ElGamal cryptosystems on Boolean functions

Here is a description of ElGamal public-key encryption and digital signature schemes constructed on the base of bijective systems of Boolean functions. The description is illustrated with a simple example in which the used Boolean functions are written in logical notation. In our encryption and signature schemes on Boolean functions, every one ciphertext or message signature is a pair of values, as in the basic ElGamal cryptosystem on a group. In our case, these values are Boolean vectors. Each vector in the pair depends on the value of a function on a plaintext or on a message, and this function is typically obtained from a given bijective vector Boolean function g by applying some random and secret negation and permutation operations on the sets of variables and coordinate functions of g. For the pair of vectors in the ciphertext or in the message signature, the decryption algorithm produces the plaintext, and the signature verification algorithm accepts the signature, performing some computation on this pair. The signature is accepted for a message if and only if the computation results in this message. All the computations in the processes of encryption, decryption, signing and verification are logical and performed for Boolean values, promising their implementation efficiency to be more high than in the basic ElGamal schemes on groups

Logical openness in Cognitive Models

It is here proposed an analysis of symbolic and sub-symbolic models for studying cognitive processes, centered on emergence and logical openness notions. The Theory of logical openness connects the Physics of system/environment relationships to the system informational structure. In this theory, cognitive models can be ordered according to a hierarchy of complexity depending on their logical openness degree, and their descriptive limits are correlated to Gödel-Turing Theorems on formal systems. The symbolic models with low logical openness describe cognition by means of semantics which fix the system/environment relationship (cognition in vitro), while the sub-symbolic ones with high logical openness tends to seize its evolutive dynamics (cognition in vivo). An observer is defined as a system with high logical openness. In conclusion, the characteristic processes of intrinsic emergence typical of “bio-logic” - emerging of new codes-require an alternative model to Turing-computation, the natural or bio-morphic computation, whose essential features we are going here to outline

Groupoid Semantics for Thermal Computing

A groupoid semantics is presented for systems with both logical and thermal degrees of freedom. We apply this to a syntactic model for encryption, and obtain an algebraic characterization of the heat produced by the encryption function, as predicted by Landauer's principle. Our model has a linear representation theory that reveals an underlying quantum semantics, giving for the first time a functorial classical model for quantum teleportation and other quantum phenomena.Comment: We describe a groupoid model for thermodynamic computation, and a quantization procedure that turns encrypted communication into quantum teleportation. Everything is done using higher category theor

Robust control in the quantum domain

Recent progress in quantum physics has made it possible to perform experiments in which individual quantum systems are monitored and manipulated in real time. The advent of such new technical capabilities provides strong motivation for the development of theoretical and experimental methodologies for quantum feedback control. The availability of such methods would enable radically new approaches to experimental physics in the quantum realm. Likewise, the investigation of quantum feedback control will introduce crucial new considerations to control theory, such as the uniquely quantum phenomena of entanglement and measurement back-action. The extension of established analysis techniques from control theory into the quantum domain may also provide new insight into the dynamics of complex quantum systems. We anticipate that the successful formulation of an input-output approach to the analysis and reduction of large quantum systems could have very general applications in non-equilibrium quantum statistical mechanics and in the nascent field of quantum information theory.Comment: 12 pages, 1 figur

Landauer's principle as a special case of Galois connection

It is demonstrated how to construct a Galois connection between two related systems with entropy. The construction, called the Landauer's connection, describes coupling between two systems with entropy. It is straightforward and transfers changes in one system to the other one preserving ordering structure induced by entropy. The Landauer's connection simplifies the description of the classical Landauer's principle for computational systems. Categorification and generalization of the Landauer's principle opens area of modelling of various systems in presence of entropy in abstract terms.Comment: 24 pages, 3 figure