Write a Thesis on the below Topics$(30-50)$pages

Topics: Post$-$Quantum Cryptography$-$Based Security for Blockchain Technology

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Thesis Outline $(3050$ Pages$)$

$1.$ Abstract

Blockchain technology: A summary of what it is and what comes after quantum.

$2.$ Introduction $3-4$ pages

$2\mathrm{.}1.$ The Blockchain Paradigm

$2\mathrm{.}2.$ Threat of Quantum Computing

$2\mathrm{.}3.$ Motivation and Scope

$3.$ Mathematical Justification $5-6$ pages

$3\mathrm{.}1.$ Mathematical Foundations of Quantum Threats

$3\mathrm{.}2.$ To understand PQCP$,$ let$$s study some principles of post$-$quantum cryptography.

$3\mathrm{.}3.$ Connection to Blockchain

$4\mathrm{.}1.$ Lattices in Cryptography

$4\mathrm{.}2.$ Learning With Errors $($LWE$)$ and its Variants

$4\mathrm{.}3.$ HE for Blockchain

$4\mathrm{.}4.$ Submissions to privacy$-$enhancing blockchain platforms.

$5.$ Security Analysis $(45$ pages$)$

$5\mathrm{.}1.$ In lattice$-$based cryptography there are some security assumptions which includes the following:

The hardness of LWE, NTRU and Ring$-$LWE problems.

$5\mathrm{.}2.$ Threat modeling: blockchain for the quantum age

Possible actions by quantum opposers.

$5\mathrm{.}3.$ Comparison with Classical Cryptographic Systems

$5\mathrm{.}4.$ Challenges and Open Questions

$6.$ Mathematical Models $(5$ pages$)$

$6\mathrm{.}1.$ PQC$-$Based Blockchain Model

$6\mathrm{.}2.$ Consensus Mechanisms

$6\mathrm{.}3.$ Security Analysis with the Help of the Calculating Methods

$7.$ Algorithms $(56$ pages$)$

$7\mathrm{.}1.$ Overview of PQC Algorithms

$7\mathrm{.}2.$ Encryption Algorithms in the Lattice Area

$7\mathrm{.}3.$ Digital signatures also consist of certain algorithms.

$8.$ Implementation and some factors to consider $(45$ pages$).$

$8\mathrm{.}1.$ The integration of PQC on Block Chain

$8\mathrm{.}2.$ Computational Costs

A comparison between PQC algorithms and classical cryptography.

$8\mathrm{.}3.$ Practical Case Studies

$9.$ Conclusion and Future work $(2-3$ pages$)$

Summarize key findings: assurances of security of PQC for blockchain.

It should also be contrasted how PQC based security will look as quantum computers continue to develop.