On the Security of Elliptic Curve Cryptosystems against Attacks with Special-Purpose Hardware

Tim Güneysu, Chris­tof Paar, Jan Pelzl

2nd Workshop on Special-purpose Hardware for Attacking Cryptographic Systems - SHARCS 2006, Cologne, Germany, April 3-4, 2006,.


Abstract

Since their invention in the mid 1980s, Elliptic Curve Cryptosystems (ECC) have become an alternative to common Public-Key (PK) cryptosystems such as, e.g., RSA. The utilization of Elliptic Curves (EC) in cryptography is very promising because of their resistance against powerful index-calculus attacks. For a similar level of security, ECC allows for ecient implementation due to a signi cantly smaller bit size of the operands. It is widely accepted that the only feasible way to attack actual cryptosystems is the application of dedicated hardware. In times of continuous technological improvements and increasing computing power, the question of the security of ECC against attacks based on special-purpose hardware arises.

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Tags: Cryptanalysis, discrete logarithm, elliptic curve cryptosystem, Hardware, Pollard's Rho, public-key