An efficient elliptic curve cryptography processor using addition chains with high information entropy

RFID tags in the supply chain provide the capabilities of bar codes without requiring a line of sight, but this benefit can compromise the privacy of the tag owner. The problem can be corrected by equipping RFID tags with public key cryptography but due to the extreme constraints on area and power, the processor must be as small and as energy-efficient as possible. We present a public key cryptography processor (based on elliptic curves over binary extension fields) that does not use the Montgomery ladder algorithm. The new algorithm has the processor perform point additions based on integer addition chains, without computing the integer chains. Point doubling is performed only once per encryption. Key bits are interpreted in a new way, but the algorithm is independent of the key, resisting simple side-channel attacks. This paper includes an analysis of information entropy, to determine the strength of keys and improve processor design. The processor´s performance results are presented, and are competitive with the smallest, lowest-energy designs in the literature.