PSEC-KEM (Provably Secured Elliptic Curve Encryption with Key Encapsulation mechanism) is an
algorithm designed by
NTT Laboratories, Japan
in 1999. PSEC-KEM is provably secured under the
computational Diffie-Hellman assumption on the elliptic curves and is an efficient integration
of both asymmetric and symmetric key cryptography to provide a secured and integrated solution.
This work aims to develop hardware and software designs for the
algorithm on FPGAs and standard processors.
OEF is a finite field in GF(p
m), where p, m and reduction polynomial is selected in such a way
that they match closely with the underlying hardware characteristic. Value of p can be selected to
fit in a single word, making the carry handling simple.
In this work we have implemented differential power analysis (DPA)
on PSEC-KEM in binary random and prime non-endomorphic curve. It is shown that these two
implementation is vulnerable to correlation power analysis (CPA) and one can extract the private
key of user from it. Power analysis for both implementations are performed on SASEBO-GII
board. Apart from this, the main objective of this work is to perform power analysis on Optimal
Extension Field, implemented in Xilinx Microblaze processor. We have implemented
OEF scalar multiplication on Microblaze processor and performed
simple power analysis (SPA) as well as differential power analysis (DPA) attack on it. We have
shown the vulnerability of the implementation to both SPA and DPA and how one can extract the
private key of an user from it. Power analysis for OEF implementation is performed on SASEBO-W
board
Microblaze implementation for OEF codes (ECPM07K and SECO427R)
Certicom Research. Standards for Efficient Cryptography, SEC 2: Recommended Elliptic Curve
Domain Parameters (Version 2.0), Working Draft (January 27, 2010)..
NTT Information Sharing Platform Laboratories, NTT Corporation. PSEC-KEM Specification (Version
2.0), June 2007.
Certicom Research. Standards for Efficient Cryptography, SEC X.1: Supplemental Document
for Odd Characteristic Extension Fields, Working Draft (Version 0.7). May 2009.
Certicom Research. Standards for Efficient Cryptography, SEC X.2: Recommended Elliptic
Curve Domain Parameters, Working Draft (Version 0.6). August 2008.
Certicom Research. Standards for Efficient Cryptography, SEC 1: Elliptic Curve Cryptography (Version
1.0), September 2000
C. Rebeiro. Architectural Explorations for Elliptic Curve Cryptography on FPGAs,Master's
Thesis February 2009.
M.K.Lee, K.T.Kim, H.Kim, and D.K.Kim. Efficient Hardware Implementation of Elliptic Curve
Cryptography over GF(pm). WISA 2005, LNCS 3786, pp. 207-217, 2006.
SHA Opencores, http://opencores.org/project,sha core
The GNU Multiple Precision Arithmetic Library, http://gmplib.org/.
D. Hankerson, A. Menezes, S. Vanstone, “Guide to Elliptic Curve Cryptography”
Xilinx Inc. MicroBlaze Processor Reference Guide Embedded Development Kit EDK 10.1i
Prabhakaran, Abirami.Side-Channel Analysis of Block Ciphers Using CERG-GMU Interface
on SASEBO-GII,Master's Thesis May 2011
T. Guneysu and Christof Paar, “Ultra High Performance ECC over NIST Primes on Commercial FPGAs”, CHES 2008
Suvadeep Hajra and Debdeep Mukhopadhyay Pushing the Limit of Non-Profiling DPA using
Multivariate Leakage Model published in IACR Cryptology ePrint Archive 2013: 849 (2013).