As we know, heuristic algorithms are effective way to search substitution-box (S-box) which has high nonlinearity. Lots of nonlinearity calculations of S-box are needed in these process which make the speed of nonlinearity calculation quite important. So, what is the approximate minimun time to calculate the nonlinearity of an 8x8 S-box (On Intel Core i7 CPU for example)? And what is the key points in programming?
Please check those:
Article Construction of Cryptographically Strong 8x8 S-boxes
https://crypto.stackexchange.com/questions/19968/how-to-calculate-non-linearity-of-aes-s-boxArticle A highly nonlinear substitution-box (S-box) design using act...
Dear Peizhao Zhou,
I suggest you to see links on topic.
https://www.scribd.com/document/191388638/A-New-Criterion-for-the-Design-of-8x8-sboxes-in-private-key
https://www.temjournal.com/content/51/11/TemJournalFebruary2016_67_75.pdf
https://engineering.purdue.edu/kak/compsec/NewLectures/Lecture8.pdf
https://go.gale.com/ps/i.do?id=GALE%7CA609889686&sid=googleScholar&v=2.1&it=r&linkaccess=abs&issn=10762787&p=AONE&sw=w&userGroupName=anon%7E7c444f18
Article Construction of Cryptographically Strong 8x8 S-boxes
Best regards
Dear Peizhao Zhou
On heuristic algorithms, using Local Search approach is a fast way to search S-boxes with high Non-Linearity. Please check this research Article An External Parameter Independent Novel Cost Function for Ev...
About the NL calculation, the key point is to use the Walsh-Hadamard Transform (Table form https://en.wikipedia.org/wiki/Fast_Walsh%E2%80%93Hadamard_transform). So, please also check Chapter BSAT: A New Tool for Analyzing Cryptographic Strength of Boo...
For testing your calculations you can use this site https://www.ceibaco.nat.cu/
Best regards.
Dear Peizhao Zhou,
Also i suggest you to see links on subject.
Article A highly nonlinear S-box based on a fractional linear transformation
Article Optimization of the High Nonlinear S-Boxes Generation Method
Article A highly nonlinear substitution-box (S-box) design using act...
https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=9447687
Best regards