Forward-Secure Multisignature, Threshold Signature and Blind Signature Schemes

In this paper, we revisit the security of factoring-based signature schemes built via the Fiat–Shamir transform and show that they can admit tighter reductions to certain decisional complexity assumptions such as the quadratic-residuosity, the high-residuosity, and the $$\phi $$ -hiding assumptions. We do so by proving that the underlying identification schemes used in these schemes are a particular case of the lossy identification notion introduced by Abdalla et al. at Eurocrypt 2012. Next, we show how to extend these results to the forward-security setting based on ideas from the Itkis–Reyzin forward-secure signature scheme. Unlike the original Itkis–Reyzin scheme, our construction can be instantiated under different decisional complexity assumptions and has a much tighter security reduction. Moreover, we also show that the tighter security reductions provided by our proof methodology can result in concrete efficiency gains in practice, both in the standard and forward-security setting, as long as the use of stronger security assumptions is deemed acceptable. Finally, we investigate the design of forward-secure signature schemes whose security reductions are fully tight.

Forward-secure multisignature and blind signature schemes

In this work, we have proposed yet another forward secure signature based on bilinear pairings. Our forward secure signature requires the general security parameters only independent to the total number of time periods. The scheme can perform key evolving for unlimited time periods while maintaining sizes of keys and signature fixed. In addition, the signing algorithm is very efficient with the simple verification algorithm. We also provide a formal definition along with a detailed security proof of our signature scheme under the assumption of Computational Diffie-Hellman problem.

Optimal resilient threshold GQ signatures

We propose a key-evolving paradigm to deal with the key exposure problem of public key encryption schemes. The key evolving paradigm is like the one used for forward-secure digital signature schemes. Let time be divided into time periods such that at time period j, the decryptor holds the secret key SKj, while the public key PK is fixed during its lifetime. At time period j, a sender encrypts a message m as ?j, c?, which can be decrypted only with the private key SKj. When the time makes a transit from period j to j + 1, the decryptor updates its private key from SKj to SKj+1 and deletes SKj immediately. The key-evolving paradigm assures that compromise of the private key SKj does not jeopardize the message encrypted at the other time periods.We propose two key-evolving public key encryption schemes with z- resilience such that compromise of z private keys does not affect confidentiality of messages encrypted in other time periods. Assuming that the DDH problem is hard, we show one scheme semantically secure against passive adversaries and the other scheme semantically secure against the adaptive chosen ciphertext attack under the random oracle.

We point out some shortcomings of a proxy signature scheme which was proposed by Wang et al. and propose an improved scheme. In the improved scheme, the proxy key is produced by original signer and proxy signer, the key evolution algorithm takes use of a secure hash function, and the key updates after each signature, so it can limit the number of signatures and save the computation, so the new scheme is strong forward-secure and more efficient. Its security is based on the discrete logarithm problem.

Identity-based cryptography plays an important role in current electronic applications. Mediated Rivest-Shamir-Adleman (RSA) is a simple method of sharing RSA secret keys between the user and the security mediator (SEM). Any signature operation must involve these two parties. In this paper, we newly propose an identity-based forward secure threshold signature scheme based on mediated RSA. In this scheme, threshold users can combine multiple mediators to generate a valid signature. The public key can be any identity information such as mail address or internet protocol (IP) address. The scheme has forward security because the secret key is useless for the adversary after it is renewed. At last, we give the related analysis.

Fine-grained forward-secure signature schemes without random oracles

In non-repudiation services where digital signatures usually serve as irrefutable cryptographic evidence for dispute resolution, trusted time-stamping and certificate revocation services, although very costly in practice, must be available, to prevent big loss due to compromising of the signing key. In [12], a new concept called intrusion-resilient signature was proposed to get rid of trusted time-stamping and certificate revocation services and a concrete scheme was presented. In this paper, we put forward a new scheme that can achieve the same effect in a much more efficient way. In our scheme, forward-secure signature serves as a building block that enables signature validation without trusted time-stamping, and a one-way hash chain is employed to control the validity of public-key certificates without the CA’s involvement for certificate revocation. We adopt a model similar to the intrusion-resilient signature in [12], where time is divided into predefined short periods and a user has two modules, signer and home base. The signer generates forward-secure signatures on his own while the home base manages the validity of the signer’s public-key certificate with a one-way hash chain. The signature verifier can check the validity of signatures without retrieving the certificate revocation information from the CA. Our scheme is more robust in the sense that loss of synchronization between the signer and the home base could be recovered in the next time period while it is unrecoverable in [12]. Our scheme is also more flexible in the real implementation as it allows an individual user to control the validity of his own certificate without using the home base.

Huang and Chang proposed a flexible forward-secure signature scheme in International Journal of Computer Science and Network Security in 2006. In this paper, we give the security analysis of this scheme and point out this scheme doesn't satisfy the forward security. The main reason is that some secret parameters are used and these secret parameters should be viewed as a part of secret key. If an adversary gets the secret key in one time period, she can forge the signatures pertaining to past time periods. In order to analyse the security, we also introduce the security of forward-secure signature scheme.

Blind signatures play an important role in both electronic cash and electronic voting systems. Blind signatures should be secure against various attacks (such as signature forgeries). The work puts a special attention to secret key exposure attacks, which totally break digital signatures. Signatures that resist secret key exposure attacks are called forward secure in the sense that disclosure of a current secret key does not compromise past secret keys. This means that forward-secure signatures must include a mechanism for secret-key evolution over time periods. This paper gives a construction of the first blind signature that is forward secure. The construction is based on the SIS assumption in the lattice setting. The core techniques applied are the binary tree data structure for the time periods and the trapdoor delegation for the key-evolution mechanism.

Certificateless threshold signature scheme from bilinear maps

A Forward Secure Threshold Signature Scheme from Bilinear Pairing

With the use of a large number of mobile devices, the problem of key leakage becomes more and more serious. In view of the excellent characteristics of lattice cipher and forward-secure digital signature scheme, the construction of identity-based forward-secure digital signature based on lattice technology has become a research hotspot. However, the identity-based forward secure digital signature scheme on the existing grid has the disadvantage of excessive signature length. This paper uses the technique (without trapdoors) of Lyubashevsky and extended Samplepre, an efficient identity-based forward secure signature scheme from lattice is proposed. Its security is based on the Small Integer Solution (SIS) difficulty assumption, and the strong non-forgery of the signature scheme is achieved. Low computing overhead; The analysis results show that, compared with the existing schemes, the key and signature are smaller in size, more efficient in computing, able to resist quantum attacks, and more practical.

A new formal model of security for proxy signature schemes is presented and a provably secure short proxy signature scheme is proposed from bilinear maps. The proposed proxy signature scheme is based on two short secure signature schemes. Finally, a security proof of the proposed proxy signature scheme is showed by reducing directly the security of the proxy scheme to the security of the two basic signature schemes. The proposed proxy signature scheme has the shortest proxy signatures, the proxy signature generation needs no pairing operation and verification needs just one pairing operation.