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Universally Composable Blind Signatures in the Plain Model

Aslak Bakke Buan, Kristian Gjøsteen, Lillian Kråkmo

Published Jan 1, 2006• 6 citations
OpenAlex

Abstract

In the universal composability framework, we define an ideal functionality for blind signatures, as an alternative to a functionality recently proposed by Fischlin. Fischlin proves that his functionality cannot be realized in the plain model, but this result does not apply to our functionality. We show that our functionality is realized in the plain model by a blind signature protocol if and only if the corresponding blind signature scheme is secure with respect to blindness and non-forgeability, as defined by Juels, Luby and Ostrovsky.

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•Jan 1, 2007•0 citations
In the universal composability framework, we define an ideal functionality for blind signatures, as an alternative to a functionality recently proposed by Fischlin. Fischlin proves that his functionality cannot be realized in the plain model, but this result does not apply to our functionality. We show that our functionality is realized in the plain model by a blind signature protocol if and only if the corresponding blind signature scheme is secure with respect to blindness and non-forgeability, as defined by Juels, Luby and Ostrovsky.
A universally composable (UC) blind signature functionality requres users to commit to the message to be blindly signed. It is thereby impossible to realize in the plain model. This paper shows that even non-committing variants of UC blind signature functionality can not be realized in the plain model. We characterize UC non-committing blind signatures in the common reference string model by presenting equivalent stand-alone security notions under static corruption. Usefulness of the characterization is demonstrated by showing that Fischlin’s basic stand-alone blind signature scheme can be transformed into a UC non-committing blind signature protocol without using extra cryptographic components. We extend the results to the adaptive corruption model and present analogous notions, theorems, and constructions both in the erasure model and the non-erasure model.
This paper studies non-committing type of universally composable (UC) blind signature protocols where an adversary does not necessarily commit to a message when requesting a signature. An ordinary UC blind signature functionality requires users to commit to the message to be blindly signed. It is thereby impossible to realise in the plain model. This paper first shows that even non-committing variants cannot be realised in the plain model. We then characterise UC non-committing blind signatures in the common reference string model by presenting equivalent stand-alone security notions under static corruption. The usefulness of the characterisation is demonstrated by showing that Fischlin’s basic stand-alone blind signature scheme can be transformed into a UC non-committing blind signature protocol without using extra cryptographic components. We extend the results to the adaptive corruption model and present analogous notions, theorems, and constructions both in the erasure model and the non-erasure model.
Blind signatures play a critical role in digital cash systems. In this paper, we investigate the blind signature functionality in the framework of universally composable (UC) security — the strongest security guarantees up to now for cryptographic protocols over the Internet. We present the universally composable blind signature functionality, [Formula: see text]. Our approach is based on a new UC signature functionality [Formula: see text], which is a modified version of the original signature functionality [Formula: see text] presented by Canetti. We also prove that [Formula: see text] and [Formula: see text] are actually equivalent with respect to non-adaptive adversaries. Our result is of both theoretical and practical consequence to future research studies and practical implementations of digital cash systems with universally composable security.
Abstract. How to define the security of undeniable signature schemes is a challenging task. This paper presents two security definitions of undeniable signature schemes which are more useful or natural than the existing definition. It then proves their equivalence. We first define the UC-security, where UC means universal composability. We next show that there exists a UC-secure undeniable signature scheme which does not satisfy the standard definition of security that has been believed to be adequate so far. More precisely, it does not satisfy the invisibility defined by [10]. We then show a more adequate definition of invisibility which captures a wider class of (naturally secure) undeniable signature schemes. We finally prove that the UC-security against non-adaptive adversaries is equivalent to this definition of invisibility and the strong unforgeability in FZK-hybrid model, where FZK is the ideal ZK functionality. Our result of equivalence implies that all the known proven secure undeniable signature schemes (including Chaum’s scheme) are UC-secure if the confirmation/disavowal protocols are both UC zero-knowledge.
Recently some efforts were made towards capturing the security requirements from digital signature schemes as an ideal functionality within a composable security framework. This modeling of digital signatures potentially has some significant analytical advantages (such as enabling component-wise analysis of complex systems that use signature schemes, as well as symbolic and automatable analysis of such systems). However, it turns out that formulating ideal functionalities that capture the properties expected from signature schemes in a way that is both sound and enjoys the above advantages is not a trivial task. This work has several contributions. We first correct some flaws in the definition of the ideal signature functionality of Canetti, 2001, and subsequent formulations. Next we provide a minimal formalization of “ideal certification authorities ” and show how authenticated communication can be obtained using ideal signatures and an ideal certification authority. This is done while guaranteeing full modularity (i.e., each component is analyzed as stand-alone), and in an unconditional and errorless way. This opens the door to symbolic and automated analysis of protocols for these tasks, in a way that is both modular and cryptographically sound.
We study the design of practical blind signatures in the universal composability (UC) setting against adaptive adversaries. We introduce a new property for blind signature schemes that is fundamental for managing adaptive adversaries: an equivocal blind signature is a blind signature protocol where a simulator can construct the internal state of the client so that it matches a simulated transcript even after a signature was released. We present a general construction methodology for building practical adaptively secure blind signatures: the starting point is a 2-move “lite blind signature”, a lightweight 2-party signature protocol that we formalize and implement both generically as well as number theoretically: formalizing a primitive as “lite ” means that the adversary is required to show all private tapes of adversarially controlled parties; this enables us to conveniently separate zero-knowledge (ZK) related security requirements from the remaining security properties in the primitive’s design methodology. We then focus on the exact ZK requirements for building blind signatures. To this effect, we formalize two special ZK ideal functionalities, single-verifier-ZK (SVZK) and single-prover-ZK (SPZK) and we investigate the requirements for realizing them in a commit-and-prove fashion as building blocks for adaptively secure UC blind signatures. SVZK can be realized without relying on a multi-session UC commitment; as