Research And Implementation With Masking Scheme Against High-order DPA Attack On Quasi-Cyclic MDPC Code Encryption Algorithm

With the rapid development of quantum computer technology,it has already been confirmed that the cryptosystem based on number theory problem,such as large integer factorization and discrete logarithm,cannot resist the quantum computing attack.However,the public key cryptosystem based on error-correcting code will be able to resist the quantum computing attack,and its encryption and decryption are more efficient.Therefore,the public key cryptosystem based on error-correcting code has received an extensive attention again and becomes one of the research hotspots in the field of cryptography in recent years.However,the key space required for the cryptosystem based on Goppa code is too larger,which results that it is difficult to apply to the resource-limited device(such as smart card,RFID tags et al).At present,the public key cryptosystem based on Quasi-Cyclic Moderate Density Parity Check code(Quasi-Cyclic MDPC code)has been proposed by experts and scholars to reduce the key size.Although the public key cryptosystem based on Quasi-Cyclic MDPC code satisfies the storage requirements of key space in the resource-limited device,but its hardware implementation is vulnerable to power analysis attack.Therefore,it is of important theoretical significance and practical value to study and propose a masking scheme against power analysis attack for the public key cryptographic algorithm based on error-correcting code.According to the method that Ishai-Sahai-Wagne(ISW)security masking scheme masks a logical AND gate,this thesis designs and implements a masking scheme for the Niederreiter algorithm based on Quasi-Cyclic MDPC code by extending the method.Therefore,the proposed scheme protects Niederreiter algorithm from high order Differential Power Analysis(high order DPA)attack in hardware implementation.The main work of this thesis is as follows:First,a higher order masking scheme for computing multiplication over GF(2')is proposed.In order to solve the problem that the hardware implementation of multiplication over GF(2')exists sensitive data leakage,this scheme extends ISW masking scheme over GF(2)to over GF(2').And then the multiplication over GF(2')protected by the scheme can resist against Differential Power Analysis(DPA)attack.The result of security and integrity analysis shows the multiplication over GF(2')protected by the proposed higher order masking scheme is high order security.Secondly,according to the above-mentioned higher order masking scheme for computing multiplication over GF(2'),this thesis proposes a Quasi-Cyclic MCPC Niederreiter cryptographic scheme which is based on higher order masking.The design of the scheme is divided into two parts.(1)According to DPA attack model,the attack point of the Quasi-Cyclic MCPC Niederreiter algorithm is determined.Then we found the existed positions in the Quasi-Cyclic MCPC Niederreiter algorithm that is vulnerable to DPA attack by analyzing all intermediate variables which are generated in the hardware implementation of the algorithm.Meanwhile,in order to verify the correctness of the attack point analysis for Niederreiter algorithm,the power analysis simulation platform is established to simulate the process of DPA attack at the attack point position.(2)Based on this,for the attack point,that is the multiplication over GF(2')in the Quasi-Cyclic MCPC Niederreiter algorithm,the higher order making scheme for computing multiplication over GF(2')is applied to the cryptographic algorithm to resist against high order DPA attack.Finally,in order to verify the effectiveness of the Quasi-Cyclic MCPC Niederreiter cryptographic algorithm which is based on higher order masking on resisting against high order DPA attack,the power acquisition and power analysis platform is established by analyzing DPA attack model,and the comparative experiment is implemented.That is DPA attack model is performed in the Quasi-Cyclic MCPC Niederreiter algorithm with and without mask protection on this platform.The result of this experiment shows the Quasi-Cyclic MCPC Niederreiter cryptographic algorithm which is based on higher order masking can resist against high order DPA attack.Moreover,the scheme consumes less resources and is suitable for the devices with little memory and weak communication capacity.