Seminar
padic precision and isogenies computation, application to cryptography

Hold Date 
20160705 15:00～20160705 16:00 


Place 
Lecture Room S W1C514, West Zone 1, Ito campus, Kyushu University 


Object person 



Speaker 
Tristan Vaccon (Rikkyo University) 

Abstract:
Isogenies are morphism between elliptic curves. Their computation is of importance in cryptography for at least two reasons. Firstly, they can be used to count the number of points on elliptic curves, which is used to discard some of them from cryptographic applications. Secondly, some propositions of quantumresistant cryptosystems, following De Feo, Jao, and Plut's 2011 article, rely directly on isogenies.
To tackle this problem, computations over the padic numbers can be a decisive tool. The field of padic numbers is a field extension of the rational numbers analogous to the real numbers, but much more suited for arithmetic applications. As for the real numbers, computation over the padic numbers has to be done at finite precision.
With X. Caruso and D. Roe, we have provided a new method to handle precision over padics that relies on differentials and firstorder approximation. In a joint work with P. Lairez, we apply this method to tackle the problem of the computation of isogenies between elliptic curves.