Publications

Contributions to cryptography, and arithmetic geometry.

Journal Article

Secure Addition of Floating Points

Thijs Veugen, Robert Wezeman, Alessandro Amadori, Sven Bootsma, Bart Kamphorst

International Journal of Applied Cryptography

2024

AbstractSecure multi-party computation (MPC) and homomorphic encryption are powerful tools for computing with secret numbers without revealing inputs or intermediate values. To securely achieve high accuracy with varying number sizes, one needs to work with floating points in the secret domain. The main bottleneck of secure floating points is addition. We improve its efficiency by designing a protocol for multiple additions, using standard building blocks available in most MPC platforms. The more additions n are combined, the larger the relative gain — up to a factor of 13 with n = 1,024. Additionally, we introduce a new protocol for securely computing the bitlength (given upper bound M), the first with linear time complexity and constant round complexity.
DOI
Master's Thesis

On Certain Elliptic Surfaces With j-Invariant Zero Over Prime Fields of Positive Characteristic

S.E. Bootsma

University of Groningen

2023

AbstractWe find prime numbers p such that the elliptic surface defined by y² = x³ + t³⁶⁰ + 1 has Mordell-Weil rank 68 over F_p. We show that, up to finite index, the generating sections are obtained from a reduction modulo p of the characteristic zero case. Furthermore, using the Tate conjecture for abelian varieties over finite fields and the theory of F_{q²}-maximal curves, we prove that the family of elliptic surfaces over F_p defined by y² = x³ + t^(p+1) + 1 has Mordell-Weil rank p − 1.
Thesis