CS 513 – System Security
Lecture 6

Lecturer: Professor Fred B. Schneider
Notes by: Vicky Weissman
Lecture Date: 2/1/00

Today’s Topics

• Definitions: (diffusion, perfect secrecy, computationally secure, and unconditionally secure)
• Perfect Substitution Cipher
• Secret Key Cryptography

Definitions

diffusion: localized information in the plaintext is spread throughout the corresponding cipher text. (Ex: 2 plaintext messages that differ by a single letter are encrypted to produce 2 cipher texts that are different throughout the text.)

perfect secrecy: the probability that a given message is encoded in the cipher text is unaltered by having the cipher text.

computationally secure: cryptosystem can be broken, if enough processing power is used

unconditionally secure: the ability to break the cryptosystem does not depend on the amount of available processing power

Perfect Substitution Cipher

· algorithm: pick a sequence of random bits, 1 for each bit in the plaintext message. The cipher text is the XOR of the plaintext with the random bits.

· the key is the randomly chosen bits

· cipher provides perfect secrecy

· problems: how are the random sequence of bits generated? how does the receiver know the key?

· first practical implementation by Gilbert Vernam who used 1-time pads to get the key and to facilitate communicating the key

Secret Key Cryptography

Notation:

k{m} = E(k, m) = apply encryption function E, to message m, using key k

D(k, m) = apply decryption function D, to message m, using key k

D(k, E(k, m)) = m, but, in general, K{D(k, m)} ¹ m

Applications:

• authentication

• maintain secrecy of stored data

• maintain secrecy despite passive wiretappers

Authentication Protocols:

Assume that Alice (A) and Bob (B) share a key (K_AB) that only they know.

Protocol 1: A proves identity by sending K_AB to B.

Problems: passive wiretapper can get the key. B gets the key before proving his identity.

Protocol 2:

Features of Protocol 2:

· random number generation deters replay attacks

· identity proof does not reveal the key (strong authentication)

· identity proof does not convince a 3^rd party (non-repudiation is not provided)

Protocol 3 ( a failed optimization of protocol 2)

Attack against Protocol 3:

Trudy (T) can convince Bob that she is Alice, by initiating 2 sessions as follows:

Patches for Protocol 3:

· use 2 keys. Ex: A sends using one key, B sends using a different key

· create asymmetry. Ex: require the challenge from the initiator to be different from the challenge from the responder

· do minimal work until the identity of the other party is proven