Browsing Mathematics (Faculty of) by Subject "Cryptography"
Now showing items 120 of 22

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 ... 
Computational Approaches to Problems in Noncommutative Algebra  Theory, Applications and Implementations
(University of Waterloo, 20160928)Noncommutative rings appear in several areas of mathematics. Most prominently, they can be used to model operator equations, such as differential or difference equations. In the Ph.D. studies leading to this thesis, ... 
Digital Signature Schemes Based on Hash Functions
(University of Waterloo, 20170419)Cryptographers and security experts around the world have been awakened to the reality that one day (potentially soon) largescale quantum computers may be available. Most of the publickey cryptosystems employed today on ... 
Fast Algorithms for Finding the Characteristic Polynomial of a Rank2 Drinfeld Module
(University of Waterloo, 20180921)This thesis introduces a new Monte Carlo randomized algorithm for computing the characteristic polynomial of a rank2 Drinfeld module. We also introduce a deterministic algorithm that uses some ideas seen in Schoof's ... 
Fast Bootstrapping in Z_q
(University of Waterloo, 20150828)In 2015, Ducas and Micciancio presented a novel technique to compute the NAND gate using the Learning With Errors cryptosystem (LWE), along with a novel bootstrapping technique that turns turns this cryptosystem into a ... 
Generic Attacks on Hash Functions
(University of Waterloo, 20100928)The subject of this thesis is a security property of hash functions, called chosentarget forcedprefix preimage (CTFP) resistance and the generic attack on this property, called the herding attack. The study of CTFP ... 
Homomorphic Encryption
(University of Waterloo, 20130124)In this thesis, we provide a summary of fully homomorphic encryption, and in particular, look at the BGV encryption scheme by Brakerski, Gentry, and Vaikuntanathan; as well the DGHV encryption scheme by van Dijk, Gentry, ... 
Implementing the SchoofElkiesAtkin Algorithm with NTL
(University of Waterloo, 20130430)In elliptic curve cryptography, cryptosystems are based on an additive subgroup of an elliptic curve defined over a finite field, and the hardness of the Elliptic Curve Discrete Logarithm Problem is dependent on the order ... 
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 ... 
MAC Constructions: Security Bounds and Distinguishing Attacks
(University of Waterloo, 20070518)We provide a simple and improved security analysis of PMAC, a Parallelizable MAC (Message Authentication Code) defined over arbitrary messages. A similar kind of result was shown by Bellare, Pietrzak and Rogaway at ... 
Message Authentication and Recognition Protocols Using TwoChannel Cryptography
(University of Waterloo, 20081202)We propose a formal model for noninteractive message authentication protocols (NIMAPs) using two channels and analyze all the attacks that can occur in this model. Further, we introduce the notion of hybridcollision ... 
Novel Secret Sharing and Commitment Schemes for Cryptographic Applications
(University of Waterloo, 20120815)In the second chapter, the notion of a social secret sharing (SSS) scheme is introduced in which shares are allocated based on a player's reputation and the way she interacts with other parties. In other words, this scheme ... 
The Number Field Sieve for BarretoNaehrig Curves: Smoothness of Norms
(University of Waterloo, 20150520)The security of pairingbased cryptography can be reduced to the difficulty of the discrete logarithm problem (DLP) in finite fields of medium characteristic. The number field sieve is the best known algorithm for this ... 
On the effectiveness of isogeny walks for extending cover attacks on elliptic curves
(University of Waterloo, 20160823)Cryptographic systems based on the elliptic curve discrete logarithm problem (ECDLP) are widely deployed in the world today. In order for such a system to guarantee a particular security level, the elliptic curve selected ... 
On the Efficiency and Security of Cryptographic Pairings
(University of Waterloo, 20121219)Pairingbased cryptography has been employed to obtain several advantageous cryptographic protocols. In particular, there exist several identitybased variants of common cryptographic schemes. The computation of a single ... 
On the Security of Leakage Resilient Public Key Cryptography
(University of Waterloo, 20120430)Side channel attacks, where an attacker learns some physical information about the state of a device, are one of the ways in which cryptographic schemes are broken in practice. "Provably secure" schemes are subject to these ... 
On the Security of Some Variants of RSA
(University of Waterloo, 20070510)The RSA cryptosystem, named after its inventors, Rivest, Shamir and Adleman, is the most widely known and widely used publickey cryptosystem in the world today. Compared to other publickey cryptosystems, such as elliptic ... 
Perfect Hash Families: Constructions and Applications
(University of Waterloo, 2003)Let <b>A</b> and <b>B</b> be finite sets with <b>A</b>=<i>n</i> and <b>B</b>=<i>m</i>. An (<i>n</i>,<i>m</i>,<i>w</i>)<i>perfect hash</i> family</i> is a collection <i>F</i> of functions from <b>A</b> to <b>B</b> ... 
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 ...