Why i need to learn so much math for my phd research
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Transcript of Why i need to learn so much math for my phd research
Why I need to learn so much math for my PhD research
Marisa W. Paryasto School of Electrical Engineering and
Informatics ITB
July 23rd, 2009
My Research
q Title: Elliptic Curve Cryptography Algorithm Implementation and Design for Constrained Devices
q Target: Make it fits constrained devices [constrained devices = some tiny little spaces about 1mm2]
Math Foundation needed
q Number Theory q Algebra
⣄ Groups ⣄ Rings ⣄ Fields ⣄ Polynomial
q Finite Fields ⣄ Basic Properties ⣄ Field Extensions ⣄ Roots of
Irreducible Polynomials
⣄ Bases of Finite Fields
⣄ Finite Fields GF(2m)
What is Elliptic Curve Cryptography?
q Point multiplication Q = kP q Repeated point addition and
doubling: 9P = 2(2(2P)) + P
q Public key operation: Q(x,y) = kP(x,y) Q = public key P = base point (curve parameter) k = private key n = order of P
q Elliptic curve discrete logarithm Given public key kP, find private key k
q Best known attack: Pollard’s rho method with running time: ((πn)½))/2
Hierarchical Model for Elliptic Curve Cryptography
Research Questions
q Implementing ECC is not simple. Especially in constrained devices.
q How do you know that it’s secure and being implemented securely?
More problems
q There is no “guide” yet for implementing ECC efficiently
q There is no tools to predict certain configurations of ECC and its level of security
Hypothesis
q There is exist some (generic) algorithm to implement ECC.
q Different implementation algorithms determine different level of security. (Notes: metric of security?)
Methods (to solve the problems)
q Improve an architecture to be resistance against side channel attacks ⣄ Asynchronous circuits implementation
q Develop a configurable, integrated ECC modules (to measure security/efficiency/space/speed)
Contribution
Efficient implementati
on of ECC
Efficient software
implementation of ECC/
Reconfigurable ECC
implementation
Hardware implementation of ECC on constrained
devices
Attack of ECC hardware
implementation on
constrained device
basis conversion
various library smart attack
algorithm circuit synthesis
math software hardware math / foundation
