An operating system kernel uses cryptographically secure pseudorandom number
generator for creating address space localization randomization offsets to
protect memory addresses to processes from exploration, storing users' password
securely and creating cryptographic keys. The paper proposes a CSPRNG called
KCS-PRNG which produces non-reproducible bitstreams. The proposed KCS-PRNG
presents an efficient design uniquely configured with two new non-standard and
verified elliptic curves and clock-controlled linear feedback shift registers
and a novel method to consistently generate non-reproducible random bits of
arbitrary lengths. The generated bit streams are statistically
indistinguishable from true random bitstreams and provably secure, resilient to
important attacks, exhibits backward and forward secrecy, exhibits exponential
linear complexity, large period and huge key space.
The `mathematical language' Automath, conceived by N.G. de Bruijn in 1968,
was the first theorem prover actually working and was used for checking many
specimina of mathematical content. Its goals and syntactic ideas inspired Th.
Coquand and G. Huet to develop the calculus of constructions, CC, which was one
of the first widely used interactive theorem provers and forms the basis for
the widely used Coq system. The original syntax of Automath is not easy to
grasp. Yet, it is essentially based on a derivation system that is similar to
the Calculus of Constructions (`CC'). The relation between the Automath syntax
and CC has not yet been sufficiently described, although there are many
references in the type theory community to Automath. In this paper we focus on
the backgrounds and on some uncommon aspects of the syntax of Automath. We
expose the fundamental aspects of a `generic' Automath system, encapsulating
the most common versions of Automath. We present this generic Automath system
in a modern syntactic frame. The obtained system makes use of {\lambda}D, a
direct extension of CC with definitions.
An iterated uniform finite-state transducer (IUFST) runs the same
length-preserving transduction, starting with a sweep on the input string and
then iteratively sweeping on the output of the previous sweep. The IUFST
accepts the input string by halting in an accepting state at the end of a
sweep. We consider both the deterministic (IUFST) and nondeterministic (NIUFST)
version of this device. We show that constant sweep bounded IUFSTs and NIUFSTs
accept all and only regular languages. We study the state complexity of
removing nondeterminism as well as sweeps on constant sweep bounded NIUFSTs,
the descriptional power of constant sweep bounded IUFSTs and NIUFSTs with
respect to classical models of finite-state automata, and the computational
complexity of several decidability questions. Then, we focus on non-constant
sweep bounded devices, proving the existence of a proper infinite nonregular
language hierarchy depending on the sweep complexity both in the deterministic
and nondeterministic case. Though NIUFSTss are "one-way" devices we show that
they characterize the class of context-sensitive languages, that is, the
complexity class DSpace(lin). Finally, we show that the nondeterministic
devices are more powerful than their deterministic variant for a sublinear
number of sweeps that is at least logarithmic.
System diagnosis is process of identifying faulty nodes in a system. An
efficient diagnosis is crucial for a multiprocessor system. The BGM diagnosis
model is a modification of the PMC diagnosis model, which is a test-based
diagnosis. In this paper, we present a specific structure and propose an
algorithm for diagnosing a node in a system under the BGM model. We also give a
polynomial-time algorithm that a node in a hypercube-like network can be
diagnosed correctly in three test rounds under the BGM diagnosis model.