Power analysis attacks and algorithmic approaches to their countermeasuresfor Koblitz curve cryptosystems

Because of their shorter key sizes, cryptosystems based on elliptic curves are being increasingly used in practical applications. A special class of e lliptic curves, namely, Koblitz curves, offers an additional, but crucial, advantage of considerably reduced processing time. In this article, power a nalysis attacks are applied to cryptosystems that use scalar multiplication on Koblitz curves. Both the simple and the differential power analysis att acks are considered and a number of countermeasures are suggested. While th e proposed countermeasures against the simple power analysis attacks rely o n making the power consumption for the elliptic curve scalar multiplication independent of the secret key, those for the differential power analysis a ttacks depend on randomizing the secret key prior to each execution of the scalar multiplication. These countermeasures are computationally efficient and suitable for hardware implementation.