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We present new candidates for quantum-resistant public-key cryptosystems based on the conjectured difficulty of finding isogenies between supersingular elliptic curves. The main technical idea in our scheme is that we transmit the images of torsion bases under the isogeny in order to allow the two parties to arrive at a common shared key despite the(More)
Eukaryotic initiation factor 5A (eIF5A) is the only protein in nature that contains hypusine, an unusual amino acid formed post-translationally in two steps by deoxyhypusine synthase and deoxyhypusine hydroxylase. Genes encoding eIF5A or deoxyhypusine synthase are essential for cell survival and proliferation. To determine the physiological function of(More)
The aim of this paper is to justify the common cryptographic practice of selecting elliptic curves using their order as the primary criterion. We can formalize this issue by asking whether the discrete log problem (dlog) has the same difficulty for all curves over a given finite field with the same order. We prove that this is essentially true by showing(More)
As hardware capabilities increase, low-power devices such as smartphones represent a natural environment for the efficient implementation of cryptographic pairings. Few works in the literature have considered such platforms despite their growing importance in a postPC world. In this paper, we investigate the efficient computation of the Optimal-Ate pairing(More)
We study the security of elliptic curve Diffie-Hellman secret keys in the presence of oracles that provide partial information on the value of the key. Unlike the corresponding problem for finite fields, little is known about this problem, and in the case of elliptic curves the difficulty of representing large point multiplications in an algebraic manner(More)
Given two elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit an isogeny between them, but finding such an isogeny is believed to be computationally difficult. The fastest known classical algorithm takes exponential time, and prior to our work no faster quantum algorithm was known.(More)
We present a construction of expander graphs obtained from Cayley graphs of narrow ray class groups, whose eigenvalue bounds follow from the Generalized Riemann Hypothesis. Our result implies that the Cayley graph of (Z/qZ)∗ with respect to small prime generators is an expander. As another application, we show that the graph of small prime degree isogenies(More)
We survey the set of all prior two-party certificateless key agreement protocols available in the literature at the time of this work. We find that all of the protocols exhibit vulnerabilities of varying severity, ranging from lack of resistance to leakage of ephemeral keys up to (in one case) a man-in-the-middle attack. Many of the protocols admit(More)
Recent work [27, 15] introduced a novel peer-to-peer application that leverages content sharing and aggregation among the peers to diagnose misconfigurations on a desktop PC. This application poses interesting challenges in preserving privacy of user configuration data and in maintaining integrity of troubleshooting results. In this paper, we provide a much(More)