Advanced Properties of Digital Signature Schemes

Licentiatavhandling, 2026

In today's digital society it is of great importance to be able to authenticate ourselves to others and verify the identity of others without any physical interaction. Digital signatures are a well established cryptographic primitive used for authentication over the internet. They are a purely asymmetric primitive and do not require any pre-shared secrets between the authenticating and the verifying parties. However, with our ever-growing dependence on digital platforms for communication, storage and computations, plain digital signatures do not cover all today's needs for secure authentication.

This thesis explores advanced properties of digital signatures, particularly it contributes to the field of multi-key homomorphic signatures and threshold signatures. Multi-key homomorphic signatures allow for verification of outsourced computations to untrusted cloud services and threshold signatures distribute trust in a system and avoid a single point of failure.

Paper 1 examines the succinctness property of multi-key homomorphic signatures and presents the most succinct multi-key homomorphic signatures in the literature. Succinctness refers to the asymptotic size of an aggregated signature in terms of the number of individual input signatures. This is an important aspect of homomorphic signatures since the overhead of verifying the correctness of an outsourced computation depends linearly on the size of the aggregated signature.

Paper 2 presents an adaptively secure universally composable threshold Schnorr signature scheme from standard assumptions. Security can be proven under a variety of assumptions and in various different frameworks that capture differently strong adversaries and more or less realistic settings. Adaptive security in the universal composability framework is considered as one of the strongest security notions. Consequently, proving security in this setting provides strong guarantees for real-world deployment.