Scalar Multiplication Algorithm Research On Elliptic Curve Cryptosystem

Elliptic Curve Cryptosystems (ECC) in recent years has been widely institude in various international standards。Elliptic Curve Crypto systems technology can be applied in encryption, digital signatures,key exchange, analysing large number , prime number judgement and so on . In the same safe intension, the length of the key of ECC which can operate much fast is smaller than the other traditional like the RSA public key cryptography algorithm. This case can make ECC quite suitable for limited resources environment such as smart card, mobile equipment and so on。Realizing Elliptic Curve Cryptosystems is more complex than the other traditional like the RSA public key cryptography algorithm, but in computing speed and storage space it has a great advantage. Most Password scholars now believe that it will replace the RSA public key cryptography algorithm to become current.The depth study based on elliptic curve discrete logarithm problem of public key cryptography has a great practical significance。The major works of this paper are as follows:At first, research the Elliptic Curve Cryptosystems basic theoretical knowledge;The second, research the key protocol of decryption, key exchange, digital signatures and so on. These protocals are based on the existing discrete logarithm codes transplant program. After transplantating the cryptographic protocol requirements of the key length, it is short and fast.Finally, research in the elliptic curve encryption and digital signatures course the greatest impact on the efficiency of the Scalar Multiplication and apply a new modified algorithm. Passing by theoretical analysis and experimental experience the new algorithm imroves the speed and reduces the stored value space in advance.It is more applicable to the limited resources equipments.