Related papers: Encryption Scheme Based on Expanded Reed-Solomon C…
Interleaved Reed-Solomon codes are applied in numerous data processing, data transmission, and data storage systems. They are generated by interleaving several codewords of ordinary Reed-Solomon codes. Usually, these codewords are decoded…
In this paper we address the problem of decoding linearized Reed-Solomon (LRS) codes beyond their unique decoding radius. We analyze the complexity in order to evaluate if the considered problem is of cryptographic relevance, i.e., can be…
Lattice based encryption schemes and linear code based encryption schemes have received extensive attention in recent years since they have been considered as post-quantum candidate encryption schemes. Though LLL reduction algorithm has…
The Shamir secret sharing scheme requires a Maximum Distance Separable (MDS) code, and in its most common implementation, a Reed-Solomon (RS) code is used. In this paper, we observe that the encoding procedure can be made simpler and faster…
We present a rank metric code-based encryption scheme with key and ciphertext sizes comparable to that of isogeny-based cryptography for an equivalent security level. The system also benefits from efficient encryption and decryption…
The Shor-Preskill proof of the security of the BB84 quantum key distribution protocol relies on the theoretical existence of good classical error-correcting codes with the ``dual-containing'' property. A practical implementation of BB84…
Encryption schemes based on the rank metric lead to small public key sizes of order of few thousands bytes which represents a very attractive feature compared to Hamming metric-based encryption schemes where public key sizes are of order of…
A secret key can be used to conceal information from an eavesdropper during communication, as in Shannon's cipher system. Most theoretical guarantees of secrecy require the secret key space to grow exponentially with the length of…
In this paper, we study the behavior of the true dimension of the subfield subcodes of Hermitian codes. Our motivation is to use these classes of linear codes to improve the parameters of the McEliece cryptosystem, such that key size and…
The paper has a threefold purpose. The first purpose is to present an explicit description of expanded cyclic codes defined in $\GF(q^m)$. The proposed explicit construction of expanded generator matrix and expanded parity check matrix…
A new Chase-type soft-decision decoding algorithm for Reed-Solomon codes is proposed, referred to as tree-based Chase-type algorithm}. The proposed tree-based Chase-type algorithm takes the set of all vectors as the set of testing patterns,…
The modified Paillier cryptosystem has become extremely popular and applied in many fields, owning to its additive homomorphism. This cryptosystem provides weak private keys and a strong private key. A weak private key only can decrypt…
In this paper, we define and discuss {\phi}-cyclic code, which may be regarded as a general form of the ordinary cyclic code. As applications, we explain how to extend two public key encryption schemes, one is McEliece and Niederriter's…
This paper puts a new light on secure data storage inside distributed systems. Specifically, it revisits computational secret sharing in a situation where the encryption key is exposed to an attacker. It comes with several contributions:…
A secret sharing scheme (SSS) was introduced by Shamir in 1979 using polynomial interpolation. Later it turned out that it is equivalent to an SSS based on a Reed-Solomon code. SSSs based on linear codes have been studied by many…
Code-based cryptography is an interesting alternative to classic number-theory PKC since it is conjectured to be secure against quantum computer attacks. Many families of codes have been proposed for these cryptosystems, one of the main…
We propose variations of the class of hidden monomial cryptosystems in order to make it resistant to all known attacks. We use identities built upon a single bivariate polynomial equation with coefficients in a finite field. Indeed, it can…
This paper presents a method to merge Generalized Minimum Distance decoding of Reed-Solomon codes with the extended Euclidean algorithm. By merge, we mean that the steps taken to perform the Generalized Minimum Distance decoding are similar…
Network coding provides the advantage of maximizing the usage of network resources, and has great application prospects in future network communications. However, the properties of network coding also make the pollution attack more serious.…
In this article, an encryption scheme based on (-1, 1) conference matrix has been developed. The decryption key comprising of fixed number of positive integers with prime power yields the high level security of message. Some popular attacks…