Foundations of Encryptment ™ : Axioms, Theorems, and Formal Structures

Reports in Advances of Physical Sciences, 2019

A logical physical ontology is code theory, wherein reality is neither deterministic nor random. In light of Conway and Kochens' free will theorem and strong free will theorem, we discuss the plausibility of a third axiomatic option-geometric language; the code theoretic axiom. We suggest free will choices at the syntactically free steps of a geometric language of space-time form the code theoretic substrate upon which particle and gravitational physics emerge.

Elsevier eBooks, 2006

Introduction xi ''inference to the best explanation''. If this line of argument is accepted, its concrete elaboration should probably go into the direction of a position according to which classical particles possess their positions directly (without embedding in space) and in which absolute accelerations also become direct particle properties. One may question the elegance or simplicity of such a scheme, but it seems certainly realizable in principle. Although the resulting position would not be relationalist in the sense that only relations between particles play a role, it would certainly be anti-substantivalist. The part ordinarily played by absolute space would be taken over by D. Dieks xiv being there at the present instant exist: the past has ceased to exist, and the future does not yet exist. But without a ''now'' the notion of ''the present moment'' does not seem to make sense, and ontological distinctions that correspond to the distinction between past, present and future have apparently to be abandoned as well. The only plausible alternative seems ''eternalism'', according to which all events in the history of the universe possess equal ontological statuses: everything exists in the same way, ''at once''. On closer inspection things are not that clear, however. It is misleading to state that in Minkowski spacetime all events exist at once: they certainly do not take place at one spacetime point. Moreover, there are objective temporal ordering relations between events according to special relativity, so that at least some events are objectively later or earlier than any given event, in spite of the fact that they all belong to the same block universe. All these spatiotemporal relations between events are fully represented within the block diagram; what temporal or existential distinctions could be missing from it? The intuitive answer is that it is the absolute distinction between past, present and future, and the associated ontological differences, that are lacking. But as Dorato, Savitt and Dolev make clear in different ways, it is questionable whether it even makes sense to think that presentism and eternalism are committed to distinct ontologies. Arguing within the context of pre-relativistic physics, so that the complication of the non-absoluteness of simultaneity does not yet play a role, Dorato and Savitt point out that at any instant both presentists and eternalists will agree that past and future do not exist now, and that the future will exist whereas the past existed. Both parties also agree that past, present and future all equally exist in a tenseless way. So what differences in existence claims can there really be between the two camps? It seems that the presentism/eternalism debate can have no consequences at all for the ontology of spacetime. The block universe already contains all distinctions that can sensibly be made, and so is in no way ontologically incomplete. In particular, the block picture faithfully represents all differences there actually are between past, future and present. Arthur and Dieks extend basically the same analysis so as to take relativity theory into account. The main new aspect introduced by relativity is the disappearance of an objective global ''now''. Still, this does not mean that it becomes impossible to speak about temporal relations and becoming. The block representation contains all events occurring in the history of the universe, exactly at the spacetime position where they actually happen. In other words, this happening of events has already been taken into account in the block universe representation. The same applies to the temporal relations between different happenings: these also are all part of the block universe. It is consequently false to maintain that the block universe offers no room for becoming. Becoming consists exactly in the occurring, or happening, of events after or before each other according to the temporal relations between them. The

who have guided me throughout my dissertation with their patience and knowledge whilst allowing me the room to work in my own way. Without their insight, guidance and effort, this dissertation would not have taken shape. I am grateful to those endless discussions with them that have inspired me and helped develop algorithms and techniques in this dissertation. I am thankful to Dr. Carl Chang who has always been supportive. With his encouragement, I was able to put new elements in teaching a class and had great experience. I am in debt to Dr. Shashi Gadia, who has taught me to pursue truth and never compromise in front of truth, and to Dr. Ying Cai, who encouraged me to continue with the Ph.D program after my Master's, which helped me make the decision. I am also thankful to Dr. Hridesh Rajan, who shared his passion for research with me. I would also like to thank my dad Shoushan Tao and my mom Yurui Chen, who raised me and my sisters and encourage us to pursue knowledge. They have always been role models to us. Their integrity, perseverance and loving-kindness are always in our hearts. I am grateful to my two sisters, Jing and Ying, my best friends. Their support has been instrumental during hard times. I appreciate that I have many friends who have been beside me to support me during the past years with numerous discussions regarding research, life and interaction of these concepts:

