Threshold signatures from VOLE

The focus of this thesis is on threshold digital signatures and in particular on Schnorr signatures (1991). Following the expiration of its patent in 2008, Schnorr signature has gained significance in the realm of digital signatures due to its simplicity, provable security, and linear structure. Additionally, the recent NIST Internal Report on Threshold EdDSA/Schnorr signatures further supports the study of an efficient implementation of threshold Schnorr signatures. This work addresses the challenge of elucidating some key steps presented in the paper of Kondi et al. (CRYPTO 2023), which introduces the first example of a deterministic two-party Schnorr signature based on VOLEs (vector oblivious linear evaluation) which also makes effective use of the underlying cryptographic protocols through a black-box approach. More concretely, the thesis gives an explicit description of the setup phase needed for the two-party Schnorr signatures scheme given by Kondi et al. and provides a generalization of the Softspoken protocol for VOLE (Roy, CRYPTO 2022) from polynomial fields to arbitrary fields, by following the same approach described by Baum et al. (CRYPTO 2023).