Why i need to learn so much math for my phd research
1. 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
2. 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]
3. Math Foundation needed
q Number Theory
q Finite Fields
q Algebra
⣄ Basic Properties
⣄ Groups
⣄ Field Extensions
⣄ Rings
⣄ Roots of
⣄ Fields
Irreducible
Polynomials
⣄ Polynomial
⣄ Bases of Finite
Fields
⣄ Finite Fields GF
(2m)
4. 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
6. 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?
7. 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
8. Hypothesis
q There is exist some (generic)
algorithm to implement ECC.
q Different implementation algorithms
determine different level of security.
(Notes: metric of security?)
9. 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)
10. Contribution
Efficient
software Attack of ECC
Hardware
implementati hardware
Efficient implementati
on of ECC/ implementati
implementati on of ECC on
Reconfigurabl on on
on of ECC
constrained
e ECC constrained
devices
implementati device
on
basis various
smart attack
conversion
library
circuit
algorithm
synthesis
math
software
hardware
math / foundation
![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]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)