Publication

Short undeniable signatures : design, analysis, and applications

Jean Monnerat
2006
Theses

Abstract

Digital signatures are one of the main achievements of public-key cryptography and constitute a fundamental tool to ensure data authentication. Although their universal verifiability has the advantage to facilitate their verification by the recipient, this property may have undesirable consequences when dealing with sensitive and private information. Motivated by such considerations, undeniable signatures, whose verification requires the cooperation of the signer in an interactive way, were invented. This thesis is mainly devoted to the design and analysis of short undeniable signatures. Exploiting their online property, we can achieve signatures with a fully scalable size depending on the security requirements. To this end, we develop a general framework based on the interpolation of group elements by a group homomorphism, leading to the design of a generic undeniable signature scheme. On the one hand, this paradigm allows to consider some previous undeniable signature schemes in a unified setting. On the other hand, by selecting group homomorphisms with a small group range, we obtain very short signatures. After providing theoretical results related to the interpolation of group homomorphisms, we develop some interactive proofs in which the prover convinces a verifier of the interpolation (resp. non-interpolation) of some given points by a group homomorphism which he keeps secret. Based on these protocols, we devise our new undeniable signature scheme and prove its security in a formal way. We theoretically analyze the special class of group characters on Z*n. After studying algorithmic aspects of the homomorphism evaluation, we compare the efficiency of different homomorphisms and show that the Legendre symbol leads to the fastest signature generation. We investigate potential applications based on the specific properties of our signature scheme. Finally, in a topic closely related to undeniable signatures, we revisit the designated confirmer signature of Chaum and formally prove the security of a generalized version.

Official source

https://infoscience.epfl.ch/entities/publication/c483f0d3-5792-4d53-8d2d-d8fd15b36b60

Jean Monnerat
2006
Theses

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/c483f0d3-5792-4d53-8d2d-d8fd15b36b60

Related concepts (28)

Digital signature

A digital signature is a mathematical scheme for verifying the authenticity of digital messages or documents. A valid digital signature on a message gives a recipient confidence that the message came from a sender known to the recipient. Digital signatures are a standard element of most cryptographic protocol suites, and are commonly used for software distribution, financial transactions, contract management software, and in other cases where it is important to detect forgery or tampering.

Homomorphism

In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient Greek language: ὁμός () meaning "same" and μορφή () meaning "form" or "shape". However, the word was apparently introduced to mathematics due to a (mis)translation of German ähnlich meaning "similar" to ὁμός meaning "same". The term "homomorphism" appeared as early as 1892, when it was attributed to the German mathematician Felix Klein (1849–1925).

Group homomorphism

In mathematics, given two groups, (G, ∗) and (H, ·), a group homomorphism from (G, ∗) to (H, ·) is a function h : G → H such that for all u and v in G it holds that where the group operation on the left side of the equation is that of G and on the right side that of H. From this property, one can deduce that h maps the identity element eG of G to the identity element eH of H, and it also maps inverses to inverses in the sense that Hence one can say that h "is compatible with the group structure".

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