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We show how to evaluate a bi-variate polynomial of degree n (i.e., having order n 2 many coefficients) at n 2 generic points simultaneously within time O(n 2.91). This means an average cost of O(n 0.91) per point whereas a single evaluation provably requires in general Ω(n 2) operations.

The key-generation algorithm for the RSA cryptosystem is specified in several standards, such as PKCS#1, IEEE 1363-2000, FIPS 186-3, ANSI X9.44, or ISO/IEC 18033-2. All of them substantially differ in their requirements. This indicates that for computing a " secure " RSA modulus it does not matter how exactly one generates RSA integers. In this work we show… (More)

The key-generation algorithm for the RSA cryptosystem is specified in several standards, such as PKCS#1, IEEE 1363-2000, FIPS 186-3, ANSI X9.44, or ISO/IEC 18033-2. All of them substantially differ in their requirements. This indicates that for computing a " secure " RSA modulus it does not matter how exactly one generates RSA integers. In this work we show… (More)

We propose a family of 6-to-4-bit S-boxes with linear branch number 3. Since they also fulfill various further desirable properties such S-boxes can serve as a building block for various block ciphers.

We count ]B, C]-grained, k-factor integers which are simultaneously B-rough and C-smooth and have a fixed number k of prime factors. Our aim is to exploit explicit versions of the prime number theorem as much as possible to get good explicit bounds for the count of such integers. This analysis was inspired by certain inner procedures in the general number… (More)

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