Quantum Proof Encryption Technology

Nowadays we use text passwords to encrypt a file. This research paper proposes to use multimedia files like images videos, audio files and even applications as the password key to encrypt sensitive information. This algorithm can encrypt bulk data as well as single data sets. Keywords: steganography, multimedia file as key, Quantum computer, cryptography, Quantum computer proof encryption.

Andrews' Conjecture on a $_4\phi_3$ Summation and its Extensions

We give a computer proof of Andrews' conjecture on a $_4\phi_3$ summation and extend the result to a family of $_4\phi_3$ summations.

Homotopy theoretic models of identity types

Quillen [17] introduced model categories as an abstract framework for homotopy theory which would apply to a wide range of mathematical settings. By all accounts this program has been a success and—as, e.g., the work of Voevodsky on the homotopy theory of schemes [15] or the work of Joyal [11,12] and Lurie [13] on quasicategories seem to indicate—it will likely continue to facilitate mathematical advances. In this paper we present a novel connection between model categories and mathematical logic, inspired by the groupoid model of (intensional) Martin–Löf type theory [14] due to Hofmann and Streicher [9]. In particular, we show that a form of Martin–Löf type theory can be soundly modelled in any model category. This result indicates moreover that any model category has an associated “internal language” which is itself a form of Martin-Löf type theory. This suggests applications both to type theory and to homotopy theory. Because Martin–Löf type theory is, in one form or another, the theoretical basis for many of the computer proof assistants currently in use, such asCoqandAgda(cf. [3] and [5]), this promise of applications is of a practical, as well as theoretical, nature.