Số nguyên tố an toàn trong các giao thức DH-KE
DOI:
https://doi.org/10.54654/isj.v1i11.97Keywords:
Safe prime generation algorithm, DH-KE protocolTóm tắt
Tóm tắt—Việc sinh các số nguyên tố “an toàn” p, mà ở đó tất cả các ước nguyên tố khác 2 của p-1 đều là ước nguyên tố lớn, là hết sức cần thiết để tránh các tấn công nhóm con nhỏ được chỉ ra bởi hai tác giả Chao Hoom Lim và Pil Joong Lee. Một thuật toán hiện có để sinh các số nguyên tố như vậy cũng đã được trình bày bởi hai tác giả này. Tuy nhiên, hạn chế của phương pháp đó là thuật toán không phải khi nào cũng trả về được một số nguyên tố an toàn. Một phần lý do cho vấn đề này là vì thuật toán không (và khó có thể) được phân tích và đánh giá kỹ lưỡng về mặt toán học. Do đó, mục đích chính của bài báo là đề xuất một thuật toán mới để sinh các số nguyên tố an toàn và kèm theo các đánh giá chi tiết về mặt toán học.
Abstract—The generate of “safe” primes p, where all prime divisors of p-1 are large prime divisors, is essential to avoid small subgroup attacks which are point out by two authors Chao Hoom Lim and Pil Joong Lee. An existing algorithm for generating such primes has also been presented by these two authors. However, the drawback of that method is that the algorithm does not always return safe prime numbers. Part of the reason for this is that the algorithm is not (and hardly) be thoroughly analyzed and evaluated mathematically. Therefore, the main purpose of this paper is to propose a new algorithm for generating safe prime numbers, including detailed mathematical evaluations.
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