CANCELLED
Isabelle Déchène, University of Ottawa
Algebraic Groups: Computational Aspects and Cryptographic Applications
Abelian varieties, genus, Jacobians, divisors, Picard group, tori,
Riemann-Roch, hyperelliptic curves are terms you all heard in one
crypto talk or another. Still confused about the relations among
them? If so, now is the time to roll-up your sleeves and get to
the bottom of this.
Indeed, in order to make a step further and pursue "new directions
in cryptography", it is sometimes wise to first get to know
what is surrounding you. During this mini-course, we will sort out
what's what in order to discuss and compare the cryptographic properties
of chosen projective varieties and linear algebraic groups. We will
then present an introduction to non-hyperelliptic curves and generalized
Jacobians, two of the most recent ideas of this field.
Phil Eisen, Cloakware
It's Not the Size of Your Key That Matters, It's How You Use
It
The strength of a cryptographic algorithm has always been discussed
in terms of its resistance to black-box attacks. As more and more
security moves into the software world, this is an increasingly
unrealistic model. In this talk, we discuss the much more realistic
(and unfortunately, much more severe) white-box attack context.
We will look at ongoing research on ways to have secure cryptography
in this context, including cipher design that takes white-box attacks
into account.
Evangelos Kranakis, Carleton University
Security Models: Prospects, Perspectives, Directions
The last decade has witnessed a surge of scientific activity in
designing secure systems that are responsive to rapid changes in
technology. Missteps are being corrected, irregularities straightened,
lessons learned and the world has never came to a halt. The next
decade looks just as promising and penetrating studies will attempt
to balance theory and practice. In this talk we peer into security's
crystal ball and look at fundamental questions that may affect the
many facets of research on this subject.
Ali Miri, University of Ottawa
Accelerating Scalar Multiplication on Elliptic Curve Cryptosystems
Scalar multiplication is the central and most time-consuming operation
in many public-key curve-based systems such as Elliptic Curve (ECC),
Hyperelliptic Curve (HECC) and Pairing-based cryptosystems. Its
algorithmic and computational structure has been the focus of extensive
research in recent years in a growing effort to reduce its time
execution and power/memory requirements and, thus, to make the corresponding
systems suitable for implementation in the myriad of new applications
using devices such as PDAs, smartcards, cellphones, RFID tags and
wireless sensor networks.
In this mini-course, we discuss various methodologies that we have
developed to accelerate scalar multiplication on ECCs over prime
fields, and show their impact in sequential and parallel implementations
that also include protection against Simple Side-Channel Attacks
(SSCA). We also present a new method for computation of scalar multiplication
that uses a generic multibase representation to reduce the number
of required operations.
This is joint work with Patrick Longa.
Kumar Murty, University of Toronto
Recent developments in Hash functions
Considerable attention has been given recently to the construction
of new hash functions. After reviewing some of this work, we shall
present the function "ERINDALE" that has been developed
in joint work with Nikolajs Volkovs of the GANITA Lab at the University
of Toronto.
Dana Neustader, Elliptic Semiconductor
Elliptic Curves over Prime and Binary Fields in Cryptography
Elliptic Curve Cryptography (ECC) is a public key crypto system
based upon a hard number theoretic problem: elliptic curve discrete
logarithms. At the base of ECC curve operations is finite field
(Galois Field) algebra with focus on prime Galois fields, GF(p),
and binary extension Galois fields, GF(2^m). The performance of
the ECC curve operations depend on the performance of the Galois
field arithmetic, as well as the choice of point representation,
and point addition/doubling formulae. Both prime and binary field
types offer advantages and disadvantages in software and hardware
based cryptosystems. These trade offs are described and analyzed
in more detail in the present paper.
