Unconditionally Secure Signature Schemes Revisited

Abstract

Unconditionally secure signature (USS) schemes provide the ability to electronically sign documents without the reliance on computational assumptions needed in traditional digital signatures. Unlike digital signatures, USS schemes require both different signing and different verification algorithms for each user in the system. Thus, any viable security definition for a USS scheme must carefully treat the subject of what constitutes a valid signature. That is, it is important to distinguish between signatures that are created using a user's signing algorithm and signatures that may satisfy one or more user verification algorithms. Moreover, given that each verifier has his own distinct verification algorithm, a USS scheme must necessarily handle the event of a disagreement. In this paper, we present a new security model for USS schemes that incorporates these notions, as well as give a formal treatment of dispute resolution and the trust assumptions required. We provide formal definitions of non-repudiation and transferability in the context of dispute resolution, and give sufficient conditions for a USS scheme to satisfy these properties. Finally, we give an analysis of the construction of Hanaoka et al. in our security model.

Advances in quantum cryptography

“…In order to achieve USS, all parties needed to share (long) secret key pairwise, while another assumption was also necessary (an authenticated broadcast channel or anonymous channels). Only a few papers followed this work [760][761][762][763]. The main reason for the limited interest was probably because such protocols were seen as impractical, specifically because they require point-to-point shared secret keys.…”

Implementation vulnerabilities in general quantum cryptography

“…Digital signatures are an important primitive in cryptography. Specifically, three security properties are required for signatures: unforgeability, nonrepudiation, and transferability [21]. Unforgeability guarantees a unique message signer, so no one else is able to forge a valid signature.…”

“…QDS based on laws of quantum physics is able to satisfy these requirements, and achieve information-theoretic security [4]. Unconditionally secure signatures are also possible based on shared secret keys [21][22][23][24], and the scaling of secret key length with respect to message length can be more favorable than for quantum signatures. The secret shared key could be generated by QKD, but otherwise these schemes remain entirely 'classical'.…”

Must the Communication Graph of MPC Protocols be an Expander?

“…In [81,84] a signature scheme satisfying the above notion of security was constructed. These signatures have a deterministic signature generation algorithm Sign.…”

“…These signatures have a deterministic signature generation algorithm Sign. In the following (Figure 14) we describe the construction from [81] (as described by [84] but for a single signer). We point out that the keys and signatures in the described scheme are elements of a sufficiently large finite field F (i.e., |F | = O(2 poly(κ) )); one can easily derive a scheme for strings of length = poly(κ) by applying an appropriate encoding: e.g., map the i'th element of F to the i'th string (in the lexicographic order) and vice versa.…”