2021

A hybrid encryption scheme is a public key encryption system that consists of a public-key part called the key encapsulation mechanism (KEM), and a (symmetric) secret-key part called data encapsulation mechanism (DEM): the public key part is used to generate a shared secret key between the two parties, and the symmetric key part is used to encrypt the message. Hybrid encryption schemes are widely used for secure communication over the Internet. In this paper we initiate the study of hybrid encryption in preprocessing model which assumes access to initial correlated variables by all the parties (including the eavesdropper). We define information theoretic KEM (iKEM) that together with a (computationally) secure DEM results in a hybrid encryption scheme in preprocessing model. We define security of each building block and prove a composition theorem that guarantees security of the final encryption system. We show that iKEM can be realized by a one-message SKA (OW-SKA) protocol with an extended security definition. Using a OW-SKA that satisfies this extended definition of security effectively allows the secret key that is generated by the OW-SKA to be used with symmetric key encryption system such as AES in counter mode. We discuss our results and future work including providing stronger security for the final encryption, and using information theoretic DEM to construct information theoretic encryption systems.

2021

In this paper, we investigate the ontological hypothesis, which implies that the spacetime is not the ultimate structure in our universe, and its existence emerges from a deeper physical entity. By using a very simple approach based on a classical problem, regarding the propagation of electromagnetic waves in empty vacuum. We were able to deduce that this deeper entity is just an omnipresent multi-rest states physical structure; aether. After that, we try to see how this ether fits in the universe that we exist in. The outcome is that its existence causes the emergence of some basic phenomena that our universe is built on. At the microscopic scale it turned out to be a source of the essential quantum phenomenon, which is currently known as the waveparticle duality. On the other hand, at the macroscopic scale it causes the emergence of spacetime curvature, around huge, massive objects like Earth. Finally, we consider a simple experiment that enables us to detect this ether, which is based on the concept of the conservation of linear momentum in nature, and the ontology of the inertial mass for the elementary particles.

We present a deductive theory of space-time which is realistic, objective, and relational. It is realistic because it assumes the existence of physical things endowed with concrete properties. It is objective because it can be formulated without any reference to knowing subjects or sensorial fields. Finally, it is relational because it assumes that space-time is not a thing, but a complex of relations among things. In this way, the original program of Leibniz is consummated, in the sense that space is ultimately an order of coexistents, and time is an order of successives. In this context, we show that the metric and topological properties of Minkowskian space-time are reduced to relational properties of concrete things. We also sketch how our theory can be extended to encompass a Riemannian space-time.

1993

Library of Congress Cataloging-in-Publication Data Engeler, Erwin. [Metamathematik der E1ementarmathematik. English] Foundations of mathematics: questions of analysis, geometry & algorithmics / Erwin Engeler ; translated by Charles B. Thomas. p. cm. Includes bibliographical references.

Handbook of Spatial Logics, 2007

arXiv (Cornell University), 2002

Some necessary and sufficient conditions allowing a previously unknown space to be explored through scanning operators are reexamined with respect to measure theory. Some generalized conceptions of distances and dimensionality evaluation are proposed, together with their conditions of validity and range of application to topological spaces. The existence of a Boolean lattice with fractal properties originating from nonwellfounded properties of the empty set is demonstrated. This lattice provides a substrate with both discrete and continuous properties, from which existence of physical universes can be proved, up to the function of conscious perception. Spacetime emerges as an ordered sequence of mappings of closed 3-D Ponicaré sections of a topological 4-space provided by the lattice, and the function of conscious perception is founded on the same properties. Self-evaluation of a system is possible against indecidability barriers through anticipatory mental imaging occurring in biological brain systems; then our embedding universe should be in principle accessible to knowledge. The possibility of existence of spaces with fuzzy dimension or with adjoined parts with decreasing dimensions is raised, together with possible tools for their study. The work presented here provides the introductory foundations supporting a new theory of space whose physical predictions (suppressing the opposition of quantum and relativistic approaches) and experimental proofs are presented in details in Parts 2 and 3 of the study.