Advances in Mathematics of Communications
May 2021 , Volume 15 , Issue 2
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We present a code-based public-key cryptosystem, in which we use Reed-Solomon codes over an extension field as secret codes and disguise it by considering its shortened expanded code over the base field. Considering shortened expanded codes provides a safeguard against distinguisher attacks based on the Schur product. Moreover, without using a cyclic or a quasi-cyclic structure we obtain a key size reduction of nearly
Subfield subcodes of algebraic-geometric codes are good candidates for the use in post-quantum cryptosystems, provided their true parameters such as dimension and minimum distance can be determined. In this paper we present new values of the true dimension of subfield subcodes of
In this paper, we define a linear code by using multi-variable functions, and construct three classes of minimal linear codes with few-weight from multi-variable functions.
In this paper, we investigate the Gowers
A key step in Regev's (2009) reduction of the Discrete Gaussian Sampling (DGS) problem to that of solving the Learning With Errors (LWE) problem is a statistical test required for verifying possible solutions to the LWE problem. We derive a lower bound on the success probability leading to an upper bound on the tightness gap of the reduction. The success probability depends on the rejection threshold
This paper deals with the problem of determining whether a PD-set exists for a given linear code
In this paper, we give an explicit representation and enumeration for negacyclic codes of length
Many modern symmetric ciphers apply MDS or almost MDS matrices as diffusion layers. The performance of a diffusion layer depends on its diffusion property measured by branch number and implementation cost which is usually measured by the number of XORs required. As the implementation cost of MDS matrices of large dimensions is high, some symmetric ciphers use binary matrices as diffusion layers to trade-off efficiency versus diffusion property. In the current paper, we investigate cyclic binary matrices (CBMs for short), mathematically. Based upon this theorical study, we provide efficient matrices with provable lower bound on branch number and minimal number of fixed-points. We consider the product of sparse CBMs to construct efficiently implementable matrices with the desired cryptographic properties.
Private information retrieval (PIR) allows a user to retrieve one out of
In the field of privacy preserving protocols, Private Set Intersection (PSI) plays an important role. In most of the cases, PSI allows two parties to securely determine the intersection of their private input sets, and no other information. In this paper, employing a Bloom filter, we propose a Multiparty Private Set Intersection Cardinality (MPSI-CA), where the number of participants in PSI is not limited to two. The security of our scheme is achieved in the standard model under the Decisional Diffie-Hellman (DDH) assumption against semi-honest adversaries. Our scheme is flexible in the sense that set size of one participant is independent from that of the others. We consider the number of modular exponentiations in order to determine computational complexity. In our construction, communication and computation overheads of each participant is
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