Efficient and Secure Elliptic Curve Scalar Multiplication
Currently, various online services are now provided by the network Various leaks on the information flow. Internet Society concerns new problems such as information wiretapping, spoofing the and importance of encryption technology to solve these problems is growing. Encryption technology has consist of common key cryptosystem and public key cryptosyte. In case of common key cryptosystem, encryption and decryption using the same key. Therefore Thre users have to exchange safety Key among those who send and receive and also keep different keys per each another user. It is difficult for users to manage keeping key when users communicate by encryption many another. In case of the public key system, encryption keys is different from decryption one. Using public key encryption key, there are no information wiretapping problems because of the users publish their own decryption key. Public key cryptography, Diffie and Hellman suggested by the concept, and the subsequent Ron Rivest, realized as RSA cryptosystemsby Adi Shamir and Len Adleman.
Elliptic curve cryptosystems proposed by Millar is publici key cryptography that the basis of safety is on elliptic curve discrete logarithm problem. RSA encryption compared to traditional, high short key length can be retained for the safety of the Smart card like devices with limited memory is to be applied. Elliptic curve encryption and smart card implementation is the secret key resistance of the device in Tampa retention Be. Information without destroying the card is to remove the key from being impossible. This side-channel attacks as a threat. Side-channel attacks are in the process of encryption And the power consumption, called side-channel information and information, especially information using a secret key power consumption for In the attack. Power consumption side-channel attack is simple to use power analysis attacks (SPA), differential power Attack classification analysis (DPA). SPA is a scalar times of power consumption curve calculated by the analysis, Smart cards seek private key in the attack. DPA is the secret key assumptions and simulation Solutions and power consumption by taking the difference between the call for a secret attack. Today cause errors and memory devices for various methods have been reported. Boneh In 1997 they were the new Side Chanel Attack: Fault Attack reported. This is a device in To restore the secret key for the RSA encryption errors in calculation methods. Biel said this Elliptic curve on the calculation applied scalar times. Elliptic curve cryptosystems code can keep safety at short key length in comparison with former RSA code. Because of that it is mounted on the device where the memory like the smart card is restricted. As the new threat where today, it confronts safety, It causes error in memory of these cryptographic devices, the method of revealing the secret key (Faults attack) it is reported. A Faults attack on elliptic curve cryptosystems presented so far changes the parameter of the elliptic curve which is mounted on the device, By the fact that cryptographic processing is executed with respect to the elliptic curve which has vulnerability, the secret key is revealed. In Sign Change Faults attack, The key is revealed by comparing the correct calculation result and a faulty result which with reverses the mark of the middle point of scalar multiplication calculation. In Sign Change Faults attack, It does not change the elliptic curve which is mounted on the device, The method of checking the system parameter which is measure technique of former Faults attack is not effective. As a countermeasure technique of Sing Change Faults attack, the method of using two elliptic curve, randomization linear-transformation coordinate.
In this paper, we proposed new measure technique whose Sign Change Faults attack. In comparison with former measure technique respectively, it succeeded in the reduction of computational complexity with this method.