Related papers: Some A Priori Torah Decryption Principles
A numeration system encodes abstract numeric quantities as concrete strings of written characters. The numeration systems used by modern scripts tend to be precise and unambiguous, but this was not so for the ancient and…
Common subword tokenization algorithms like BPE and UnigramLM assume that text can be split into meaningful units by concatenative measures alone. This is not true for languages such as Hebrew and Arabic, where morphology is encoded in…
Assessing spoken language is challenging, and quantifying pronunciation metrics for machine learning models is even harder. However, for the Holy Quran, this task is simplified by the rigorous recitation rules (tajweed) established by…
This paper provides a preparatory introduction to sheaves and topoi, written as a conceptual continuation of the author's earlier introduction to torsors and as preparatory background for the author's arXiv paper \emph{Grothendieck…
Aggregation of values that need to be kept confidential while guaranteeing the robustness of the process and the correctness of the result is required in an increasing number of applications. We propose an aggregation algorithm, which…
We propose a new homomorphic encryption scheme based on the hardness of decoding under independent random noise from certain affine families of codes. Unlike in previous lattice-based homomorphic encryption schemes, where the message is…
Caesar cipher is an ancient, elementary method of encrypting plain text message to protect it from adversaries. However, with the advent of powerful computers there is a need for increasing the complexity of such algorithms. In this paper,…
Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of…
In poly alphabetic substitution the plain texts letters are enciphered differently according to their position. The name poly alphabetic suggests that there are more than one key so we have used two keys combination instead of just one, in…
For h=3 or 4, Egyptian decompositions into h unit fractions, like 2/D = 1/D1 + ... +1/Dh, were given by using (h-1) divisors (di) of D1. This ancient modus operandi, well recognized today, provides Di=DD1/di for i greater than 1.…
The goal of this chapter is to present a survey of homomorphic encryption techniques and their applications. After a detailed discussion on the introduction and motivation of the chapter, we present some basic concepts of cryptography. The…
A symmetric encryption method based on properties of quasicrystals is proposed. The advantages of the cipher are strict aperiodicity and everywhere discontinuous property as well as the speed of computation, simplicity of implementation and…
We show that many known schemes of the public key exchange protocols in the algebraic cryptography, that use two-sided multiplications, are the specific cases of the general scheme of such type. In most cases, such schemes are built on…
This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability…
In this paper an elementary (cryptographic system) for the codification and decodification of texts written in Romanian language is presented. This method is based on the alphabet A and the 7x7-Square. The theme presented is at the…
We define a virtual projection of a Reed-Solomon code $RS(q^{l},n,k)$ to an $RS(q,n,k)$ Reed-Solomon code. A new probabilistic decoding algorithm that can be used to perform fractional decoding beyond the $\alpha$- decoding radius is…
We consider the problem of erasure/list decoding using certain classes of simplified decoders. Specifically, we assume a class of erasure/list decoders, such that a codeword is in the list if its likelihood is larger than a threshold. This…
This research note suggests a new way to realize a high speed direct encryption based on quantum detection theory. The conventional cipher is designed by a mathematical algorithm and its security is evaluated by the complexity of the…
Motivated by the widespread increase in the phenomenon of code-switching between Egyptian Arabic and English in recent times, this paper explores the intricacies of machine translation (MT) and automatic speech recognition (ASR) systems,…
Autoregressive language models are constrained by their inherently sequential nature, generating one token at a time. This paradigm limits inference speed and parallelism, especially during later stages of generation when the direction and…