THEORETICALLY UNBREAKABLE CIPHERS AS THEY SHOULD BE UNDERSTOOD

Perfectly-secret ciphers according to the Claude Shannon's theory, which are considered as unbreakable, and more specifically random keystream ciphers, are discussed. An analysis of the sources mentioned in the reference list showed that all of them come to the point that the perfect ciphers according to Claude Shannon's theory are unbreakable. The article introduces some concepts, such as: the probabilistic model of cipher; the perfect cipher, which is secure against a plaintext recovery ciphertext-only attack; the perfect cipher, which is secure against a key recovery ciphertext-only attack; effective plaintext or key recovery attack; ineffective plaintext or key recovery attack; decipherable model of cipher; undecipherable model cipher. The introduced concepts were used to clarify Shannon’s mathematical model and to prove that a statement about unbreakability of the perfect ciphers according to the Claude Shannon's theory, including random keystream cipher, were wrong. The purpose of the article is to attract the attention of specialists to the problem of developing methods for decrypting Vizhener cipher and using them in solving the problem of determining the cipher key of a random gamming according to a ciphertext, as well as developing methods for estimating the complexity and reliability of deciphering the cipher class in question

Small Strong Blocking Sets by Concatenation

Strong blocking sets and their counterparts, minimal codes, attracted lots of attention in the last years. Combining the concatenating construction of codes with a geometric insight into the minimality condition, we explicitly provide infinite families of small strong blocking sets, whose size is linear in the dimension of the ambient projective spaces. As a byproduct, small saturating sets are obtained.Comment: 16 page

Linear codes with few weights from weakly regular bent functions based on a generic construction

We contribute to the knowledge of linear codes with few weights from special polynomials and functions. Substantial eorts (especially due to C. Ding) have been directed towards their study in the past few years. Such codes have several applications in secret sharing, authentication codes, association schemes and strongly regular graphs. Based on a generic construction of linear codes from mappings and by employing weakly regular bent functions, we provide a new class of linear p-ary codes with three weights given with its weight distribution. The class of codes presented in this paper is dierent from those known in literature. Also, it contains some optimal codes meeting certain bound on linear codes

Secret Sharing Schemes with General Access Structures (Full version)

Secret sharing schemes with general monotone access structures have been widely discussed in the literature. But in some scenarios, non-monotone access structures may have more practical significance. In this paper, we shed a new light on secret sharing schemes realizing general (not necessarily monotone) access structures. Based on an attack model for secret sharing schemes with general access structures, we redefine perfect secret sharing schemes, which is a generalization of the known concept of perfect secret sharing schemes with monotone access structures. Then, we provide for the first time two constructions of perfect secret sharing schemes with general access structures. The first construction can be seen as a democratic scheme in the sense that the shares are generated by the players themselves. Our second construction significantly enhance the efficiency of the system, where the shares are distributed by the trusted center (TC)