We develop a novel method to completely solve the 3-term partial exponential Diophantine equation that represents a generalization of the standard discrete logarithm problem. Our method not only ...reveals the internal structure of the equation's solution and yields a numerical algorithm to solve it systematically, but also provides an alternative approach to the discrete logarithm problem.
Vehicular ad-hoc networks (VANETs) have been emerging based on the state-of-art technologies in wireless and network communications. The message authentications between vehicles and roadside units ...are essential for the security of VANETs. Messages should be signed and verified before they could be trusted. The real identity of vehicles should not be revealed, but which is only traceable by authorized parties. Existing solutions either rely heavily on a tamper-proof hardware device or cannot satisfy the security requirement. Communication overhead as another issue has also not been well addressed in previously reported studies. To address these issues, in this paper, we propose the SPACF scheme that is based on software without relying on any special hardware. We use the Cuckoo filter and the binary search methods to achieve higher success rate than the previous schemes in the batch verification phase. In order to guarantee that it can satisfy message authentication requirement, existential unforgeability of underlying signature against adaptively chosen-message attack is proved under the elliptic curve discrete logarithm problem in the random oracle model. The evaluation results show that our proposed scheme is more efficient than the previous schemes since it is pairing free and does not use map-to-point hash functions, and it satisfies security and privacy requirements of vehicular ad hoc networks.
The security of the most of the existing strong designated verifier signature (SDVS) scheme are based on a single cryptographic hard problem. Although these schemes seem secure today, there is a ...possibility for an adversary to find a solution for this problem in the future and if this happens, then such SDVS schemes will no longer be secure. We develop a new SDVS scheme based on hybrid problems; factorization and discrete logarithm. The new developed scheme provides a greater security level than those previous designated SDVS schemes and satisfies the security properties and requirements of a SDVS scheme.
Recently many pairing-based cryptographic protocols have been designed with a wide variety of new novel applications including the ones in the emerging technologies like cloud computing, internet of ...things (IoT), e-health systems, and wearable technologies. There have been, however, a wide range of incorrect use of these primitives mainly because of their use in a “black-box” manner. Some new attacks on the discrete logarithm problem lead to either totally insecure or highly inefficient pairing-based protocols, and extend considerably the issues related to pairings originally pointed out by Galbraith et al. (2008). Other reasons are the implementation attacks, the minimal embedding field attacks, and the issues due to the existence of auxiliary inputs. Although almost all these issues are well-known to mathematical cryptographers, there is no state-of-the-art assessment covering all these new issues which could be used by the applied cryptography researchers and the IT-security developers. In order to illustrate this point, we give a list of recent papers having either wrong security assumptions or realizability/efficiency issues. Furthermore, we give a compact and an state-of-the-art recipe of the correct use of pairings for the correct design with a view towards efficient and secure implementation of security solutions using these primitives.
Recent progress on NFS imposed a new estimation of the security of pairings. In this work we study the best attacks against some of the most popular pairings and propose new key sizes using an ...analysis which is more precise than the analysis in a recent article of Menezes, Sarkar and Singh. We also select pairing-friendly curves for standard security levels.
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