Advances in Mathematics of Communications
August 2022 , Volume 16 , Issue 3
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Some important properties of lattices are packing density and full diversity, which may be good for signal transmission over both Gaussian and Rayleigh fading channel, respectively. The algebraic lattices are constructed through twisted homomorphism of some modules in the ring of integers of a number field
The present work reports progress in discrete logarithm computation for the general medium prime case using the function field sieve algorithm. A new record discrete logarithm computation over a 1051-bit field having a 22-bit characteristic was performed. This computation builds on and implements previously known techniques. Analysis indicates that the relation collection and descent steps are within reach for fields with 32-bit characteristic and moderate extension degrees. It is the linear algebra step which will dominate the computation time for any discrete logarithm computation over such fields.
Cyclotomy, firstly introduced by Gauss, is an important topic in Mathematics since it has a number of applications in number theory, combinatorics, coding theory and cryptography. Depending on
In this paper, based on the theory of
The theory of linear codes over finite rings has been generalized to linear codes over infinite rings in two special cases; the ring of
For any odd prime
In this paper, we introduce two classes of MacDonald codes over the finite non-chain ring
Uniformity in binary tuples of various lengths in a pseudorandom sequence is an important randomness property. We consider ideal
In this paper, we present a practicable chosen ciphertext timing attack retrieving the secret key of HQC. The attack exploits a correlation between the weight of the error to be decoded and the running time of the decoding algorithm of BCH codes. For the 128-bit security parameters of HQC, the attack runs in less than a minute on a desktop computer using roughly 6000 decoding requests and has a success probability of approximately 93 percent. To prevent this attack, we provide an implementation of a constant time algorithm for the decoding of BCH codes. Our implementation of the countermeasure achieves a constant time execution of the decoding process without a significant performance penalty.
In this paper, we generalize the notion of self-orthogonal codes to
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