Research Of ECC Scalar Multiplication Algorithm In Side-channel Attack Resistance

With the rapid development of the mobile internet and the e-commerce, information security is a cause for concern. The cryptographic technique is the important method and means to ensure the information security. Compared with RSA and other traditional public cryptosystems, the elliptic curve cryptography(ECC) has advantages of high safety level, low computation, small storage space and low bandwidth demand,etc, which makes it especially suitable for environments where processing power, storage, bandwidth, or power consumption are constrained,so it attracts wide attention. But in recent years,a new and emerging type of cryptanalysis which is known as the side channel attack(SCA),put a great threat to ECC.Scalar multiplication is the most important and computationally costliest operation in ECC, and its security and efficiency will affect the whole safety and implementation efficiency of ECC. Although the existing ECC scalar multiplications have better safety and computational efficiency, they are still difficult to meet the needs of many specific occasions, so improving the safety and computational efficiency of scalar multiplication becomes necessary.To raise the safety and efficiency of ECC, two SCA resistant ECC scalar multiplication algorithms were presented based on original SCA and scalar multiplication algorithms. One was the safe and efficient scalar multiplication based on the binary algorithm, it used the fast computational speed characteristic of the window method,and made the point addition and doubling operation undistinguishable on the premise of not inserting the pseudo operation,meanwhile recoded the scalar to prevent the leakage of the key related information,theoretical analysis proved that not only could the new algorithm resist to SCA,but also reduced the storage requirement of the window method; the other was the safe and efficient multiplication algorithm based on the multi-base number representation, Firstly,revised the 7P fast algorithm on the affine coordinates, Secondly,random number and the masking technology of base point were introduced to hide the related side channel information of the algorithm so as to enhance its security, Finally,fast point halving and the multi-base representation of scalar were combined to improve the algorithm’s efficiency, Under the experimental environment of VC++6.0 and MATLAB 2010 b, the efficiency of the algorithm was tested,results of the experiment demonstrated that the new algorithm improved the efficiency of the previous multi-base scalar multiplication algorithms. Hence,the two kinds of algorithms both could be applied to the domains of smart cards and other limited storage resources,which made ECC more secure and efficient to the encryption and decryption of sensitive data.