We propose a log signing scheme that enables (a) verification of the integrity of the whole log, and (b) presentation of any record, along with a compact proof that the record has not been altered since the log was signed, without leaking any information about the contents of other records in the log. We give a formal proof of the security of the proposed scheme, discuss practical consideration...

We are now investigating an "executable" fragment of classical mathematics for testing formal proofs to make formal proof developments less laborious. Several theories of execution of full classical proofs are known. In these theories, some kind of abstract values such as continuations, are necessary. It makes them illegible from computational point of view, although they are mathematically int...

This paper presents an algorithm that, given a prime n, finds and verifies a proof of the primality of n in random time (lg n)4+o(1). Several practical speedups are incorporated into the algorithm and discussed in detail.

Proof Theory and Computation. Recent developments in proof theory have led to major advances in the theory of programming languages. The modelling of computation using proofs impacted deeply the foundational studies of programming languages as well as many of their practical issues. Declarative programming languages have been related mainly in two ways to the mathematical theory of proofs: on t...

We give a new proof of a theorem of Mints that the positive fragment of minimal predicate logic is decidable. The idea of the proof is to replace the eigenvariable condition of sequent calculus by an appropriate scoping mechanism. The algorithm given by this proof seems to be more practical than that given by the original proof. A naive implementation is given at the end of the paper. Another c...

We present several new and fairly practical public-key encryption schemes and prove them secure against adaptive chosen ciphertext attack. One scheme is based on Paillier’s Decision Composite Residuosity (DCR) assumption [7], while another is based in the classical Quadratic Residuosity (QR) assumption. The analysis is in the standard cryptographic model, i.e., the security of our schemes does ...

‎Our aim in this very short note is to show that the proof of the‎ ‎following well-known fundamental lemma of Zariski follows from an‎ ‎argument similar to the proof of the fact that the rational field‎ ‎$mathbb{Q}$ is not a finitely generated $mathbb{Z}$-algebra.

In this paper, we give a new and direct proof for the recently proved conjecture raised in Soltani and Roozegar (2012). The conjecture can be proved in a few lines via the integral representation of the Gauss-hypergeometric function unlike the long proof in Roozegar and Soltani (2013).

given the importance of intellect in inference, especially in new issues, it is befitting to study the jurists’ works, such as examining the jurisprudential mode of life (sīra) of fayḍ kāshānī as an influential jurist in the evolution of jurisprudence in proving the above issue. to this end, his various books have been examined on the basis of content analysis method and every one of his legal ...

in this paper‎, ‎we give a complete proof of theorem 4.1(ii) and a new‎ ‎elementary proof of theorem 4.1(i) in [li and shen‎, ‎on the‎ ‎intersection of the normalizers of the derived subgroups of all‎ ‎subgroups of a finite group‎, ‎ j‎. ‎algebra, ‎323  (2010) 1349--1357]‎. ‎in addition‎, ‎we also give a generalization of baer's theorem‎.