2025
Number Theory and Cryptography
Name: Number Theory and Cryptography
Code: MAT11687D
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese
Regime de Frequência: Presencial
Sustainable Development Goals
Learning Goals
In this course will be presented the basic methods of modern cryptography. We will describe the methods
more common of symmetric key and of public key as well as the methods of safe transmission of
cryptography keys. Since the modern cryptography is indissociable from the theory of numbers, will be
approached the necessary requirements of this area of the Mathematics.
more common of symmetric key and of public key as well as the methods of safe transmission of
cryptography keys. Since the modern cryptography is indissociable from the theory of numbers, will be
approached the necessary requirements of this area of the Mathematics.
Contents
1.Introduction of the objectives, Notion of symmetricl cipher, Notion of Public-key: ciphers, signatures and
protocols.
2. Number theory and cryptography. Prime divisibility, Numbers and factorization, congruences and
residue rings, function of Euler-Phi, Fermats little theorem, and Chinese theorem of, Cyclic Groups
and discrete Logarithms.
3.Symmetrical ciphers. Study of the ciphers guided to the computational efficiency, sequential ciphers for
processing of information in real time, ciphers for blocks; its ways and standards: DES and AES, linear
Cryptoanalysis.
4. Cryptography of public key (based in the integer factorization and the Problem of the Discrete
Logarithms). The techniques RSA, Rabin and ElGamal. Digital ciphers, signatures (RSA, ElGamal and
DSA), the protocol of Diffie-Hellman.
5. Cryptography based in public key in elliptic curves.
protocols.
2. Number theory and cryptography. Prime divisibility, Numbers and factorization, congruences and
residue rings, function of Euler-Phi, Fermats little theorem, and Chinese theorem of, Cyclic Groups
and discrete Logarithms.
3.Symmetrical ciphers. Study of the ciphers guided to the computational efficiency, sequential ciphers for
processing of information in real time, ciphers for blocks; its ways and standards: DES and AES, linear
Cryptoanalysis.
4. Cryptography of public key (based in the integer factorization and the Problem of the Discrete
Logarithms). The techniques RSA, Rabin and ElGamal. Digital ciphers, signatures (RSA, ElGamal and
DSA), the protocol of Diffie-Hellman.
5. Cryptography based in public key in elliptic curves.
Teaching Methods
Oral exposition and problem classes.
The evaluation will have individuals tasks, middle term tests and a final examination.
The evaluation will have individuals tasks, middle term tests and a final examination.
Teaching Staff
- Carlos Correia Ramos [responsible]
Certificações
