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Module Objective: To introduce students to Cryptography.
Basic concepts: enciphering, deciphering, plaintext, ciphertext. Simple cryptosystems: substitution cipher, Vigenere cipher, Caesar cipher, Hill cipher. 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. Public key cryptosystems, one-way functions. Factoring, Fermat’s method, other methods. Primality testing, Carmichael numbers. The RSA cryptosystem. Possible attacks on RSA. Discrete Logarithm as a one-way function. Diffie-Hellman key exchange. Other applications. Coin toss over a telephone. Digital signatures. Authentication. The Data Encryption Standard (DES), Advanced Encryption Standard (AES). Computation using mathematical/statistical software.
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