Course

Unit 1

Basic Cryptographic Knowledge

Introduction to cryptography; security goals: confidentiality, integrity, authentication, non-repudiation; classical cryptography and modern cryptography; basic attack models; mathematical foundations for cryptography; number theory; divisibility; greatest common divisor; Euclidean algorithm; extended Euclidean algorithm; prime numbers; modular arithmetic; congruences; solving congruence equations; residue classes; complete residue systems; Chinese remainder theorem; Fermat’s theorem; Euler’s theorem; primitive roots and their cryptographic relevance

Unit 2

Symmetric Cryptography

Classical symmetric-key ciphers; Caesar cipher; affine cipher; monoalphabetic substitution cipher; transposition cipher; homophonic substitution cipher; Vigenère cipher; one-time pad; product ciphers; iterated ciphers; block ciphers; Data Encryption Standard; Advanced Encryption Standard; modes of operation: Electronic Codebook and Cipher Block Chaining; stream ciphers; linear feedback shift registers; random number generators and pseudorandom number generators; practical stream cipher constructions; Salsa20 and ChaCha; security analysis of symmetric ciphers; cryptanalysis of symmetric-key systems; attack models; brute-force attack; frequency analysis; linear cryptanalysis; differential cryptanalysis; meet-in-the-middle attack; design principles and implementation considerations.

Unit 3

Public-Key Cryptographic Schemes

Introduction to public-key cryptography; advantages and limitations of public-key systems; trapdoor one-way functions; Diffie-Hellman key exchange; RSA cryptosystem; Rabin cryptosystem; ElGamal cryptosystem; security assumptions; integer factorization problem; discrete logarithm problem; implementation issues and common attacks; basic elliptic curve cryptography; elliptic curves over finite fields; point addition; point doubling; elliptic curve Diffie-Hellman key exchange; advantages and implementation considerations of elliptic curve cryptography.

Unit 4

Digital Signatures, Hash Functions, and Message Authentication Codes

Digital signatures; requirements of digital signature schemes; RSA digital signatures; ElGamal digital signatures; Digital Signature Standard; Elliptic Curve Digital Signature Algorithm; multiple signatures; security weaknesses and implementation issues in digital signatures; hash functions; properties of cryptographic hash functions; collision resistance; preimage resistance; second preimage resistance; Merkle-Damgård construction; security weaknesses of MD4, MD5, and SHA-1; overview of SHA-2 and SHA-3; message authentication codes; construction and use of MACs; comparison between digital signatures and MACs; applications in authentication and integrity protection.

Unit 5

Key Establishment Protocols

Key exchange and key establishment protocols; symmetric and asymmetric key establishment; Diffie-Hellman-based protocols; authenticated key exchange; Kerberos; certificates; public key infrastructure; certificate authorities; certificate validation; man-in-the-middle attacks; replay attacks; protocol weaknesses; secure protocol design principles; practical applications of cryptographic protocols in network security.

Unit 6

Introduction to Post-Quantum Cryptography

Limitations of classical public-key cryptography; impact of quantum computing on RSA, Diffie-Hellman, and elliptic curve cryptography; Shor’s algorithm and Grover’s algorithm: basic security implications; motivation for post-quantum cryptography; concept of quantum-secure asymmetric cryptography; overview of post-quantum cryptographic families: lattice-based cryptography, code-based cryptography, hash-based signatures, multivariate cryptography, and isogeny-based cryptography; basic idea of Learning With Errors; basic idea of syndrome decoding; hash-based digital signatures; introduction to NIST post-quantum cryptography standardization; practical need for crypto-agility and migration to quantum-safe systems.

Text Books / References

Text Book / References

• William Stallings, Cryptography and Network Security: Principles and Practice, 5th Edition, Prentice Hall, 2011.
• Alfred J. Menezes, Paul C. van Oorschot, and Scott A. Vanstone, Handbook of Applied Cryptography, CRC Press, 1996.
• William Stein, Elementary Number Theory: Primes, Congruences, and Secrets: A Computational Approach.
• Neal Koblitz, A Course in Number Theory and Cryptography, Springer-Verlag, 1994.
• Christof Paar and Jan Pelzl, Understanding Cryptography, From Established Symmetric and Asymmetric Ciphers to Post-Quantum Algorithms Springer-Verlag, 2024.

Cryptography is a fundamental component of modern cybersecurity, providing the mathematical and algorithmic foundations for confidentiality, integrity, authentication, non-repudiation, and secure communication. This course introduces students to the principles of classical and modern cryptography, beginning with the essential number theory required for cryptographic constructions. It then covers symmetric-key cryptography, public-key cryptographic schemes, digital signatures, hash functions, message authentication codes, and key establishment protocols. The course emphasizes both theoretical understanding and practical security considerations, including attacks, weaknesses, and correct implementation of cryptographic protocols.

Course Objectives

• Understand the mathematical foundations required for cryptographic algorithms and protocols.
• Analyze symmetric and public-key cryptographic schemes, including their design principles, advantages, limitations and attacks.
• Understand the construction and security requirements of digital signatures, hash functions, and message authentication codes.
• Apply cryptographic techniques to secure communication systems, authentication mechanisms, and key establishment protocols

Course Outcomes

CO-PO Mapping

Correlation Levels: 3 = High, 2 = Moderate, 1 = Low

Evaluation Pattern – 60:40

• Midterm Exam – 30% (Written Theory Examination)
• Class Test – 30%

End Sem Exam – 40%