Research On Elliptic Curve Cryptography Algorithm And Chip Implementation Method

Elliptic Curve Cryptography (ECC) is one of the public key cryptographies proposed in 1985. Compared with RSA, it has smaller key length, less store information and more hardware implementation efficiency, with the same security level. Thus, it has brilliant prospect in application. In fact, it has been adopted by many security standards, such as IPsec and WAPI, etc.The research about ECC mainly includes two aspects: security and implementation efficiency. Research on security is developed theoretically with topics such as discrete logarithm problem, parameter selection of elliptic curve and attack algorithm. Meanwhile, it is developed in engineering with topics such as timing analysis attack, power analysis attack, electromagnetism analysis attack and fault analysis attack, etc. Research on implementation efficiency is mainly about the calculation about scalar multiplication of k⊙P, whereas k is a big integer and P is a point on elliptic curve. It involves the research fields of scalar multiplication algorithm, finite field calculation, software and hardware system structure design and hardware datapath optimization, etc.As one of the hottest research areas in the 21st century, ECC has obtained many achievements. The problem of theoretical security has been clarified in substance. Now more research is aimed at increasing efficiency and preventing attacks launched in engineer. The paper reviewed briefly the existing achievements on ECC, then, targeted research mainly about hardware implementation of the scalar multiplication, finte field multiplier and secure scan chain design, giving the detailed relevant data. Meanwhile, the other related techniques were discussed. The main achievements of this paper are listed as below: 1. Proposed an unbalanced modular reduction method in finite field. Based on the method, an ECC configurable accelerator was advised. The accelerator adopted pipeline design like CPU, controlled operation with intern instructions generated by finite state machine. Meanwhile, a field flexible method based on subsection operation was adopted, thus, many different fields were supported.2. A parallel computation method for ECC scalar multiplication over characteristic 2 finite fields was proposed. The method made use of hardware dynamic instruction schedule technique which applied both instruction level parallelism and thread level parallelism to improve the parallel computation performance.3. An attack method was presented in allusion to a kind of hardware implementation of elliptic curve cryptography. Then an easy and valid secure scan method was proposed against the attack. It maintained high test fault coverage and would not compromise the chip security.4. A normalized finite field multiplier was presented which can realize partial parallel multiplication according to a chosen parameter. Time complexity and space complexity was analyzed. The analyzed result can guide the design parameter selection.