Abstract-This work describes the smallest known hardware implementation for Elliptic/Hyperelliptic Curve Cryptography (ECC/HECC). We propose two solutions for Publickey Cryptography (PKC), which are based on arithmetic on elliptic/hyperelliptic curves. One solution relies on ECC over binary fields F2n where n is a composite number of the form 2p (p is a prime) and another on HECC on curves of genus 2 over F2p . This implies the same arithmetic unit for both cases which supports arithmetic in a field F2p . Our best solution that still results in a feasible performance features less than 5 kgates with an average power consumption smaller than 10 µW .
I. INTRODUCTIONThe field of embedded systems is growing at a rapid rate, as devices such as mobile phones, PDAs, smart cards and more recently RFID tags, sensor nodes and key immobilizers have become unavoidable in our everyday life. Hence, the distinguishing characteristics of embedded security can be divided into two categories: resource-limitation and physical accessibility. The former one specifies severe resource constraints on the security architecture in terms of memory, computational capacity, and energy for embedded devices. The most challenging tasks for embedded security are implementations of Public-key Cryptography (PKC).RFID tags are small wireless devices for pervasive computing. Despite their rigorous constraints featuring extremely low budget for power and die size they also give rise to serious security and privacy issues. Typical security services include authentication, key management and encryption. Although some experts are a priori giving up on public key solutions, assuming it being too expensive and too power hungry, there exists a line of research exploring the limits of compact public key implementations for low-cost applications such as RFIDs and sensor networks.In our previous work we investigated standardized low cost solutions for Elliptic Curve Cryptography (ECC) processors supporting security algorithms and protocols for RFID [1]. Namely, in standards it is mainly recommended to use ECC over a field F 2 p , where p is a prime. In this work we describe a new solution based on Hyperelliptic Curve Cryptography (HECC) and on ECC over composite fields. HECC has some advantages over ECC because of the possibility to work in a smaller field e.g. for HECC (in the case of genus 2 curves) one can work in the field F 2 n whilst obtaining the same level of security as for ECC over fields of bit-lengths that are twice as large. The same holds for ECC over composite fields. This property allows for more compact ALU than in the case of ECC.