Cryptography I
A.Y. 2025/2026
Learning objectives
The course aims to provide an in-depth knowledge of the cryptographic algorithms and protocols widely used in real life (symmetrical, asymmetric, hash functions, KDFs, key exchange), paying particular attention to applications that protect data in-transit data, at-rest, and end-to-end.
Expected learning outcomes
At the end of the course the students will be able to: (1) Understand and properly use symmetric/asymmetric encryption algorithms, hash functions, digital signatures; (2) Describe and use key exchange protocols, secret sharing schemes, secure communication protocols; (3) Analyze the security of a system and the attacks known in literature: collisions of hash functions, differential cryptanalysis, attacks on implementations..
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
Introduction to the course, general information about cryptology.
Attacks: Ciphertext only, known plaintext, chosen plaintext, chosen ciphertext
Classical Cryptosystems: Vigenère, Affine cipher, Hill cipher, etc.
One time pad.
Divisibility, greatest common divisor, Euclidean Algorithm
Modular arithmetic, invertibility mod m, Euler's totient function
DES, a simplified DES, Triple-DES, AES.
Prime numbers, pseudo-random bit generation, the generation of large primes.
Fermat's Little Theorem and primality test,
One-way functions and one-way trapdoor functions.
Chinese Remainder Theorem, factoring algorithms (e.g. Quadratic sieve).
RSA encryption scheme.
Discrete logarithm problem, algorithms to solve the discrete logarithms.
Diffie-Hellman key exchange.
ElGamal encryption scheme.
Hash functions: SHA-1 and SHA-2.
Digital signatures.
Key distribution, Public Key Infrastructures, X.509, PGP.
Zero-knowledge protocols.
HMAC.
KDF: an example PBKDF2
Blockchain and cryptocurrency.
Elliptic curves.
Attacks: Ciphertext only, known plaintext, chosen plaintext, chosen ciphertext
Classical Cryptosystems: Vigenère, Affine cipher, Hill cipher, etc.
One time pad.
Divisibility, greatest common divisor, Euclidean Algorithm
Modular arithmetic, invertibility mod m, Euler's totient function
DES, a simplified DES, Triple-DES, AES.
Prime numbers, pseudo-random bit generation, the generation of large primes.
Fermat's Little Theorem and primality test,
One-way functions and one-way trapdoor functions.
Chinese Remainder Theorem, factoring algorithms (e.g. Quadratic sieve).
RSA encryption scheme.
Discrete logarithm problem, algorithms to solve the discrete logarithms.
Diffie-Hellman key exchange.
ElGamal encryption scheme.
Hash functions: SHA-1 and SHA-2.
Digital signatures.
Key distribution, Public Key Infrastructures, X.509, PGP.
Zero-knowledge protocols.
HMAC.
KDF: an example PBKDF2
Blockchain and cryptocurrency.
Elliptic curves.
Prerequisites for admission
A basic knowledge of statistics, discrete mathematics, and programming would help you better understand the concepts taught in this course.
Teaching methods
Classroom Lectures: Although attendance is not compulsory, it is strongly recommended.
Teaching Resources
Home page: https://aviscontic1.ariel.ctu.unimi.it/, https://visconti.di.unimi.it/
Main textbooks:
W.Stallings, Cryptography and Network Security, Prentice Hall.
D.R.Stinson, M.Paterson, Cryptography: Theory and Practice, 4th Ed. CRC Press.
Alternatives:
A.Languasco, A.Zaccagnini MANUALE DI CRITTOGRAFIA Teoria, algoritmi e protocolli, Hoepli
A.J.Menezes, et al., Handbook of Applied Cryptography, CRC Press.
Additional resources (papers, slides, etc.) can be found here: https://aviscontic1.ariel.ctu.unimi.it/
Main textbooks:
W.Stallings, Cryptography and Network Security, Prentice Hall.
D.R.Stinson, M.Paterson, Cryptography: Theory and Practice, 4th Ed. CRC Press.
Alternatives:
A.Languasco, A.Zaccagnini MANUALE DI CRITTOGRAFIA Teoria, algoritmi e protocolli, Hoepli
A.J.Menezes, et al., Handbook of Applied Cryptography, CRC Press.
Additional resources (papers, slides, etc.) can be found here: https://aviscontic1.ariel.ctu.unimi.it/
Assessment methods and Criteria
Oral Exam: To pass the exam, students must demonstrate sufficient knowledge of the subject, including crypto algorithms, proofs, and exercises. Scores will range from 0 to 30.
Professor(s)
Reception:
By email appointment
Room 5008, 5th Floor, via Celoria 18, Computer Science Department