Kubične krivulje v kriptografiji : magistrsko delo

Avsec, Miha (avtor), Buckley, Anita (mentor), Praprotnik, Matjaž (komentor)

Skozi delo bomo spoznali osnovne pojme in definicije kubičnih krivulj, ter si ogledali nekaj načinov njihove uporabe v kriptografiji. V primerjavi z drugimi kriptosistemi, kubične krivulje veljajo za bolj varne. Predstavili bomo različne napade na krivulje in na podlagi napadov ocenili, katere krivulje niso oziroma so primerna izbira.

• Jezik: Slovenski jezik
• Ključne besede: kubična krivulja, kriptografija, Weilovo parjenje, anomalne krivulje, supersingularne krivulje, MOV napad, izračun indeksa, Millerjev algoritem, torzijske točke
• Vrsta gradiva: Magistrsko delo/naloga
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2020
• PID: 20.500.12556/RUL-116144
• UDK: 511
• COBISS.SI-ID: 25986051
• Datum objave v RUL: 18.05.2020

Sekundarni jezik

• Jezik: Angleški jezik
• Naslov: Eliptic curves in cryptography

Izvleček

Cubic curves in cryptography offer some advantages compared to the other cryptosystems, and they are considered safer if using the same length key. In the master thesis we will first learn some basic definitions and theorems about cubic curves. Then we will present the uses of cubic curves in cryptography, where we will study some cryptosystems and analyze their weaknesses. An important topic discussed will also be safety, which will be studied with multiple attacks on curves. This way we will get a basic idea of which curves are (not) suitable for the use in cryptography.

• Ključne besede: cubic curve, cryptography, Weil pairing, anomalous curves, supersingular curves, MOV attack, Index calculus, Miller's algorithm, torsion points