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- Parallel FFT Hashing (1994)
- We propose two families of scalable hash functions for collision resistant hashing that are highly parallel and based on the generalized fast Fourier transform (FFT). FFT hashing is based on multipermutations. This is a basic cryptographic primitive for perfect generation of di®usion and confusion which generalizes the boxes of the classic FFT. The slower FFT hash functions iterate a compression function. For the faster FFT hash functions all rounds are alike with the same number of message words entering each round.

- Computation of highly regular nearby points (1995)
- We call a vector x/spl isin/R/sup n/ highly regular if it satisfies =0 for some short, non-zero integer vector m where <...> is the inner product. We present an algorithm which given x/spl isin/R/sup n/ and /spl alpha//spl isin/N finds a highly regular nearby point x' and a short integer relation m for x'. The nearby point x' is 'good' in the sense that no short relation m~ of length less than /spl alpha//2 exists for points x~ within half the x'-distance from x. The integer relation m for x' is for random x up to an average factor 2/sup /spl alpha//2/ a shortest integer relation for x'. Our algorithm uses, for arbitrary real input x, at most O(n/sup 4/(n+log A)) many arithmetical operations on real numbers. If a is rational the algorithm operates on integers having at most O(n/sup 5/+n/sup 3/(log /spl alpha/)/sup 2/+log(/spl par/qx/spl par//sup 2/)) many bits where q is the common denominator for x.

- The nontoxic natural compound Curcumin exerts anti-proliferative, anti-migratory, and anti-invasive properties against malignant gliomas (2010)
- Background: New drugs are constantly sought after to improve the survival of patients with malignant gliomas. The ideal substance would selectively target tumor cells without eliciting toxic side effects. Here, we report on the anti-proliferative, anti-migratory, and anti-invasive properties of the natural, nontoxic compound Curcumin observed in five human glioblastoma (GBM) cell lines in vitro. Methods: We used monolayer wound healing assays, modified Boyden chamber trans-well assays, and cell growth assays to quantify cell migration, invasion, and proliferation in the absence or presence of Curcumin at various concentrations. Levels of the transcription factor phospho-STAT3, a potential target of Curcumin, were determined by sandwich-ELISA. Subsequent effects on transcription of genes regulating the cell cycle were analyzed by quantitative real-time PCR. Effects on apoptosis were determined by caspase assays. Results: Curcumin potently inhibited GBM cell proliferation as well as migration and invasion in all cell lines contingent on dose. Simultaneously, levels of the biologically active phospho-STAT3 were decreased and correlated with reduced transcription of the cell cycle regulating gene c-Myc and proliferation marking Ki-67, pointing to a potential mechanism by which Curcumin slows tumor growth. Conclusions: Curcumin is part of the diet of millions of people every day and is without known toxic side effects. Our data show that Curcumin bears anti-proliferative, anti-migratory, and anti-invasive properties against GBM cells in vitro. These results warrant further in vivo analyses and indicate a potential role of Curcumin in the treatment of malignant gliomas.

- Security of 2t-root identification and signatures (1996)
- Korrektur zu: C.P. Schnorr: Security of 2t-Root Identification and Signatures, Proceedings CRYPTO'96, Springer LNCS 1109, (1996), pp. 143-156 page 148, section 3, line 5 of the proof of Theorem 3. Die Korrektur wurde präsentiert als: "Factoring N via proper 2 t-Roots of 1 mod N" at Eurocrypt '97 rump session.

- Efficient signature generation by smart cards (1991)
- 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.

- Improved low-density subset sum algorithms (1992)
- The general subset sum problem is NP-complete. However, there are two algorithms, one due to Brickell and the other to Lagarias and Odlyzko, which in polynomial time solve almost all subset sum problems of sufficiently low density. Both methods rely on basis reduction algorithms to find short nonzero vectors in special lattices. The Lagarias-Odlyzko algorithm would solve almost all subset sum problems of density < 0.6463 . . . in polynomial time if it could invoke a polynomial-time algorithm for finding the shortest non-zero vector in a lattice. This paper presents two modifications of that algorithm, either one of which would solve almost all problems of density < 0.9408 . . . if it could find shortest non-zero vectors in lattices. These modifications also yield dramatic improvements in practice when they are combined with known lattice basis reduction algorithms.

- On the structure of P(n)*P(n) for p=2 (2002)
- We show that P(n)*(P(n)) for p = 2 with its geometrically induced structure maps is not an Hopf algebroid because neither the augmentation Epsilon nor the coproduct Delta are multiplicative. As a consequence the algebra structure of P(n)*(P(n)) is slightly different from what was supposed to be the case. We give formulas for Epsilon(xy) and Delta(xy) and show that the inversion of the formal group of P(n) is induced by an antimultiplicative involution Xi : P(n) -> P(n). Some consequences for multiplicative and antimultiplicative automorphisms of K(n) for p = 2 are also discussed.

- Lattice Reduction by Random Sampling and Birthday Methods (2003)
- We present a novel practical algorithm that given a lattice basis b1, ..., bn finds in O(n exp 2 *(k/6) exp (k/4)) average time a shorter vector than b1 provided that b1 is (k/6) exp (n/(2k)) times longer than the length of the shortest, nonzero lattice vector. We assume that the given basis b1, ..., bn has an orthogonal basis that is typical for worst case lattice bases. The new reduction method samples short lattice vectors in high dimensional sublattices, it advances in sporadic big jumps. It decreases the approximation factor achievable in a given time by known methods to less than its fourth-th root. We further speed up the new method by the simple and the general birthday method. n2

- Security of DL-encryption and signatures against generic attacks - a survey (2001)
- We survey recent results on the security of DL-cryptosystems and DL-signatures against generic attacks assuming the random oracle model (ROM) and the generic group model (GM). We comment on the relevance of these results towards applications.