Browsing Mathematics (Faculty of) by Supervisor "Jao, David"
Now showing items 111 of 11

Abstract and Explicit Constructions of Jacobian Varieties
(University of Waterloo, 20180810)Abelian varieties, in particular Jacobian varieties, have long attracted interest in mathematics. Their influence pervades arithmetic geometry and number theory, and understanding their construction was a primary motivator ... 
Combinatorial Arithmetic on Elliptic Curves
(University of Waterloo, 20170927)We propose a scalar multiplication technique on an elliptic curve, which operates on triples of collinear points. The computation of this operation requires a new approach to operation chains, with similarities to Montgomery ... 
Design, Analysis, and Optimization of IsogenyBased Key Establishment Protocols
(University of Waterloo, 20200819)We analyze the Commutative Supersingular Isogeny DiffieHellman protocol (CSIDH), a novel supersingular isogenybased key establishment protocol. Our analysis is from three perspectives: Quantum Cryptanalysis. Building ... 
Key Compression for IsogenyBased Cryptosystems
(University of Waterloo, 20160421)We present a method for key compression in quantumresistant isogenybased cryptosystems, which reduces storage and transmission costs of perparty public information by a factor of two, with no effect on the security level ... 
A postquantum digital signature scheme based on supersingular isogenies
(University of Waterloo, 20170920)We present the first generalpurpose digital signature scheme based on supersingular elliptic curve isogenies secure against quantum adversaries in the quantum random oracle model with small key sizes. This scheme is ... 
PostQuantum Elliptic Curve Cryptography
(University of Waterloo, 20160516)We propose and develop new schemes for postquantum cryptography based on isogenies over elliptic curves. First we show that ordinary elliptic curves are have less than exponential security against quantum computers. These ... 
PostQuantum Security of Authenticated Key Establishment Protocols
(University of Waterloo, 20160420)We present a security model for authenticated key establishment that allows for quantum interactions between the adversary and quantum oracles that emulate classical parties, resulting in a truly postquantum security ... 
Privately Constrained Testable Pseudorandom Functions
(University of Waterloo, 20180920)Privately Constrained Pseudorandom Functions allow a PRF key to be delegated to some evaluator in a constrained manner, such that the key’s functionality is restricted with respect to some secret predicate. Variants of ... 
Security Analysis of IsogenyBased Cryptosystems
(University of Waterloo, 20200820)Let $E$ be a supersingular elliptic curve over a finite field. In this document we study publickey encryption schemes which use nonconstant rational maps from $E$. The purpose of this study is to determine if such ... 
Smoothening Functions and the Homomorphism Learning Problem
(University of Waterloo, 20200902)This thesis is an exploration of certain algebraic and geometrical aspects of the Learning With Errors (LWE) problem introduced in Reg05. On the algebraic front, we view it as a Learning Homomorphisms with Noise problem, ... 
UserControlled Computations in Untrusted Computing Environments
(University of Waterloo, 20190115)Computing infrastructures are challenging and expensive to maintain. This led to the growth of cloud computing with users renting computing resources from centralized cloud providers. There is also a recent promise in ...