An RSA Scheme based on Improved AKS Primality Testing Algorithm
نویسندگان
چکیده
منابع مشابه
Deterministic Primality Testing - understanding the AKS algorithm
Prime numbers play a very vital role in modern cryptography and especially the difficulties involved in factoring numbers composed of product of two large prime numbers have been put to use in many modern cryptographic designs. Thus, the problem of distinguishing prime numbers from the rest is vital and therefore there is a need to have efficient primality testing algorithms. Although there had...
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The AKS (Agrawal-Kayal-Saxena) algorithm is the first ever deterministic polynomialtime primality-proving algorithm whose asymptotic run time complexity is O(log n), where > 0. Despite this theoretical breakthrough, the algorithm serves no practical use in conventional cryptologic applications, as the existing probabilistic primality tests like ECPP in conjunction with conditional usage of sub-...
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We remark that AKS primality testing algorithm needs about 1,000,000,000 G (gigabyte) storage space for a number of 1024 bits. Such storage requirement is hard to meet in practice. To the best of our knowledge, it is impossible for current operating systems to write and read data in so huge storage space. Thus, the running time for AKS algorithm should not be simply estimated as usual in terms ...
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Input: An integer n > 1. 0: if n is a power then output composite fi; 1: r := 2; 2: while (r < n) do 3: if gcd(r, n) 6= 1 then output composite fi; 4: if r is prime then 5: q := largest prime factor of r − 1; 6: if (q ≥ 4√r log n) and (n(r−1)/q 6≡ 1 mod r) then break fi; 7: fi; 8: r := r + 1; 9: od; 10: for a = 1 to 2 √ r log n do 11: if (x− a)n 6≡ (xn − a) mod (xr − 1, n) then output composite...
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We remark that the AKS primality testing algorithm [Annals of Mathematics 160 (2), 2004] needs about 1,000,000,000 G (gigabyte) storage space for a number of 1024 bits. The requirement is very hard to meet. The complexity class P which contains all decision problems that can be solved by a deterministic Turing machine using a polynomial amount of computation time, is generally believed to be “e...
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ژورنال
عنوان ژورنال: MATEC Web of Conferences
سال: 2016
ISSN: 2261-236X
DOI: 10.1051/matecconf/20164401032