Các ma trận MDS truy hồi hiệu quả cho thực thi từ mã Reed-Solomon và phép lũy thừa trực tiếp
DOI:
https://doi.org/10.54654/isj.v1i16.235Keywords:
MDS matrix, recursive MDS matrices, RS codesTóm tắt
Tóm tắt— Hiện nay, có nhiều mã khối sử dụng các ma trận của mã tách khoảng cách cực đại (MDS) như một phần quan trọng trong tầng khuếch tán của chúng. Tuy nhiên, các ma trận MDS luôn có một mô tả lớn, gây ra các thực thi phần cứng/phần mềm tốn chi phí. Các ma trận MDS truy hồi cho phép giải quyết bài toán này vì chúng có thể là lũy thừa của một ma trận Companion đơn giản, do đó chúng có thể phù hợp cho cả các môi trường bị ràng buộc, hạn chế. Trong bài báo này, phương pháp xây dựng các ma trận MDS truy hồi hiệu quả cho thực thi từ mã Reed-Solomon sẽ được trình bày. Sau đó, khả năng tạo ra các ma trận MDS truy hồi hiệu quả cho thực thi từ một ma trận MDS truy hồi hiệu quả ban đầu, nhờ phép biến đổi lũy thừa trực tiếp sẽ được chỉ ra. Các ma trận MDS truy hồi hiệu quả cho thực thi sẽ có ý nghĩa trong thực thi phần cứng. Chúng có thể được sử dụng cho tầng khuếch tán của nhiều mã khối và hàm băm, đặc biệt là các mã khối và hàm băm hạng nhẹ nhằm tiết kiệm tài nguyên và chi phí thực thi.
Abstract— Nowaday, many block ciphers have used MDS matrices for their diffusion layer. However, the MDS matrices are always the components that cause large implementation cost for ciphers. Recursive MDS matrices will help to deal with this problem because they can be the power of a simple Companion matrix that is very sparse. In this paper, the ability to generate different efficient recursive MDS matrices for implementation from an original efficient recursive MDS matrix by direct exponential transformation is shown. These recursives MDS matrices are meaningful in hardware implementation. These matrices can be used in the diffusion layer of some block ciphers and hash functions ciphers and hash functions especially lightweight block ciphers and hash functions to save resources and implementation cost.
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