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European Journal of Pure and Applied Mathematics

Group and Cipher in Wormhole and Quantum Entanglement

Yonghong Liu

Published May 18, 2021• 0 citations
Publisher

Abstract

In this article, we present wormholes cryptosystems (WCS). The first is the wormhole key distribution centre theorem, which asserts that the WCS is a public key group. The second is the security theorem, which asserts that the WCS are a one-way function. The third is new version of the definition for the WCS, and we introduce the notion of groups of WCS. The fourth ingredient is the encryption algorithm and decryption algorithm, and design principle. Here, we present a toy example to illustrate the computation of these encryptions and decryptions. The finally we present the unsymmetrical WCS theorem.

DOI
10.29020/nybg.ejpam.v14i2.3972

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In this article, we present wormholes cryptosystems (WCS). The first is the wormhole key distribution centre theorem, which asserts that the WCS is a public key group. The second is the security theorem, which asserts that the WCS are a one-way function. The third is new version of the definition for the WCS, and we introduce the notion of groups of WCS. The fourth ingredient is the encryption algorithm and decryption algorithm, and design principle. Here, we present a toy example to illustrate the computation of these encryptions and decryptions. The finally we present the unsymmetrical WCS theorem.
Abstract. This paper presents a new paradigm of cryptography, quantum public-key cryptosystems. In quantum public-key cryptosystems, all parties including senders, receivers and adversaries are modeled as quantum (probabilistic) poly-time Turing (QPT) machines and only classical channels (i.e., no quantum channels) are employed. A quantum trapdoor one-way function, f, plays an essential role in our system, in which a QPT machine can compute f with high probability, any QPT machine can invert f with negligible probability, and a QPT machine with trapdoor data can invert f. This paper proposes a concrete scheme for quantum public-key cryptosystems: a quantum public-key encryption scheme or quantum trapdoor one-way function. The security of our schemes is based on the computational assumption (over QPT machines) that a class of subset-sum problems is intractable against any QPT machine. Our scheme is very efficient and practical if Shor’s discrete logarithm algorithm is efficiently realized on a quantum machine.
We discuss cryptographic applications of single-qubit rotations from the perspective of trapdoor one-way functions and public-key encryption. In particular, we present an asymmetric cryptosystem whose security relies on fundamental principles of quantum physics. A quantum public key is used for the encryption of messages while decryption is possible by means of a classical private key only. The trapdoor one-way function underlying the proposed cryptosystem maps integer numbers to quantum states of a qubit and its inversion can be infeasible by virtue of the Holevo's theorem.
It is well known that Shor's quantum algorithm for integer factorization can break down the RSA public-key cryptosystem, which is widely used in many cryptographic applications. Thus, public-key cryptosystems in the quantum computational setting are longed for cryptology. In order to define the security notions of public-key cryptosystems, we have to model the power of the sender, receiver, adversary and channel. While we may consider a setting where quantum computers are available only to adversaries, we generally discuss what are the right security notions for (quantum) public-key cryptosystems in the quantum computational setting. Moreover, we consider the security of quantum public-key cryptosystems known so far.
Public-key cryptosystems for quantum messages are considered from two aspects: public-key encryption and public-key authentication. Firstly, we propose a general construction of quantum public-key encryption scheme, and then construct an information-theoretic secure instance. Then, we propose a quantum public-key authentication scheme, which can protect the integrity of quantum messages. This scheme can both encrypt and authenticate quantum messages. It is information-theoretic secure with regard to encryption, and the success probability of tampering decreases exponentially with the security parameter with regard to authentication. Compared with classical public-key cryptosystems, one private-key in our schemes corresponds to an exponential number of public-keys, and every quantum public-key used by the sender is an unknown quantum state to the sender.