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Module Objective: To introduce students to Cryptography.
Basic concepts: enciphering, deciphering, plaintext, ciphertext, primes and primality testing.
Simple cryptosystems: substitution cipher, Vigenere cipher, Caesar cipher, Hill cipher.
Public key cryptograpy: RSA and possible attacks on RSA. Discrete Logarithm as a one-way function. Diffie-Hellman key exchange.
Primality testing, Carmichael numbers. Factoring, Fermatís method, other methods.
Some of the following topics may also be included:
Stream ciphers, one-time pad. Randomness and pseudo-randomness of a bit sequence. Shift registers and linear recursions. Attacks on shift register sequences for one-time pad, Berlekamp-Massey algorithm, one-way functions.
Coin toss over a telephone. Digital signatures. Authentication. The Data Encryption Standard (DES), Advanced Encryption Standard (AES). Perfect Secrecy. Unicity Distance. Certificate authorities and trust.
Computation using mathematical/statistical software.