Adaptively Secure 5 Round Threshold Signatures from MLWE/MSIS and DL with Rewinding
METADATA ONLY
Loading...
Author / Producer
Date
2024
Publication Type
Conference Paper
ETH Bibliography
yes
Citations
Altmetric
METADATA ONLY
Data
Rights / License
Abstract
T-out-of-N threshold signatures have recently seen a renewed interest, with various types now available, each offering different tradeoffs. However, one property that has remained elusive is adaptive security. When we target thresholdizing existing efficient signatures schemes based on the Fiat-Shamir paradigm such as Schnorr, the elusive nature becomes clear. This class of signature schemes typically rely on the forking lemma to prove unforgeability. That is, an adversary is rewound and run twice within the security game. Such a proof is at odds with adaptive security, as the reduction must be ready to answer 2(T - 1) secret key shares in total, implying that it can reconstruct the full secret key. Indeed, prior works either assumed strong idealized models such as the algebraic group model (AGM) or modified the underlying signature scheme so as not to rely on rewinding based proofs. In this work, we propose a new proof technique to construct adaptively secure threshold signatures for existing rewinding-based Fiat-Shamir signatures. As a result, we obtain the following:
1. The first adaptively secure 5 round lattice-based threshold signature under the MLWE and MSIS assumptions in the ROM. The resulting signature is a standard signature of Raccoon, a lattice-based signature scheme by del Pino et al., submitted to the additional NIST call for proposals.
2. The first adaptively secure 5 round threshold signature under the DL assumption in the ROM. The resulting signature is a standard Schnorr signature. To the best of our knowledge, this is the first adaptively secure threshold signature based on DL even assuming stronger models like AGM.
Our work is inspired by the recent statically secure lattice-based 3 round threshold signature by del Pino et al. (Eurocrypt 2024) based on Raccoon. While they relied on so-called one-time additive masks to solve lattice specific issues, we notice that these masks can also be a useful tool to achieve adaptive security. At a very high level, we use these masks throughout the signing protocol to carefully control the information the adversary can learn from the signing transcripts. Intuitively, this allows the reduction to return a total of 2(T - 1) randomly sampled secret key shares to the adversary consistently and without being detected, resolving the above paradoxical situation. Lastly, by allowing the parties to maintain a simple state, we can compress our 5 round schemes into 4 rounds.
Permanent link
Publication status
published
External links
Book title
Advances in Cryptology – CRYPTO 2024
Journal / series
Volume
14926
Pages / Article No.
459 - 491
Publisher
Springer
Event
44th Annual International Cryptology Conference (CRYPTO 2024)
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Organisational unit
09693 - Hofheinz, Dennis / Hofheinz, Dennis