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4 search hits
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Black Box Cryptanalysis of Hash Networks based on Multipermutations
(1994)
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Claus Peter Schnorr
Serge Vaudenay
- Black box cryptanalysis applies to hash algorithms consisting of many small boxes, connected by a known graph structure, so that the boxes can be evaluated forward and backwards by given oracles. We study attacks that work for any choice of the black boxes, i.e. we scrutinize the given graph structure. For example we analyze the graph of the fast Fourier transform (FFT). We present optimal black box inversions of FFT-compression functions and black box constructions of collisions. This determines the minimal depth of FFT-compression networks for collision-resistant hashing. We propose the concept of multipermutation, which is a pair of orthogonal latin squares, as a new cryptographic primitive that generalizes the boxes of the FFT. Our examples of multipermutations are based on the operations circular rotation, bitwise xor, addition and multiplication.
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A Stable Integer Relation Algorithm
(1994)
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Claus Peter Schnorr
Carsten Rössner
- We study the following problem: given x element Rn either find a short integer relation m element Zn, so that =0 holds for the inner product <.,.>, or prove that no short integer relation exists for x. Hastad, Just Lagarias and Schnorr (1989) give a polynomial time algorithm for the problem. We present a stable variation of the HJLS--algorithm that preserves lower bounds on lambda(x) for infinitesimal changes of x. Given x \in {\RR}^n and \alpha \in \NN this algorithm finds a nearby point x' and a short integer relation m for x'. The nearby point x' is 'good' in the sense that no very short relation exists for points \bar{x} within half the x'--distance from x. On the other hand if x'=x then m is, up to a factor 2^{n/2}, a shortest integer relation for \mbox{x.} Our algorithm uses, for arbitrary real input x, at most \mbox{O(n^4(n+\log \alpha))} many arithmetical operations on real numbers. If x is rational the algorithm operates on integers having at most \mbox{O(n^5+n^3 (\log \alpha)^2 + \log (\|q x\|^2))} many bits where q is the common denominator for x.
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Algebraic values of Schwarz triangle functions
(2005)
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Hironori Shiga
Jürgen Wolfart
- 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.
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Die Stammbäume zufällig verzweigender Populationen
(2001)
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Jochen Geiger
- Bei der Untersuchung des Langzeitverhaltens von Verzweigungsprozessen und räumlich verzweigenden Populationen ist die Betrachtung von Stammbäumen zunehmend in den Vordergrund gerückt. Probabilistische Methoden haben die in der Theorie vorherrschenden analytischen Techniken ergänzt und zu wesentlichen neuen Einsichten geführt. Die vorliegende Synopse diskutiert eine Auswahl meiner Veröffentlichungen der letzten Jahre. Den Arbeiten ist gemeinsam, dass durch das Studium der genealogischen Verhältnisse in der Population Aussagen über deren Langzeitverhalten gewonnen werden konnten. Zwei dieser Arbeiten behandeln den klassischen Galton-Watson Prozess. Eine weitere Arbeit befasst sich mit Verzweigungsprozessen in zufälliger Umgebung, sie ist technische wesentlich anspruchsvoller. Die vierte der hier besprochenen Arbeiten beschäftigt sich mit dem Wählermodell, einem der Prototypen interagierender Teilchensysteme.
