For \natural enough" systems of ordinal notation we show that times iterated local reeection schema over a suuciently strong arithmetic T proves the same 0 1-sentences as ! times iterated consistency. A corollary is that the two hierarchies catch up modulo relative interpretability exactly at-numbers. We also derive the following more general \mixed" formulas estimating the consistency strength...

The inference rule semi-resolution is introduced and shown to be complete for ground CNF formulas. It can be employed in a connection-graph setting, and preservation of the spanning property is shown to hold when activated links are deleted. Potential advantages from the employment of semi-resolution as the inference engine in prime implicate computations are brieey discussed .

A pnovubW y 2.acgtica,2 ztudy o6 zysteni with built-in cones tevccy Alb ent V,iss etc 1 Introduction Consistency can be built into a system in various ways. The two best known constructions are Rosser's and Feferman's. Both construction's take a given formal system in the usual sense as initial data. Consider for example Peano Arithmetic (PA). A proof in the Peano System will count as a proof i...

Classes with few models have 'homogeneous-universal' models This paper is concerned with a class K of models and an abstract notion of submodel ≤. Experience in first order model theory has shown the desirability of finding a 'monster model' to serve as a universal domain for K. In the original constructions of Jónsson and Fraissè, K was a universal class and ordinary substructure played the ro...

We present a new protocol for efficient distributed computation modulo a shared secret. We further present a protocol to distributively generate a random shared prime or safe prime that is much more efficient than previously known methods. This allows to distributively compute shared RSA keys, where the modulus is the product of two safe primes, much more efficiently than was previously known.

This paper develops the philosophy and technology needed for adding a supremum operator to the interpretability logic ILM of Peano Arithmetic (PA). It is wellknown that any theories extending PA have a supremum in the interpretability ordering. While provable in PA, this fact is not reflected in the theorems of the modal system ILM, due to limited expressive power. Our goal is to enrich the lan...

Classes with few models have 'homogeneous-universal' models This paper is concerned with a class K of models and an abstract notion of submodel ≤. Experience in first order model theory has shown the desirability of finding a 'monster model' to serve as a universal domain for K. In the original constructions of Jónsson and Fraissè, K was a universal class and ordinary substructure played the ro...

We proposed the first threshold GQ signature scheme. The scheme is unforgeable and robust against any adaptive adversary if the base GQ signature scheme is unforgeable under the chosen message attack and computing the discrete logarithm modulo a safe prime is hard. Our scheme achieve optimal resilience, that is, the adversary can corrupt up to a half of the players. As an extension of our work,...

Classes with few models have 'homogeneous-universal' models This paper is concerned with a class K of models and an abstract notion of submodel ≤. Experience in first order model theory has shown the desirability of finding a 'monster model' to serve as a universal domain for K. In the original constructions of Jónsson and Fraissè, K was a universal class and ordinary substructure played the ro...

Given an elliptic curve E over a finite field Fq of q elements, we say that an odd prime l ∤ q is an Elkies prime for E if tE − 4q is a quadratic residue modulo l, where tE = q+1−#E(Fq) and #E(Fq) is the number of Fq-rational points on E. These primes are used in the presently most efficient algorithm to compute #E(Fq). In particular, the bound Lq(E) such that the product of all Elkies primes f...