Strong RSA Assumption Research Articles

An Effective Method to Implement Group Signature with Revocation

This paper presents an effective method to integrate the revocation mechanism into some group signature schemes that are based on the strong RSA assumption. The mechanism enables the group manager to either update a group member's certificates, or revoke a group member. More specifically, a generic method has been proposed for the protocols of sign, verify, and revocation. We demonstrate the effectiveness of the method by applying it to a well known group signature scheme. The new construction has better performance while enjoying an efficient revocation mechanism.

Signature Scheme in Multi-User Setting

Recently, Boneh and Boyen proposed a new provably secure short signature scheme under the q-strong Diffie-Hellman assumption without random oracles. This scheme is based on bilinear map which is different from Cramer-Shoup signature scheme (which is based on the strong RSA assumption). However, Tan TC[17] showed that Boneh- Boyen scheme is subjected to key substitution attacks in the multi-user setting. In this paper, we propose a new signature scheme. We prove that the proposed scheme is provably secured against existential forgery under adaptive chosen message attack in the standard model and also secure against key substitution attacks.

A new signature scheme without random oracles

Digital signature is commonly used for authentication of a user or data. In order to ensure the security of a signature scheme, it is important to design a signature scheme with a security proof. In 1999, Gennaro et al. and Cramer et al. respectively proposed practical and provably secure signature schemes under the standard assumption without the random oracle model. Since then, some provably secure signature schemes in the standard model were constructed, for example, Camenisch Lysyanskaya scheme in 2002; Fischlin scheme and Tan-Yi-Siew scheme in 2003. In this paper, we construct a new provably secure signature scheme based on the strong RSA assumption against existential forgery under adaptive chosen message attack in the standard model. The proposed scheme is also more efficient than other provable secure schemes in the standard model.

Secure scalable group signature with dynamic joins and separable authorities

To date, a group signature construction that is efficient, scalable, allows dynamic adversarial joins, and proven secure in a formal model has not been suggested. In this work we give the first such construction in the random oracle model. The demonstration of an efficient construction proven secure in a formal model that captures all intuitive security properties of a certain primitive is a basic goal in cryptographic design. To this end we adapt a formal model for group signatures capturing all the basic requirements that have been identified as desirable in the area and we construct an efficient scheme and prove its security. Our construction is based on the Strong-RSA assumption (as in the work of Ateniese et al.). In our system, due to the requirements of provable security in a formal model, we give novel constructions as well as innovative extensions of the underlying mathematical requirements and properties.

Strengthening Zero-Knowledge Protocols Using Signatures

Recently there has been an interest in zero-knowledge protocols with stronger properties, such as concurrency, simulation soundness, non-malleability, and universal composability. In this paper we show a novel technique to convert a large class of existing honest-verifier zero-knowledge protocols into ones with these stronger properties in the common reference string model. More precisely, our technique utilizes a signature scheme existentially unforgeable against adaptive chosen-message attacks, and transforms any Σ-protocol (which is honest-verifier zero-knowledge) into a simulation sound concurrent zero-knowledge protocol. We also introduce Ω-protocols, a variant of Σ-protocols for which our technique further achieves the properties of non-malleability and/or universal composability. In addition to its conceptual simplicity, a main advantage of this new technique over previous ones is that it avoids the Cook-Levin theorem, which tends to be rather inefficient. Indeed, our technique allows for very efficient instantiation based on the security of some efficient signature schemes and standard number-theoretic assumptions. For instance, one instantiation of our technique yields a universally composable zero-knowledge protocol under the Strong RSA assumption, incurring an overhead of a small constant number of exponentiations, plus the generation of two signatures.

Fine-grained forward-secure signature schemes without random oracles

We propose the concept of fine-grained forward-secure signature schemes. Such signature schemes not only provide non-repudiation w.r.t. past time periods the way ordinary forward-secure signature schemes do but, in addition, allow the signer to specify which signatures of the current time period remain valid when revoking the public key. This is an important advantage if the signer produces many signatures per time period as otherwise the signer would have to re-issue those signatures (and possibly re-negotiate the respective messages) with a new key. Apart from a formal model for fine-grained forward-secure signature schemes, we present practical schemes and prove them secure under the strong RSA assumption only, i.e., we do not resort to the random oracle model to prove security. As a side-result, we provide an ordinary forward-secure scheme whose key-update time is significantly smaller than that of known schemes which are secure without assuming random oracles.

Signature schemes based on the strong RSA assumption

We describe and analyze a new digital signature scheme. The new scheme is quite efficient, does not require the signer to maintain any state, and can be proven secure against adaptive chosen message attack under a reasonable intractability assumption, the so-called strong RSA assumption. Moreover, a hash function can be incorporated into the scheme in such a way that it is also secure in the random oracle model under the standard RSA assumption.

A group blind signature scheme based on the strong RSA assumption

A group blind signature require that a group member signs on group's behalf a document without knowing its content. In this paper we propose an efficient and probably secure group blind signature scheme. Our scheme is an extension of Camenisch and Michel's group signature scheme [2] that adds to the blindness property. The proposed group blind signature scheme is more efficient and secure than Lysyanskaya-Ramzan scheme [12].

A Group Signature Scheme Based on an RSA-Variant

The concept of group signatures allows a group member to sign messages anonymously on behalf of the group. However, in the case of a dispute, the identity of a signature’s originator can be revealed by a designated entity. In this paper we propose a new group signature scheme that is well suited for large groups, i.e., the length of the group’s public key and of signatures do not<br />depend on the size of the group. Our scheme is based on a variation of the RSA problem called strong RSA assumption. It is also more efficient than previous ones satisfying these requirements.