Speaker: Luis Sordo Vieira
Title: The benefits of elliptic curve cryptography
Abstract: We will introduce the basis of elliptic curve cryptography. Roughly speaking ECC is based on the group structure of the points defined on an elliptic curve over a finite field and the difficulty of solving the discrete log problem. The applications are many, such as signature verification and pseudo random generators. No knowledge of algebraic geometry is required.

Speaker: Luis Sordo Vieira
Title: The benefits of elliptic curve cryptography
Abstract: We will introduce the basis of elliptic curve cryptography. Roughly speaking ECC is based on the group structure of the points defined on an elliptic curve over a finite field and the difficulty of solving the discrete log problem. The applications are many, such as signature verification and pseudo random generators. No knowledge of algebraic geometry is required.

Speaker: Luis Sordo Vieira
Title: The benefits of elliptic curve cryptography
Abstract: We will introduce the basis of elliptic curve cryptography. Roughly speaking ECC is based on the group structure of the points defined on an elliptic curve over a finite field and the difficulty of solving the discrete log problem. The applications are many, such as signature verification and pseudo random generators. No knowledge of algebraic geometry is required.

Speaker: Luis Sordo Vieira
Title: The benefits of elliptic curve cryptography
Abstract: We will introduce the basis of elliptic curve cryptography. Roughly speaking ECC is based on the group structure of the points defined on an elliptic curve over a finite field and the difficulty of solving the discrete log problem. The applications are many, such as signature verification and pseudo random generators. No knowledge of algebraic geometry is required.

Title:  Quasi-optimality in the backward Euler-Galerkin method for linear parabolic problems

Abstract:  We analyse the backward Euler-Galerkin method for linear parabolic problems, looking for quasi-optimality results in the sense of Céa's > Lemma. We study first the spatial discretization, proving that the H1-stability of the L2- projection is also a necessary condition for quasi-optimality. Regarding the discretization in time with backward Euler, we prove that the error is equivalent to the sum of the best errors with piecewise constants for the exact solution and its time derivative. Concerning the case when the spatial discretization is allowed to change with time, we bound  the error with the best error and an additional term, which vanishes if there are not modifications of the spatial dicretization and it is consistent with the example of non convergence in Dupont '82. We combine these elements in an analysis of the backward Euler-Galerkin method and derive error estimates in case the spatial discretization is based on finite elements.