent, or recover from a security attack. Security Service: A service that enhances the security of data processing systems and information transfers. A security service makes use of one or more security mechanisms

Definition: Group A set G of elements and operator @ form a group if: for all x,y in G, x @ y is also in G (inclusion) there is an identity element e such that for all x in G, e@x = x for all x in G, there is an inverse element x

Numbers Integers Real Arithmetic Operations Addition and subtraction Multiplication and division Exponentiation and logarithm

Digital Signatures and Message Authentication Code (MAC) overview Suppose Alice and Bob share a secret key k which determines hash function hk Alice sends (x, y) to Bob where y = hk

Definitions – Digital Signature - a data string which associates a message with some originating entity – Digital Signature Generation Algorithm – a method for producing a digital signature – Digital signature verification algorithm - a method for verifying that a digital signature is authentic (i.e., was indeed created by the specified entity)

Modular arithmetic – Used to define a finite field – a = b mod n means that if a and b are divided by n they produce the same remainder – a*b mod n can result in 0 even if a and b are not 0

Iterating Block ciphers Definition A product cipher combines two or more transformations in a manner intending that the resulting cipher is more secure than the individual components. Definition An iterated block cipher is a block cipher involving the sequential repetition of an internal function called a round function. Parameters include the number of rounds Nr, the block bitsize n, and the bitsize k of the input key K from which Nr subkeys Ki (round keys) are derived. For invertibility (allowing unique decryption), for each value Ki the round function is a bijection on the round input