The Study On Cryptographic Function Against DPA Attack

Recently,the Differential Power Analysis(DPA)attack have received a lot of attention in the field of cryptography,since the DPA attack is very powerful and efficient.To find approaches to defend DPA attacks,constructing and generating cryptographic functions that are inherently resistant against DPA attacks is a very important and interesting research topic.Up till now,the notion of the transparency order including transparency order(TO)and modified transparency order(MTO)has received considerable attention and is one of the best metrics to measure the resistance of cryptographic functions against DPA attacks.In 2019,Li et al.revisited the notion of TO and MTO.They spotted a flaw that is overlooked and provided a revised definition(Revised transparency order,RTO).Therefore,we mainly contribute the findings as the flowing shows:Firstly,to find balanced Boolean functions with high nonlinearity and good DPA resistance,an efficient algorithm based on the Gradient Descent algorithm is proposed.As a result,we obtain some 5?11-variable Boolean functions with better transparency order(we are the first to contribute the results on transparency order of 9,10,11-variable highly nonlinear balanced Boolean functions):1.For 8-variable Boolean functions,we give the improved results compared with those given by Ashish Jain and Narendra S.Chaudhari and Stjepan Picek et al.Besides,these obtained Boolean functions have improved algebraic degree and absolute indicator.2.For 9?11-variable Boolean Functions,some results with good cryptographic properties have obtained.In particular,Wang and St(?)nic(?) constructed a 9-variable balanced Boolean function with nonlinearity 240 and transparency order 0.9745 in Designs,Codes and Cryptography.They proposed a challenging question: how to find9-variable balanced functions with nonlinearity 240 and lower transparency order using search algorithms? As our work,we contribute some 9-variable balanced Boolean functions with nonlinearity 240 and transparency order 0.9617 using our search algorithms,which solves the question proposed by Wang and St(?)nic(?).Further,we obtain balanced functions with nonlinearity 240 and transparency order 0.9645,1-order propagation and 1-order resilient.3.Also,we make a brute-force exhaustive experiment on 5?7-variable Boolean functions,which shows that the functions obtained in this work are global optimal in rotation symmetric Boolean functions class,that is the obtained results possess the highest nonlinearity and lowest transparency order at the same time.Secondly,an efficient and easy-to-implement search strategy to construct and generate balanced S-boxes with high nonlinearity,low differential uniformity and better DPA-resistance is proposed(we are the first contribute some results with good RTO values based on a heuristic search algorithm).Using developed algorithm,some S-boxes and S-boxes with very high nonlinearity,low differential uniformity,lower signal-to-noise ratio and much better DPA-resistance are captured.1.For 6-bit output S-boxes,in 2021 IEEE Transactions on Information Forensics and Security,Carlet et al.proposed S-box having the best TO 5.714 with nonlinearity24,differential uniformity 4 and RTO 5.4603.Further,Evic and Kavut had confirmed the TO 5.714 is optimal in rotation symmetric class.The results we obtained have improved TO,RTO and absolute indicator.2.For 8-bit output S-boxes,to the best of our knowledge,we are the first to take the revised transparency order proposed by Li et al.into the account and contribute some cryptographically interesting results on S-boxes with a level of 112 and differential uniformity 4.The results proposed possess the best nonlinearity 112,the best algebraic degree 7,and the best absolute indicator 32.Among these results,the optimal MTO value is 6.8822,and the optimal RTO value is 7.5022.For comparison,the S-box used in the AES Rijndael algorithm has MTO 6.9161,RTO 7.5402 and SNR9.6000,which shows that the S-boxes generated in this paper has much better DPA resistantivity.3.Some cryptographically strong S-boxes with a nonlinearity level of 102?110and very nice RTO values are captured.In particular,some cryptographically interesting results contributed by Mazumdar and Mukhopadhyay in IEEE Transactions on Computers 2019 and Georgi et al.in Cryptography and Communications Discrete Structures 2016.As a comparison,our proposed S-boxes possess improved cryptographically important properties,such as absolute indicator,differential uniformity,MTO,and RTO.