A Short Term Course on Cryptography

LECTURE	TOPIC	DESCRIPTION
1.	Introduction to cryptography.	Fundamental objective of Cryptography, Conventional Cryptography, Cryptanalysis, Cryptosystem.
2.	Classical Cryptosystem.	Classical Cryptosystem, Shift Cipher, Ceaser Cipher, Cryptanalysis of Shift Cipher, Shift Cipher is not secure, Substitution Cipher.
3.	Attack on Substitution Cipher.	Frequency analysis on Substitution Cipher, Monoalphabetic Cipher, Polyalphabetic Cipher, Transportation, Rail fence, Permutation Cipher.
4.	Play fair Cipher.	Polyalphabetic Cipher, Playfair Cipher.
5.	Block Cipher.	Introduction to Block Cipher, Substitution and Permutation network.
6.	Data Encryption Standard (DES).	DES encryption, Feistel Cipher, DES Key Scheduling.
7.	DES (Contd.).	Attacks on DES, Generic attack, Exhaustive search, DES is not secure, Attack models-Ciphertext only, Known plaintext, etc.
8.	Triple DES and Modes of Operation.	Triple DES, Problem with Triple DES, Modes of Operation, ECB, Problem with ECB, CBC, CFB, OFB, CTR.
9.	Stream Cipher.	Key Stream Generation, Shannon Perfect Secrecy, One Time Pad, Pseudorandom sequence generation, LFSR .
10.	Pseudorandom Sequence.	Key stream generation, Pseudo-randomness, Golomb's randomness test.
11.	LFSR based Stream Cipher.	LFSR as Pseudorandom bit generator, LFSR based Stream Cipher, Linear, non-linear function, Synchronous Stream Cipher.
12.	Mathematical background.	Abstract algebra, Group.
13.	Abstract algebra (cont..)	Ring, Field
14.	Number Theory.	Prime number, Composite Number, Greatest Common Divisor (GCD).
15.	Number Theory (Contd.).	Euclid Algorithm, Modular Arithmetic, Congruence relation.
16.	Modular Inverse.	Z_n, Multiplication operation over Z_n,Multiplicative inverse mod n, Z_n*.
17.	Extended Euclid Algorithm.	Existence of Multiplicative inverse modulo n, gcd(a,b)=ax+by, Extended Euclid Algorithm.
18.	Fermat's Little Theorem, Eular Phi-Function	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	Eular's theorem, Quadratic residue, Quadratic non-residue, Eular criterion for quadratic residue.
20.	Polynomial Arithmetic.	Addition, multiplication, division, irreducible and primitive polynomial, Galois fields.
21.	Advanced Encryption Standard (AES).	AES, Rounds of AES, Add Round Key, Shift Row .
22.	AES (Contd.).	AES Sub Byte, Min Column, Key Scheduling Algorithm.
23.	Introduction to Public Key Cryptosystem, Diffie-Hellman Key Exchange.	Disadvantage of Private Key Cryptosystem, Diffie-Hellman Key Exchange Protocol, Discrete Log Problem, Introduction to Public Key Cryptosystem.
24.	Knapsack Cryptosystem.	Knapsack Problem, Subset Sum Problem, Super increasing Sequence, Easy Knapsack, Merkle-Hellman Knapsack Cryptosystem.
25.	RSA Cryptosystem.	RSA cryptosystem, Factorisation is hard.
26.	More on RSA	Exponentiation, square and multiply method, side channel attack, prime numbers
27.	Primarily Testing	Fermat's test, Miller-Rabin test.
28.	ElGamal Cryptosystem.	Discrete log Problem, ElGamal Cryptosystem over Z_p.
29.	Elliptic Curve over the Reals.	Non-singular Elliptic curve over R, Addition, Elliptic curve points form a Group over addition.
30.	Elliptic curve Modulo a Prime.	Elliptic curve over Z_p, Points of Elliptic curve over Z₁₁.
31.	Generalised ElGamal Public Key Cryptosystem.	ElGamal over a general group, Elliptic Curve Points over Z_p, ElGamal Cryptosystem over Elliptic Curve over Z_p.
32.	Chinese Remainder Theorem.	System of linear equations modulo n, Chinese Remainder Theorem.
33.	Rabin Cryptosystem.	Quadratic Residue, Rabin Cryptosystem.
34.	Legendre and Jacobi Symbol.	Definition of Legendre Symbol, Properties of Legendre Symbol, Definition of Jacobi Symbol, Properties of Jacobi Symbol.
35.	Jacobi Symbol (Contd.).	Jacobi Symbol, Pseudo prime base ‘a’, Solovay-Strassen primality test, Goldwasser-Micali Cryptosystem.
36.	Message Authentication.	Authentication, MAC, Problem with Symmetric key authentication scheme, Digital Signature, Confidentiality and Authentication .
37.	Digital Signature.	RSA Signature Scheme, ElGamal Signature Scheme.
38.	Key Management.	Distributing the Public Key, Public-Key Authority, Public-Key Certificate.
39.	Key Exchange	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.	Hash Function	Symbol table problem, hash function, chaining, load factor, open addressing, linear probing, double probing.
41.	Universal Hashing.	Universal Hashing, Universality is good? Example of Universal Hashing, Perfect Hashing.
42.	Cryptographic Hash Function.	Uses of Hash Function, Authentication, Confidentiality, Properties of Hash Functions, Weak Hash Function, Strong Hash Function, Contraction of General Hash Functions.
43.	Secure Hash Algorithm (SHA).	SHA, SHA-I, MD5, HMD5, Birthday Paradox, Birthday attack on Hash Function.
44.	Digital Signature Standard (DSS)	Digital Signature Algorithm (DSA), Elgammal Signature Scheme, Secure Hash Algorithm (SHA), Digital Signature Standard.
45.	More on Key Exchange Protocol	3 parties key exchange scheme, two round diffie-hellman, bilinear pairing, single round 3 party key exchange: Joux protocol.
46.	Cryptanalysis	Cryptology = Cryptography + Cryptanalysis, Breaking the code, Attack models, non-generic attack, exhaustive search, one-way function, table lookup.
47.	Time-Memory Trade-off Attack	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.	Differential Cryptanalysis	Generic attack, differential tails, differential attack on block cipher.
49.	More on Differential Cryptanalysis	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.

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