A Digital Signature Scheme for Long-Term Security

In this paper we propose a signature scheme based on two intractable problems, namely the integer factorization problem and the discrete logarithm problem for elliptic curves. It is suitable for applications requiring long-term security and provides a more efficient solution than the existing ones

On the Design of Cryptographic Primitives

The main objective of this work is twofold. On the one hand, it gives a brief overview of the area of two-party cryptographic protocols. On the other hand, it proposes new schemes and guidelines for improving the practice of robust protocol design. In order to achieve such a double goal, a tour through the descriptions of the two main cryptographic primitives is carried out. Within this survey, some of the most representative algorithms based on the Theory of Finite Fields are provided and new general schemes and specific algorithms based on Graph Theory are proposed

Efficient asynchronous accumulators for distributed PKI

Cryptographic accumulators are a tool for compact set representation and secure set membership proofs. When an element is added to a set by means of an accumulator, a membership witness is generated. This witness can later be used to prove the membership of the element. Typically, the membership witness has to be synchronized with the accumulator value, and to be updated every time another element is added to the accumulator. In this work we propose an accumulator that, unlike any prior scheme, does not require strict synchronization. In our construction a membership witness needs to be updated only a logarithmic number of times in the number of subsequent element additions. Thus, an out-of-date witness can be easily made current. Vice versa, a verifier with an out-of-date accumulator value can still verify a current membership witness. These properties make our accumulator construction uniquely suited for use in distributed applications, such as blockchain-based public key infrastructures

Forgery-Resilience for Digital Signature Schemes

We introduce the notion of forgery-resilience for digital signature schemes, a new paradigm for digital signature schemes exhibiting desirable legislative properties. It evolves around the idea that, for any message, there can only be a unique valid signature, and exponentially many acceptable signatures, all but one of them being spurious. This primitive enables a judge to verify whether an alleged forged signature is indeed a forgery. In particular, the scheme considers an adversary who has access to a signing oracle and an oracle that solves a “hard” problem, and who tries to produce a signature that appears to be acceptable from a verifier’s point of view. However, a judge can tell apart such a spurious signature from a signature that is produced by an honest signer. This property is referred to as validatibility. Moreover, the scheme provides undeniability against malicious signers who try to fabricate spurious signatures and deny them later by showing that they are not valid. Last but not least, trustability refers to the inability of a malicious judge trying to forge a valid signature. This notion for signature schemes improves upon the notion of fail-stop signatures in different ways. For example, it is possible to sign more than one messages with forgery-resilient signatures and once a forgery is found, the credibility of a previously signed signature is not under question. A concrete instance of a forgery-resilient signature scheme is constructed based on the hardness of extracting roots of higher residues, which we show to be equivalent to the factoring assumption. In particular, using collision-free accumulators, we present a tight reduction from malicious signers to adversaries against the factoring problem. Meanwhile, a secure pseudorandom function ensures that no polynomially-bounded cheating verifier, who can still solve hard problems, is able to forge valid signatures. Security against malicious judges is based on the RSA assumption