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We prove a functional equation for a vector valued real analytic Eisenstein series transforming with the Weil representation of Sp(n, Z) on C[(L'/L)(n)]. By relating such an Eisenstein series with a real analytic Jacobi Eisenstein series of degree n, a functional equation for such an Eisenstein series is proved. Employing a doubling method for Jacobi forms of higher degree established by Arakawa, we transfer the aforementioned functional equation to a zeta function defined by the eigenvalues of a Jacobi eigenform. Finally, we obtain the analytic continuation and a functional equation of the standard L-function attached to a Jacobi eigenform, which was already proved by Murase, however in a different way.
We present a ready to compute trace formula for Hecke operators on vector-valued modular forms of integral weight for SL2(Z) transforming under the Weil representation. As a corollary, we obtain a ready to compute dimension formula for the corresponding space of vector-valued cusp forms, which is more general than the dimension formulae previously published in the vector-valued setting.
A Novel Design Flow for a Security-Driven Synthesis of Side-Channel Hardened Cryptographic Modules
(2017)
Over the last few decades, computer-aided engineering (CAE) tools have been developed and improved in order to ensure a short time-to-market in the chip design business. Up to now, these design tools do not yet support an integrated design strategy for the development of side-channel-resistant hardware implementations. In order to close this gap, a novel framework named AMASIVE (Adaptable Modular Autonomous SIde-Channel Vulnerability Evaluator) was developed. It supports the designer in implementing devices hardened against power attacks by exploiting novel security-driven synthesis methods. The article at hand can be seen as the second of the two contributions that address the AMASIVE framework. While the first one describes how the framework automatically detects vulnerabilities against power attacks, the second one explains how a design can be hardened in an automatic way by means of appropriate countermeasures, which are tailored to the identified weaknesses. In addition to the theoretical introduction of the fundamental concepts, we demonstrate an application to the hardening of a complete hardware implementation of the block cipher PRESENT.
We compute the Fourier expansion of Hecke operators on vector-valued modular forms for the Weil representation associated to a lattice L. The Hecke operators considered in this paper include operators T(p^2l) where p is a prime dividing the level of the lattice L. Additionally, an explicit formula for a general type of Gauss sum associated to a lattice L drops out as a by-product.
On analytic properties of the standard zeta function attached to a vector-valued modular form
(2022)
We proof a Garrett–Böcherer decomposition of a vector-valued Siegel Eisenstein series E2l,0 of genus 2 transforming with the Weil representation of Sp2(Z) on the group ring C[(L′/L)2]. We show that the standard zeta function associated to a vector-valued common eigenform f for the Weil representation can be meromorphically continued to the whole s-plane and that it satisfies a functional equation. The proof is based on an integral representation of this zeta function in terms of f and E2l,0.