Electrum: UC Fail-Stop Server-Supported Signatures
摘要
Migration to quantum-safe cryptography represents a significant technological shift, addressing the vulnerabilities of traditional cryptographic primitives, such as KEMs and digital signatures. Yet, a number of challenges remain, especially in the development of secure solutions for sophisticated cryptographic applications. One of them is Smart-ID, European server-supported (threshold) signing service. To address this issue, we present Electrum, a fail-stop server-supported signature scheme designed to enhance security of existing Smart-ID service. Electrum combines multiprime RSA-based signatures with fail-stop features: providing not only unforgeability against classical adversaries but also allowing to prove that a given signature is a forgery made by classical and/or quantum adversaries. Proposed protocol can be seen as a temporary remedy against the quantum threat until standardised threshold signature schemes become a common practice. To prove security of Electrum, we introduce a new ideal functionality \(\mathcal {F}^{\textsf {SplFS}}\) for a fail-stop server-supported signing in the Universal Composability model. We show that Electrum protocol securely realizes the proposed functionality \(\mathcal {F}^{\textsf {SplFS}}\) .