The Design And Implementation Of FPGA Over Elliptic Curves Cryptography

With the rapid development of information technology and computer network,information security is given moer and more attention.How to ensure the security,secreey,verity and integrity of the information in computer system and communication network is the main research task of information security.Crypto technology is the core of information security technology.Elliptic Curve Cryptography is one of the branch of crypto technology,which can effectively solv Problems about digital signature,identification and key distribution in public channel.Elliptic Curve cryptosystem as a public crypto method has the advantages of higher security,the less calculational complexity,shorter key size,less space,higher speed and limited band width and so on,it has become the public key cryptology gradually and has broad application value in the fields.This dissertation analyzed the theory of Elliptic Curve Cryptosystem in details and studied the material algorithms of FPGA implementation of Elliptic Cuvre Cyrptosystem.According to the idea of hiberarchy and modularization,the design scheme of Elliptic Cuvre Cyrptosystem base on FPGA has been gived.This dissertation mainly completes these following works:1、The dissertation researches the mathematic theory of Elliptic Curve Cryptosystem and find out the methods suitable for FPGA implementation after analyse and compair many methods.The key computing modules in elliptic curve cryptography are analyzed.In order to achieve the balance of area and performance,the key modules are implemented by the method of speed first,and the other modules are implemented by the method of resource first.2、Point addition and double point are the basis of elliptic curve operation.Based on the characteristics of the underlying finite field operation and the parallel computing characteristics of FPGA,the dissertation choose the Jacobian projective coordinate system,and design a computing method of point adding operation and multiple point operation.3、Point multiplication is a time-consuming issue in Elliptic Curve Cryptography.After analyzing the point multiplication in elliptic curve cryptosystem,this paper designs a fast implementation method according to the parallel computing characteristics of FPGA,which greatly improves the performance of elliptic curve cryptosystem.4、The finite field operation and elliptic curve operation are encapsulated into a large number library,and the large number library is used to implement the ECC algorithm based on the prime domain.The design is compiled in the ISE of Xilinx Company and verified and tested in the Virtex5 development board.The test results show that under the 100 MHZ working frequency,the signature performance of ECC256 is 422 times per second,the performance of the verification is 216 times per second,the key exchange performance is 217 times per second,the encryption performance is 221 times per second,and the decryption performance is 442 times per second.