62 research outputs found
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Finite Fields: Theory and Applications
Finite fields are the focal point of many interesting geometric, algorithmic and combinatorial problems. The workshop was devoted to progress on these questions, with an eye also on the important applications of finite field techniques in cryptography, error correcting codes, and random number generation
Algebraic Techniques for Low Communication Secure Protocols
Internet communication is often encrypted with the aid of mathematical problems that are hard to solve. Another method to secure electronic communication is the use of a digital lock of which the digital key must be exchanged first. PhD student Robbert de Haan (CWI) researched models for a guaranteed safe communication between two people without the exchange of a digital key and without assumptions concerning the practical difficulty of solving certain mathematical problems.
In ancient times Julius Caesar used secret codes to make his messages illegible for spies. He upped every letter of the alphabet with three positions: A became D, Z became C, and so on. Usually, cryptographers research secure communication between two people through one channel that can be monitored by malevolent people. De Haan studied the use of multiple channels. A minority of these channels may be in the hands of adversaries that can intercept, replace or block the message. He proved the most efficient way to securely communicate along these channels and thus solved a fundamental cryptography problem that was introduced almost 20 years ago by Dole, Dwork, Naor and Yung
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Contemporary Coding Theory
Coding Theory naturally lies at the intersection of a large number
of disciplines in pure and applied mathematics. A multitude of
methods and means has been designed to construct, analyze, and
decode the resulting codes for communication. This has suggested to
bring together researchers in a variety of disciplines within
Mathematics, Computer Science, and Electrical Engineering, in order
to cross-fertilize generation of new ideas and force global
advancement of the field. Areas to be covered are Network Coding,
Subspace Designs, General Algebraic Coding Theory, Distributed
Storage and Private Information Retrieval (PIR), as well as
Code-Based Cryptography
Hardware design of cryptographic accelerators
With the rapid growth of the Internet and digital communications, the volume of sensitive electronic transactions being transferred and stored over and on insecure media has increased dramatically in recent years. The growing demand for cryptographic systems to secure this data, across a multitude of platforms, ranging from large servers to small mobile devices and smart cards, has necessitated research into low cost, flexible and secure solutions. As constraints on architectures such as area, speed and power become key factors in choosing a cryptosystem, methods for speeding up the development and evaluation process are necessary. This thesis investigates flexible hardware architectures for the main components of a cryptographic system. Dedicated hardware accelerators can provide significant performance improvements when compared to implementations on general purpose processors. Each of the designs proposed are analysed in terms of speed, area, power, energy and efficiency. Field Programmable Gate Arrays (FPGAs) are chosen as the development platform due to their fast development time and reconfigurable nature. Firstly, a reconfigurable architecture for performing elliptic curve point scalar multiplication on an FPGA is presented. Elliptic curve cryptography is one such method to secure data, offering similar security levels to traditional systems, such as RSA, but with smaller key sizes, translating into lower memory and bandwidth requirements. The architecture is implemented using different underlying algorithms and coordinates for dedicated Double-and-Add algorithms, twisted Edwards algorithms and SPA secure algorithms, and its power consumption and energy on an FPGA measured. Hardware implementation results for these new algorithms are compared against their software counterparts and the best choices for minimum area-time and area-energy circuits are then identified and examined for larger key and field sizes. Secondly, implementation methods for another component of a cryptographic system, namely hash functions, developed in the recently concluded SHA-3 hash competition are presented. Various designs from the three rounds of the NIST run competition are implemented on FPGA along with an interface to allow fair comparison of the different hash functions when operating in a standardised and constrained environment. Different methods of implementation for the designs and their subsequent performance is examined in terms of throughput, area and energy costs using various constraint metrics. Comparing many different implementation methods and algorithms is nontrivial. Another aim of this thesis is the development of generic interfaces used both to reduce implementation and test time and also to enable fair baseline comparisons of different algorithms when operating in a standardised and constrained environment. Finally, a hardware-software co-design cryptographic architecture is presented. This architecture is capable of supporting multiple types of cryptographic algorithms and is described through an application for performing public key cryptography, namely the Elliptic Curve Digital Signature Algorithm (ECDSA). This architecture makes use of the elliptic curve architecture and the hash functions described previously. These components, along with a random number generator, provide hardware acceleration for a Microblaze based cryptographic system. The trade-off in terms of performance for flexibility is discussed using dedicated software, and hardware-software co-design implementations of the elliptic curve point scalar multiplication block. Results are then presented in terms of the overall cryptographic system
On the Application of Identity-Based Cryptography in Grid Security
This thesis examines the application of identity-based cryptography
(IBC) in designing security infrastructures for grid applications.
In this thesis, we propose a fully identity-based key infrastructure
for grid (IKIG). Our proposal exploits some interesting properties
of hierarchical identity-based cryptography (HIBC) to replicate
security services provided by the grid security infrastructure (GSI)
in the Globus Toolkit. The GSI is based on public key infrastructure
(PKI) that supports standard X.509 certificates and proxy
certificates. Since our proposal is certificate-free and has small
key sizes, it offers a more lightweight approach to key management
than the GSI. We also develop a one-pass delegation protocol that
makes use of HIBC properties. This combination of lightweight key
management and efficient delegation protocol has better scalability
than the existing PKI-based approach to grid security.
Despite the advantages that IKIG offers, key escrow remains an issue
which may not be desirable for certain grid applications. Therefore,
we present an alternative identity-based approach called dynamic key
infrastructure for grid (DKIG). Our DKIG proposal combines both
identity-based techniques and the conventional PKI approach. In this
hybrid setting, each user publishes a fixed parameter set through a
standard X.509 certificate. Although X.509 certificates are involved
in DKIG, it is still more lightweight than the GSI as it enables the
derivation of both long-term and proxy credentials on-the-fly based
only on a fixed certificate.
We also revisit the notion of secret public keys which was
originally used as a cryptographic technique for designing secure
password-based authenticated key establishment protocols. We
introduce new password-based protocols using identity-based secret
public keys. Our identity-based techniques can be integrated
naturally with the standard TLS handshake protocol. We then discuss
how this TLS-like identity-based secret public key protocol can be
applied to securing interactions between users and credential
storage systems, such as MyProxy, within grid environments
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