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Public key signature schemes are necessary for the access control to communication networks and for proving the authenticity of sensitive messages such as electronic fund transfers. Since the invention of the RSA scheme by Rivest, Shamir and Adleman (1978) research has focused on improving the e±ciency of these schemes. In this paper we present an efficient algorithm for generating public key signatures which is particularly suited for interactions between smart cards and terminals.
We present a novel parallel one-more signature forgery against blind Okamoto-Schnorr and blind Schnorr signatures in which an attacker interacts some times with a legitimate signer and produces from these interactions signatures. Security against the new attack requires that the following ROS-problem is intractable: find an overdetermined, solvable system of linear equations modulo with random inhomogenities (right sides). There is an inherent weakness in the security result of POINTCHEVAL AND STERN. Theorem 26 [PS00] does not cover attacks with 4 parallel interactions for elliptic curves of order 2200. That would require the intractability of the ROS-problem, a plausible but novel complexity assumption. Conversely, assuming the intractability of the ROS-problem, we show that Schnorr signatures are secure in the random oracle and generic group model against the one-more signature forgery.
We present a practical algorithm that given an LLL-reduced lattice basis of dimension n, runs in time O(n3(k=6)k=4+n4) and approximates the length of the shortest, non-zero lattice vector to within a factor (k=6)n=(2k). This result is based on reasonable heuristics. Compared to previous practical algorithms the new method reduces the proven approximation factor achievable in a given time to less than its fourthth root. We also present a sieve algorithm inspired by Ajtai, Kumar, Sivakumar [AKS01].
Let G be a Fuchsian group containing two torsion free subgroups defining isomorphic Riemann surfaces. Then these surface subgroups K and alpha-Kalpha exp(-1) are conjugate in PSl(2,R), but in general the conjugating element alpha cannot be taken in G or a finite index Fuchsian extension of G. We will show that in the case of a normal inclusion in a triangle group G these alpha can be chosen in some triangle group extending G. It turns out that the method leading to this result allows also to answer the question how many different regular dessins of the same type can exist on a given quasiplatonic Riemann surface.
We consider Schwarz maps for triangles whose angles are rather general rational multiples of pi. Under which conditions can they have algebraic values at algebraic arguments? The answer is based mainly on considerations of complex multiplication of certain Prym varieties in Jacobians of hypergeometric curves. The paper can serve as an introduction to transcendence techniques for hypergeometric functions, but contains also new results and examples.
The main subject of this survey are Belyi functions and dessins d'enfants on Riemann surfaces. Dessins are certain bipartite graphs on 2-mainfolds defining there are conformal and even an algebraic structure. In principle, all deeper properties of the resulting Riemann surfaces or algebraic curves should be encoded in these dessins, but the decoding turns out to be difficult and leads to many open problems. We emphasize arithmetical aspects like Galois actions, the relation to the ABC theorem in function filds and arithemtic questions in uniformization theory of algebraic curves defined over number fields.
The large conductance voltage- and Ca2+-activated potassium (BK) channel has been suggested to play an important role in the signal transduction process of cochlear inner hair cells. BK channels have been shown to be composed of the pore-forming alpha-subunit coexpressed with the auxiliary beta-1-subunit. Analyzing the hearing function and cochlear phenotype of BK channel alpha-(BKalpha–/–) and beta-1-subunit (BKbeta-1–/–) knockout mice, we demonstrate normal hearing function and cochlear structure of BKbeta-1–/– mice. During the first 4 postnatal weeks also, BKalpha–/– mice most surprisingly did not show any obvious hearing deficits. High-frequency hearing loss developed in BKalpha–/– mice only from ca. 8 weeks postnatally onward and was accompanied by a lack of distortion product otoacoustic emissions, suggesting outer hair cell (OHC) dysfunction. Hearing loss was linked to a loss of the KCNQ4 potassium channel in membranes of OHCs in the basal and midbasal cochlear turn, preceding hair cell degeneration and leading to a similar phenotype as elicited by pharmacologic blockade of KCNQ4 channels. Although the actual link between BK gene deletion, loss of KCNQ4 in OHCs, and OHC degeneration requires further investigation, data already suggest human BK-coding slo1 gene mutation as a susceptibility factor for progressive deafness, similar to KCNQ4 potassium channel mutations. © 2004, The National Academy of Sciences. Freely available online through the PNAS open access option.