Large number factorization method and system
A technology of factorization and factoring, which is applied in the field of large number factorization methods and systems, can solve problems such as high cost and time-consuming calculations, and achieve fast, efficient solutions and high efficiency
Pending Publication Date: 2022-04-29
SHENZHEN Y& D ELECTRONICS CO LTD
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[0004] The technical problem to be solved by the present invention is to construct a large number factorization method and system for the above-mentioned defects of the prior art, by converting the large number factorization task that is extremely complex in calculation, costly and time-consuming, into a high-efficiency, high-speed Fast table lookup tasks can provide a new and efficient solution for large number factorization
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[0049] In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.
[0050] After analyzing the nature of large composite numbers that are easy to construct but difficult to decompose, the present invention gets rid of the fixed thinking of traditional decomposition algorithms, adopts a retrograde thinking method, and first constructs a list of large composite numbers by multiplying the smallest prime number in pairs. The row and column values of the list correspond to the prime numbers formed, and the content in the table is the composite value corresponding to the product of the prime numbers. Since the number of prime numbers is infinite, this table is in a sta...
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The invention relates to a large number factorization method and system. The method comprises the following steps: continuously creating a large composite number table, wherein the large composite number table comprises a first prime number factor, a second prime number factor and a product of the first prime number factor and the second prime number factor; and searching a to-be-decomposed composite number in the product of the large composite number table, and taking the first prime number factor and the second prime number factor corresponding to the product as a decomposition result of the to-be-decomposed composite number. According to the method, the large number factorization task which is extremely complex in calculation and high in cost and time consumption is converted into the table look-up task which is high in efficiency and speed, and a brand-new efficient solution can be provided for large number factorization.
Description
technical field [0001] The present invention relates to the field of large number calculation, more specifically, relates to a large number factorization method and system. Background technique [0002] RSA is currently the most important public key algorithm, which is widely used in various fields. The principle of RSA is that, according to number theory, it is relatively simple to find two large prime numbers, but it is extremely difficult to factorize their product, so the product can be made public as an encryption key. Therefore, the security of RSA depends on the difficulty of decomposing large numbers. In the past ten years, in order to ensure security, the binary length of the RSA key has increased from 512 bits to the current 1024, and the high level of security requires the use of 2048 bits. [0003] So far, the factorization problem of large numbers has not been proved to be solvable in polynomial time, nor has it been proved that RSA deciphering is as difficult...
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IPC IPC(8): G06F7/72
CPCG06F7/72
Inventor 戚建淮成飏何润民孙丁郑伟范唐娟刘建辉崔宸
Owner SHENZHEN Y& D ELECTRONICS CO LTD