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School of Science
Course unit
SC04111836, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course Second cycle degree in
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2019/20
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Degree course track ALGANT [001PD]
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination CRYPTOGRAPHY
Website of the academic structure
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit


Course unit code Course unit name Teacher in charge Degree course code

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines INF/01 Computer Science 1.0
Educational activities in elective or integrative disciplines MAT/02 Algebra 2.0
Educational activities in elective or integrative disciplines MAT/03 Geometry 1.0
Educational activities in elective or integrative disciplines MAT/05 Mathematical Analysis 2.0

Course unit organization
Period First semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Practice 1.0 8 17.0 No turn
Lecture 5.0 40 85.0 No turn

Start of activities 30/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2011 course timetable

Examination board
Board From To Members of the board
6 Crittografia - a.a. 2019/2020 01/10/2019 30/09/2020 LANGUASCO ALESSANDRO (Presidente)
RANZATO FRANCESCO (Membro Effettivo)
FILE' GILBERTO (Supplente)
PUTTI MARIO (Supplente)

Prerequisites: The topics of the following courses: Algebra (congruences, groups and cyclic groups, finite fields), Calculus (differential and integral calculus, numerical series) both for the BA in Mathematics.
Target skills and knowledge: The main goal of the Cryptography course is to give an overview
of the theoretical basis of the field in order to allow a critical study of the cryptographic protocols used in many applications (authentication, digital commerce). In the first part we will give the mathematical basic tools (essentially from elementary and analytic number theory) that are required to understand modern public-key methods. In the second part we will see how to apply this know-how to study and criticize some protocols currently used.
Examination methods: Written exam
Assessment criteria: During the written exam the student will have to reply to some questions about the topics taught during the lectures.
The maximal mark (30/30) will be conferred to error-free exams only. If the written exam will not be sufficient to decide
the evaluation mark, the teacher will ask to the candidate some further questions to be directly replied on the blackboard.
Course unit contents: First Part: Basic theoretical facts: Modular arithmetic. Prime numbers. Little Fermat theorem. Chinese remainder theorem. Finite fields: order of an element and primitive roots. Pseudoprimality tests. Agrawal-Kayal-Saxena's test. RSA method: first description, attacks. Rabin's method and its connection with the integer factorization. Discrete logarithm methods. How to compute the discrete log in a finite field. Elementary factorization methods. Some remarks on Pomerance's quadratic sieve.
Second Part: Protocols and algorithms. Fundamental crypto algorithms. Symmetric methods (historical ones, DES, AES) . Asymmetric methods. Attacks. Digital signature. Pseudorandom generators (remarks). Key exchange, Key exchange in three steps, secret splitting, secret sharing, secret broadcasting, timestamping. Signatures with RSA and discrete log.
Planned learning activities and teaching methods: Classroom lectures.
Additional notes about suggested reading: We will use the following textbooks:
1) A.Languasco, A.Zaccagnini - Manuale di Crittografia - Hoepli Editore, 2015. (italian).
2) N.Koblitz - A Course in Number Theory and Cryptography, Springer, 1994.
3) R.Crandall, C.Pomerance - Prime numbers: A computational perspective - Springer, 2005.
4) B. Schneier - Applied Cryptography - Wiley, 1994
Textbooks (and optional supplementary readings)
  • A. Languasco e A. Zaccagnini, Manuale di Crittografia. Milano: Hoepli, 2015. in lingua italiana Cerca nel catalogo
  • Koblitz, Neal, A course in number theory and cryptography. New York: Springer, 1987. Cerca nel catalogo

Innovative teaching methods: Teaching and learning strategies
  • Lecturing
  • Loading of files and pages (web pages, Moodle, ...)

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)
  • Latex

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