20410428 - CR510 – ELLIPTIC CRYPTOSYSTEMS

Acquire a basic knowledge of the concepts and methods related to the theory of public key cryptography using the group of points of an elliptic curve on a finite field. Apply the theory of elliptic curves to classical problems of computational number theory such as factorization and primality testing.

Curriculum

teacher profile | teaching materials

Mutuazione: 20410428 CR510 – CRITTOSISTEMI ELLITTICI in Scienze Computazionali LM-40 TURCHET AMOS

Programme

- Affine and projective curves
- Cubics and elliptic curves
- The group law and equations of elliptic curves
- Isogenies
- Torsion points
- Elliptic curves over finite fields and Hasse's Theorem
- Brief discussion of symmetric and public key cryptosystems
- Algorithms on Elliptic Curves: Double and Add and Schoof Algorithm
- Public Key and Digital Signature algorithms on Elliptic Curves
- Weil Pairing and Identity based elliptic cryptosystems

Core Documentation

Professor notes

Type of delivery of the course

In person lectures by the professor

Type of evaluation

Oral exam consisting of a short seminar on a topic chosen together with the professor, and a classical oral exam on the Theorems discussed in class (from a fixed list)

teacher profile | teaching materials

Mutuazione: 20410428 CR510 – CRITTOSISTEMI ELLITTICI in Scienze Computazionali LM-40 TURCHET AMOS

Programme

- Affine and projective curves
- Cubics and elliptic curves
- The group law and equations of elliptic curves
- Isogenies
- Torsion points
- Elliptic curves over finite fields and Hasse's Theorem
- Brief discussion of symmetric and public key cryptosystems
- Algorithms on Elliptic Curves: Double and Add and Schoof Algorithm
- Public Key and Digital Signature algorithms on Elliptic Curves
- Weil Pairing and Identity based elliptic cryptosystems

Core Documentation

Professor notes

Type of delivery of the course

In person lectures by the professor

Type of evaluation

Oral exam consisting of a short seminar on a topic chosen together with the professor, and a classical oral exam on the Theorems discussed in class (from a fixed list)