Related papers: Design of Ciphers based on the Geometric Structure…
Till now geometric structures don't play a major role in cryptography. Gilbert, MacWilliams and Sloane introduced an authentication scheme in the projective plane and showed its perfectness in the sense of Shannon. In arXiv:2102.10321 we…
Shannon's perfect-secrecy theorem states that a perfect encryption system that yields zero information to the adversary must be a one-time pad (OTP) with the keys randomly generated and never reused. In this work we design the first…
The famous Shannon impossibility result says that any encryption scheme with perfect secrecy requires a secret key at least as long as the message. In this paper we provide its quantum analogue with imperfect secrecy and imperfect…
Most cryptosystems are defined over finite algebraic structures where arithmetic operations are performed modulo natural numbers. This applies to private key as well as to public key ciphers. No secure cryptosystems defined over the field…
We establish a construction of optimal authentication codes achieving perfect multi-fold secrecy by means of combinatorial designs. This continues the author's work (ISIT 2009) and answers an open question posed therein. As an application,…
The rapid development of advanced computing technologies such as quantum computing imposes new challenges to current wireless security mechanism which is based on cryptographic approaches. To deal with various attacks and realize…
Using a finite geometric framework for studying the pentagon and heptagon codes we show that the concepts of quantum secret sharing and contextuality can be studied in a nice and unified manner. The basic idea is a careful study of the…
Until now the discussion on perfect security for steganographic systems has remained confined within the realm of mathematicians and information theory experts whose concise and symbolic representation of their philosophies, postulates, and…
A blind decryption scheme enables a user to query decryptions from a decryption server without revealing information about the plaintext message. Such schemes are useful, for example, for the implementation of privacy preserving encrypted…
Cryptographic security is traditionally formulated using game-based or simulation-based definitions. In this paper, we propose a structural reformulation of cryptographic security based on Grothendieck topologies and sheaf theory. Our key…
Shannon sought security against the attacker with unlimited computational powers: *if an information source conveys some information, then Shannon's attacker will surely extract that information*. Diffie and Hellman refined Shannon's…
A fully homomorphic encryption system hides data from unauthorized parties, while still allowing them to perform computations on the encrypted data. Aside from the straightforward benefit of allowing users to delegate computations to a more…
Secret sharing is an important building block in cryptography. All explicitly defined secret sharing schemes with known exact complexity bounds are multi-linear, thus are closely related to linear codes. The dual of such a linear scheme, in…
This paper redefines the foundations of asymmetric cryptography's homomorphic cryptosystems through the application of the Yoneda Lemma. It demonstrates that widely adopted systems, including ElGamal, RSA, Benaloh, Regev's LWE, and…
Fully homomorphic encryption is an encryption method with the property that any computation on the plaintext can be performed by a party having access to the ciphertext only. Here, we formally define and give schemes for quantum homomorphic…
The One-time-pad (OTP) was mathematically proven to be perfectly secure by Shannon in 1949. We propose to extend the classical OTP from an n-bit finite field to the entire symmetric group over the finite field. Within this context the…
Recently, an image block encryption algorithm was proposed based on some well-known chaotic maps. The authors claim that the encryption algorithm achieves enough security level and high encryption speed at the same time. In this paper, we…
Fully homomorphic encryption is a kind of encryption scheme, which enables arbitrary computation on encrypted data without accessing the data. We present the quantum version of fully homomorphic encryption scheme, which is constructed based…
Complementarity is an essential feature of quantum mechanics. The preparation of an eigenstate of one observable implies complete randomness in its complementary observable. In quantum cryptography, complementarity allows us to formulate…
We investigate, in the Shannon model, the security of constructions corresponding to double and (two-key) triple DES. That is, we consider F_{k1}(F_{k2}(.)) and F_{k1}(F_{k2}^{-1}(F_{k1}(.))) with the component functions being ideal…