First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
CRYPTOGRAPHY
SC04111836, A.A. 2018/19

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course Second cycle degree in
MATHEMATICS
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2018/19
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Degree course track GENERALE [010PD]
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination CRYPTOGRAPHY
Website of the academic structure http://matematica.scienze.unipd.it/2018/laurea_magistrale
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
Branch PADOVA
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

Lecturers
Teacher in charge ALESSANDRO LANGUASCO MAT/05

Mutuated
Course unit code Course unit name Teacher in charge Degree course code
SC04111836 CRYPTOGRAPHY ALESSANDRO LANGUASCO SC1176
SC04111836 CRYPTOGRAPHY ALESSANDRO LANGUASCO SC1172
INP7080692 CRYPTOGRAPHY ALESSANDRO LANGUASCO IN2371
INP7080692 CRYPTOGRAPHY ALESSANDRO LANGUASCO IN2371

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
Hours of
Individual study
Shifts
Practice 1.0 8 17.0 No turn
Lecture 5.0 40 85.0 No turn

Calendar
Start of activities 01/10/2018
End of activities 18/01/2019

Examination board
Board From To Members of the board
5 Crittografia - a.a. 2018/2019 01/10/2018 30/09/2019 LANGUASCO ALESSANDRO (Presidente)
TONOLO ALBERTO (Membro Effettivo)
FILE' GILBERTO (Supplente)
PUTTI MARIO (Supplente)
RANZATO FRANCESCO (Supplente)

Syllabus
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
  • Loading of files and pages (web pages, Moodle, ...)

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

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