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Lecture 1 Introduction
Lecture 2 Euclid's gcd algorithm, Congruences, Baby Group Theory
Lecture 3 More on Euclid's gcd algorithm, The multiplicative group Z/nZ^{*}, Linear Congruences, Subgroups
Lecture 4 Solving Linear Congruences, Subgroup generated by < x >, Lagrange's theorem, phi(n) and Chinese Remainder Theorem
Lecture 5, 6 phi(n) and Chinese Remainder Theorem, An interesting identity, Caesar Ciphers and Digraphs, Matrix ciphers
Lecture 7 How big is GL_{2}(Z/NZ)?, Security of Matrix Ciphers
Lecture 8 Review of Group Theory, Cyclic groups, RSA cryptosystem, E(x) and D(x)
Lecture 9,10 Homomorphisms, RSA security, RSA problem, Group Membership test, Breaking RSA
Lecture 11,12 Public Key Certification, Attacking RSA, Chosen Ciphertext Attack, Protocol Failure, Bilnded Signatues
Lecture 13,14,15 Blinded signatures contd., Continued Fractions, Low Decryption Exponent Attack, Theory of Resultants, Low Encryption Exponent Attack
Lecture 16 Field, Finite Fields, Vector Spaces, Finite Field Construction
Lecture 17,18 Finite Field Construction contd., Field Arithmetic, Construction of an extension field, Uniqueness of finite fields
Lecture 19,20 Quadratic Reciprocity, Solovay-Strassen Test, Discrete Logarithm Problem, Diffie-Hellman key exchange
Lecture 21,22 Diffie Hellman contd., Massey Omura Cryptosystem, El Gamal Public Key System, Digital Signature Scheme
Lecture 23,24 Silver-Pohlig-Hellman method, Index Calculus attack, Birthday Paradox Attack
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