Tesi etd-09282021-170026 |
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Tipo di tesi
Tesi di laurea magistrale
Autore
SISINNI, FABRIZIO
URN
etd-09282021-170026
Titolo
Isogeny-based key-exchange in binary fields
Dipartimento
MATEMATICA
Corso di studi
MATEMATICA
Relatori
relatore Lombardo, Davide
correlatore Orsini, Emmanuela
correlatore Orsini, Emmanuela
Parole chiave
- binary fields
- crs
- isogeny-based cryptography
- key-exchange protocol
Data inizio appello
29/10/2021
Consultabilità
Completa
Riassunto
We adapt the ordinary isogeny-based cryptosystems of Couveignes, Rostovtsev and Stolbunov (CRS) to the case where the base field is a binary field. To make the protocol work in this setting, we modify some of the algorithms used in the original protocol. In particular, we study and implement an algorithm of Lercier for the computation of isogenies between elliptic curves defined over binary fields, an algorithm to compute fast scalar multiplication using only the x-coordinates of the point and a version of the SEA algorithm in characteristic two, due to Vercauteren. Then we describe in detail the whole cryptosystem by providing pseudocodes of the different algorithms involved and give an overview of the other isogeny-based cryptosystems. Finally we talk about our implementation and give some experimental results, comparing these results with the ones obtained using a revised version of CRS due to De Feo, Kieffer and Smith.
File
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Isogeny_...ields.pdf | 946.23 Kb |
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