The classical class invariants of Weber are introduced as quotients of Thetanullwerte, enabling the computation of these invariants more efficiently than as quotients of values of the Dedekind η-function. We show also how to compute the unit group of suitable ring class fields by means of proving the fact that most of the invariants introduced by Weber are… (More)
Several pairing-based cryptographic protocols are recently proposed with a wide variety of new novel applications including the ones in 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. The paper of Galbraith, Paterson,… (More)
One of the most important benefits of public cloud storage is outsourcing of management and maintenance with easy accessibility and retrievability over the internet. However, outsourcing data on the cloud brings new challenges such as integrity verification and privacy of data. More concretely, once the users outsource their data on the cloud they have no… (More)
We introduce generalized class invariants as quotients of Thetanull-werte, which realize the computation of class polynomials more efficiently than as quotients of values of the Dedekind η−function. Furthermore, we prove that these invariants are units in the corresponding class field as most of their classical counterparts.
—Bilinear maps are popular cryptographic primitives which have been commonly used in various modern cryptographic protocols. However, the cost of computation for bilinear maps is expensive because of their realization using variants of Weil and Tate pairings of elliptic curves. Due to increasing availability of cloud computing services, devices with limited… (More)
An important attack on multi-power RSA (N = p r q) was introduced by Sarkar in 2014, by extending the small private exponent attack of Boneh and Durfee on classical RSA. In particular, he showed that N can be factored efficiently for r = 2 with private exponent d satisfying d < N 0.395. In this paper, we generalize this work by introducing a new partial key… (More)
Recent results of Cascudo, Cramer, and Xing on the construction of arithmetic secret sharing schemes are improved by using some new bounds on the torsion limits of algebraic function fields. Furthermore, new bounds on the torsion limits of certain towers of function fields are given.
Bilinear maps are popular cryptographic primitives which have been commonly used in various modern cryptographic protocols. However, the cost of computation for bilinear maps is expensive because of their realization using variants of Weil and Tate pairings of ellip-tic curves. Due to increasing availability of cloud computing services, devices with limited… (More)