A Practical Fault Attack on Square and Multiply(1).pdf

(366 KB) Pobierz
Institute for Applied Information Processing and Communications (IAIK) - VLSI & Security
A Practical Fault Attack on Square and
Multiply
¨
Jorn-Marc Schmidt
Christoph Herbst
Institute for Applied Information Processing and Communications (IAIK)
Graz University of Technology
Inffeldgasse 16a, A-8010 Graz, Austria
{joern-marc.schmidt,christoph.herbst}@iaik.tugraz.at
¨
Jorn-Marc Schmidt, Christoph Herbst
A Practical Fault Attack on Square and Multiply
Institute for Applied Information Processing and Communications (IAIK) - VLSI & Security
1
Introduction
Motivation
Square and Multiply
Recent Work
Our Fault Model
Our Attack
Practical Issues
Fault Injection
Problems
Outlook and Conclusion
2
3
4
¨
Jorn-Marc Schmidt, Christoph Herbst
A Practical Fault Attack on Square and Multiply
Institute for Applied Information Processing and Communications (IAIK) - VLSI & Security
Motivation
Square and multiply is a common stragegy for
implementing modular exponentiation
Modular exponentiation is used in public key cryptography
RSA is based on modular exponentiation
Fault attack on RSA implementations without CRT
¨
Jorn-Marc Schmidt, Christoph Herbst
A Practical Fault Attack on Square and Multiply
Institute for Applied Information Processing and Communications (IAIK) - VLSI & Security
Other Modular Exponentiation Methods
Left-to-right square and multiply
Right-to-left square and multiply
k-ary exponentiation
Sliding window method
Montgomery powering ladder
¨
Jorn-Marc Schmidt, Christoph Herbst
A Practical Fault Attack on Square and Multiply
Institute for Applied Information Processing and Communications (IAIK) - VLSI & Security
Square and Multiply
Function 1
Left-to-Right Square and Multiply Algorithm
Input:
Message
m,
Exponent
e
= (e
t
, . . . ,
e
0
)
2
, Modulus
N
R
=
1
for
i
=
t
downto 0
do
R
=
R
·
R
mod
N
if
e
i
=
1
then
R
=
R
·
m
mod
N
end if
end for
return
R
¨
Jorn-Marc Schmidt, Christoph Herbst
A Practical Fault Attack on Square and Multiply

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika:

Zgłoś jeśli naruszono regulamin