Designs, Codes and Cryptography
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Constructing differentially 4-uniform permutations over GF(22m ) from quadratic APN permutations over GF(22m+1)
Designs, Codes and Cryptography - Tập 72 - Trang 249-264 - 2012
In this paper, by means of the idea proposed by Carlet (ACISP 1-15, 2011), differentially 4-uniform permutations with the best known nonlinearity over
$${\mathbb{F}_{2^{2m}}}$$
are constructed using quadratic APN permutations over
...... hiện toàn bộ
Resolvable Maximum Packings with Quadruples
Designs, Codes and Cryptography - Tập 35 - Trang 287-302 - 2005
Let V be a finite set of v elements. A packing of the pairs of V by k-subsets is a family F of k-subsets of V, called blocks, such that each pair in V occurs in at most one member of F. For fixed v and k, the packing problem is to determine the number of blocks in any maximum packing. A maximum packing is resolvable if we can partition the blocks into classes (called parallel classes) such that ev...... hiện toàn bộ
Extremal 1-codes in distance-regular graphs of diameter 3
Designs, Codes and Cryptography - Tập 65 - Trang 29-47 - 2012
We study 1-codes in distance-regular graphs of diameter 3 that achieve three different bounds. We show that the intersection array of a distance-regular graph containing such a code has the form
$${\{a(p+1), cp, a+1; 1, c, a p\}\quad{\rm or}\quad\{a(p+1), (a+1)p,c; 1, c, a p\}}$$
for c = c
...... hiện toàn bộ
Breaking LWC candidates: sESTATE and Elephant in quantum setting
Designs, Codes and Cryptography - Tập 89 - Trang 1405-1432 - 2021
The competition for lightweight cryptography (LWC) launched by the National Institute of Standards and Technology (NIST) is an ongoing project calling for the standardization of lightweight cryptographic algorithms. The Report on Lightweight Cryptography specifically asks that submissions be quantum safe when long-term security is needed. However, this was not included in the “Submission Requireme...... hiện toàn bộ
Optimal quaternary Hermitian LCD codes and their related codes
Designs, Codes and Cryptography - Tập 91 - Trang 1527-1558 - 2022
Linear codes with complementary dual (LCD codes) play an important role in armoring implementations against side-channel attacks and fault injection attacks. Hermitian LCD codes are a special class of LCD codes, which were proved to be asymptotically good. In this paper, several classes of optimal quaternary Hermitian LCD codes are constructed via constacyclic codes. The binary images of these cla...... hiện toàn bộ
Polar sampler: A novel Bernoulli sampler using polar codes with application to integer Gaussian sampling
Designs, Codes and Cryptography - Tập 91 - Trang 1779-1811 - 2023
Cryptographic constructions based on hard lattice problems have emerged as a front runner for the standardization of post-quantum public-key cryptography. As the standardization process takes place, optimizing specific parts of proposed schemes, e.g., Bernoulli sampling and integer Gaussian sampling, becomes a worthwhile endeavor. In this work, we propose a novel Bernoulli sampler based on polar c...... hiện toàn bộ
Distance-regular graphs with intersection arrays {52, 35, 16; 1, 4, 28} and {69, 48, 24; 1, 4, 46} do not exist
Designs, Codes and Cryptography - Tập 65 - Trang 49-54 - 2012
We prove that the arrays {52, 35, 16; 1, 4, 28} and {69, 48, 24; 1, 4, 46} cannot be realized as the intersection arrays of distance-regular graphs. In the proof we use some inequalities bounding the size of substructures (cliques, cocliques) in a distance-regular graph.
Symplectic Spreads
Designs, Codes and Cryptography - Tập 32 - Trang 9-14 - 2004
We construct an infinite family of symplectic spreads in spaces of odd rank and characteristic.
On the algebraic degree of iterated power functions
Designs, Codes and Cryptography - Tập 91 - Trang 997-1033 - 2022
New symmetric primitives are being designed to address a novel set of design criteria. Instead of being executed on regular processors or smartcards, they are instead intended to be run in abstract settings such as multi-party computations or zero-knowledge proof systems. This implies in particular that these new primitives are described using operations over large finite fields. As the number of ...... hiện toàn bộ
A family of quadriphase sequences of period 4(2 n − 1) with low correlation and large linear span
Designs, Codes and Cryptography - - 2011
In this paper, a new family of quadriphase sequences with period 4(2
n
− 1) is proposed for n = me, where m is an odd integer. The correlation values of the family, their distribution, and the linear spans of the proposed sequences are completely determined under two situations.
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