On computing subfields. A detailed description of the algorithm

Jürgen Klüners

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Displaying similar documents to “On computing subfields. A detailed description of the algorithm”

A fast algorithm for polynomial factorization over $ℚ_{p}$

David Ford, Sebastian Pauli, Xavier-François Roblot (2002)

Journal de théorie des nombres de Bordeaux

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We present an algorithm that returns a proper factor of a polynomial $Φ (x)$ over the $p$ -adic integers $ℤ_{p}$ (if $Φ (x)$ is reducible over $ℚ_{p}$ ) or returns a power basis of the ring of integers of $ℚ_{p} [x] / Φ (x) ℚ_{p} [x]$ (if $Φ (x)$ is irreducible over $ℚ_{p}$ ). Our algorithm is based on the Round Four maximal order algorithm. Experimental results show that the new algorithm is considerably faster than the Round Four algorithm.

Algorithms for function fields.

Klüners, Jürgen (2002)

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A polynomial reduction algorithm

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Journal de théorie des nombres de Bordeaux

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The algorithm described in this paper is a practical approach to the problem of giving, for each number field $K$ a polynomial, as canonical as possible, a root of which is a primitive element of the extension $K / ℚ$ . Our algorithm uses the $L L L$ algorithm to find a basis of minimal vectors for the lattice of $ℝ^{n}$ determined by the integers of $K$ under the canonical map.

A new construction of the block systems B(4,1,25) and B(4,1, 28)

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On modifying constructed normal numbers

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Topics in computational algebraic number theory

Karim Belabas (2004)

Journal de Théorie des Nombres de Bordeaux

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We describe practical algorithms from computational algebraic number theory, with applications to class field theory. These include basic arithmetic, approximation and uniformizers, discrete logarithms and computation of class fields. All algorithms have been implemented in the system.

Plaintext Recovery in DES-like Cryptosystems Based on S-boxes with Embedded Parity Check

Angelova, Vesela, Borissov, Yuri (2013)

Serdica Journal of Computing

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We describe an approach for recovering the plaintext in block ciphers having a design structure similar to the Data Encryption Standard but with improperly constructed S-boxes. The experiments with a backtracking search algorithm performing this kind of attack against modified DES/Triple-DES in ECB mode show that the unknown plaintext can be recovered with a small amount of uncertainty and this algorithm is highly efficient both in time and memory costs for plaintext sources with relatively...