LECTURE TOPIC DESCRIPTION 1. Fundamental objective of Cryptography, Conventional Cryptography, Cryptanalysis, Cryptosystem. 2. Classical Cryptosystem, Shift Cipher, Ceaser Cipher, Cryptanalysis of Shift Cipher, Shift Cipher is not secure, Substitution Cipher. 3. Frequency analysis on Substitution Cipher, Monoalphabetic Cipher, Polyalphabetic Cipher, Transportation, Rail fence, Permutation Cipher. 4. Polyalphabetic Cipher, Playfair Cipher. 5. Introduction to Block Cipher, Substitution and Permutation network. 6. DES encryption, Feistel Cipher, DES Key Scheduling. 7. Attacks on DES, Generic attack, Exhaustive search, DES is not secure, Attack models-Ciphertext only, Known plaintext, etc. 8. Triple DES, Problem with Triple DES, Modes of Operation, ECB, Problem with ECB, CBC, CFB, OFB, CTR. 9. Key Stream Generation, Shannon Perfect Secrecy, One Time Pad, Pseudorandom sequence generation, LFSR . 10. Key stream generation, Pseudo-randomness, Golomb's randomness test. 11. LFSR as Pseudorandom bit generator, LFSR based Stream Cipher, Linear, non-linear function, Synchronous Stream Cipher. 12. Abstract algebra, Group. 13. Ring, Field 14. Prime number, Composite Number, Greatest Common Divisor (GCD). 15. Euclid Algorithm, Modular Arithmetic, Congruence relation. 16. Zn, Multiplication operation over Zn,Multiplicative inverse mod n, Zn*. 17. Existence of Multiplicative inverse modulo n, gcd(a,b)=ax+by, Extended Euclid Algorithm. 18. Fermat Little Theorem, Euler Phi-function (Φ(n)), Φ(p) = p-1, Φ(n.m) = Φ(n). Φ(m) 19. Eular's theorem, Quadratic residue, Quadratic non-residue, Eular criterion for quadratic residue. 20. Addition, multiplication, division, irreducible and primitive polynomial, Galois fields. 21. AES, Rounds of AES, Add Round Key, Shift Row . 22. AES Sub Byte, Min Column, Key Scheduling Algorithm. 23. Disadvantage of Private Key Cryptosystem, Diffie-Hellman Key Exchange Protocol, Discrete Log Problem, Introduction to Public Key Cryptosystem. 24. Knapsack Problem, Subset Sum Problem, Super increasing Sequence, Easy Knapsack, Merkle-Hellman Knapsack Cryptosystem. 25. RSA cryptosystem, Factorisation is hard. 26. Exponentiation, square and multiply method, side channel attack, prime numbers 27. Fermat's test, Miller-Rabin test. 28. Discrete log Problem, ElGamal Cryptosystem over Zp. 29. Non-singular Elliptic curve over R, Addition, Elliptic curve points form a Group over addition. 30. Elliptic curve over Zp, Points of Elliptic curve over Z11. 31. ElGamal over a general group, Elliptic Curve Points over Zp, ElGamal Cryptosystem over Elliptic Curve over Zp. 32. System of linear equations modulo n, Chinese Remainder Theorem. 33. Quadratic Residue, Rabin Cryptosystem. 34. Definition of Legendre Symbol, Properties of Legendre Symbol, Definition of Jacobi Symbol, Properties of Jacobi Symbol. 35. Jacobi Symbol, Pseudo prime base ‘a’, Solovay-Strassen primality test, Goldwasser-Micali Cryptosystem. 36. Authentication, MAC, Problem with Symmetric key authentication scheme, Digital Signature, Confidentiality and Authentication . 37. RSA Signature Scheme, ElGamal Signature Scheme. 38. Distributing the Public Key, Public-Key Authority, Public-Key Certificate. 39. private key vs. public key cryptosystem, How to exchange a symmetric key? Active attack on Diffie-Hellman  Key Exchange. Distribute symmetric key in a public key setup. 40. Symbol table problem, hash function, chaining, load factor, open addressing, linear probing, double probing. 41. Universal Hashing, Universality is good? Example of Universal Hashing, Perfect Hashing. 42. Uses of Hash Function, Authentication, Confidentiality, Properties of Hash Functions, Weak Hash Function, Strong Hash Function, Contraction of General Hash Functions. 43. SHA, SHA-I, MD5, HMD5, Birthday Paradox, Birthday attack on Hash Function. 44. Digital Signature Algorithm (DSA), Elgammal Signature Scheme, Secure Hash Algorithm (SHA), Digital Signature Standard. 45. 3 parties key exchange scheme, two round diffie-hellman, bilinear pairing, single round 3 party key exchange: Joux protocol. 46. Cryptology = Cryptography + Cryptanalysis, Breaking the code, Attack models, non-generic attack, exhaustive search, one-way function, table lookup. 47. One-way function, Block cipher and Stream cipher as one-way function, inverting an one-way function, generic attack, Hellman time-memory trade-off attack. 48. Generic attack, differential tails, differential attack on block cipher. 49. Impossible differential attack, Boomerang attack, Slide Attack. 50. Linear Cryptanalysis Linear attack on block cipher, linearity in S-box, pilling up lemma. 51. Cryptanalysis on Stream Cipher LFSR based stream ciphers, linear, non liner, algebraic attack. 52. Modern Stream Ciphers Synchronous Stream cipher: Snow, Grain, Asynchronous Stream cipher: Helix 53. Shamir's secret sharing and BE (t, n) threshold secret sharing scheme, polynomial based broadcast encryption. 54. Identity based Encryption (IBE) Identity based encryption, ID (email id, biometric, etc.) as public key, Boneh and Franklin's IBE 55. Attribute based Encryption (ABE) 1-to-1 public key encryption (PKE), identity based encryption, 1-to-many PKE, attribute based encryption, fuzzy identity based encryption, broadcast encryption.