Kenny Paterson, Royal Holloway,
University of London
Recent Advances in Identity-based Encryption
We give an overview of recent advances in the field of Identity-based
Encryption (IBE). We will discuss schemes that enjoy security proofs
in the standard model. We will also describe schemes that avoid
the use of bilinear maps. Finally, we will identify open problems
in IBE and connections between IBE and others areas of cryptography.
Renate Scheidler, University of
Calgary
Real Hyperelliptic Curves
Algebraic geometers and cryptographers are very familiar with what
the traditional "imaginary" model of a hyperelliptic curve.
Another less familiar description of such a curve is the so-called
"real" model; the terminology stems from the analogy to
real and imaginary quadratic number fields. Structurally and arithmetically,
the real model behaves quite differently from its imaginary counterpart.
While divisor addition with subsequent reduction ("giant steps")
is still essentially the same, the real model no longer allows for
efficiently computable unique representation of elements in the
Jacobian via reduced representatives. However, the real model exhibits
a so-called infrastructure, with an additional much faster operation
("baby steps"). We present the real model of a hyperelliptic
curve and its two-fold baby step giant step divisor arithmetic.
We also indicate how to use these algorithms for potential cryptographic
and number theoretic applications.
Francesco Sica, Mount Allison University
Complex Double Bases applied to Scalar Multiplication on Algebraic
Curves
In elliptic curve cryptography, the costliest operation is the
computation of nP=P+...+P, called scalar multiplication. It is acknowledged
that the existence of fast endomorphisms (such as the Frobenius
on Koblitz curves) results in clear performance speedup. I will
expose how the use of double base expansions of n gives way to a
new class of scalar multiplication algorithms capable of provably
beating the fastest known implementations on Koblitz curves, with
negligible additional memory.
Douglas Stinson, University of Waterloo
Recent Results on the Design and Analysis of Manual Authentication
Protocols
There has been considerable recent interest in manual authentication
protocols, where a Sender S and a Receiver R are connected by an
insecure channel as well as a narrowband authenticated (i.e., a
"manual") channel. S wishes to send a "long"
message over the insecure channel, which is authenticated to R using
a short authenticator sent over the manual channel. S and R are
assumed to have have no shared secret key, nor is there is an infrastructure
to support public-key cryptography. It is of interest to design
protocols in this setting that are secure against an active adversary.
In this talk, we will discuss how manual authentication protocols
can be designed and analyzed. We consider non-interactive as well
as interactive schemes, and we look at both unconditionally secure
prootcols and protocols that are provably secure in the random oracle
model.
This talk is based on joint work with Atefeh Mashatan.
Rene Struik, Certicom Research, Canada
Speed-ups of elliptic curve-based schemes
We discuss several methods that can be used to accelerate the verification
step of ECC-based signature schemes. We show how to obtain a 40%
efficiency improvement of ordinary ECDSA signature verification
and even a factor 2.4x efficiency improvement when ECDSA certificate
verification is combined with the key computation step in Diffie-Hellman-based
protocols, such as static-ECDH and ECMQV. This challenges the conventional
wisdom that with ECC-based signature schemes, signature verification
is always considerably slower than signature generation and slower
than RSA signature verification. Results apply to all prime curves
standardized by NIST, the NSA 'Suite B' curves, and the so-called
Brainpool curves.
Amr Youssef, Concordia University
OnCryptographic Properties of Boolean Functions
The security of symmetric key primitives, such as block ciphers,
stream ciphers and hash functions, depends on the cryptographic
properties of the underlying Boolean functions. Cryptographic Boolean
functions should satisfy several properties such as balance, high
nonlinearity, high resiliency degree, and high algebraic immunity
degree.
In this talk, we review different classes of Boolean functions
of cryptographic interest. Then, we show how the generalizations
of several earlier attacks on symmetric ciphers have led to the
definition of new properties that can be used to ensure the ciphers'
resistance against these attacks. We will also discuss the recently
developed algebraic attacks and provide a brief summary of recent
results related to the construction of Boolean functions with high
algebraic immunity degree.
