A Research About The Decomposition Of Large Numbers

Diffie and Hellman[1]put forwarded the idea about public-key cryptography in 1976,it was fully set up in the difficult of decomposition of large numbers,which gave a broader space for developing password study;At the same time,it is also a new challenge for analysts of password.Today,there is still no any effective program which can solve the problem of break downing large numbers.However,the good news is that,for a given large numbers n,we can use a variety of ways to try to decompose it,there is a large of literature about factorization algorithms,including now the best factorization algorithms and their informal discussions use in practice. For a lump sum n,we have three more effective algorithm:the second screening, elliptic curve and domain selection method,as well as some well-known algorithms, including Pollard's rho-method and p-1,William's p+1,even fraction algorithm,as well as test division and so on.However,so far,there is no any kind of algorithm can completely resolve the problem of breaking down large numbers.Several algorithms mentioned earlier are only attempt to carry out large numbers of decomposition under the condition of a specific,it can not be successful in many cases.Designer of the password is concerned,as long as the algorithm can avoid the assumption that in front of several conditions,in theory,the password he designed is safe.However,with development of the large-scale and expansion of computer networks,quantum computers,DNA computers,wave-particle two machine continues to develop,improve computing speed at the rapid,the decimal number 100 seems to be not difficult to be decomposed,the "security" we assumed is facing a severe test. the literature[2]is on the progress of quantum computers and future development trends in detail,the literature[3]introduced the improved p-1 by use of DNA computer.In addition,the algorithm has been improved,the literature[4]improved the efficiency of test computing division according to the distribution of prime numbers,it is more effective to decomposit the integer of 32-bit decimal integer; literature[5]by the original decomposition algorithm improvement,the original factorization problem of large numbers n times from one meeting to achieve a reduction of quality factorization of large numbers of computational complexity.This requires us to constantly update the password system,to design a better password system performance and to service our practical application.The author's main research results is:1.Through existing factorization algorithm analysis,summary,comparison, proposed a new factorization algorithm and its application of the practical value and gave a profound analysis of the conditions. 2.Give the decomposition of large numbers both with similar problems,the difficulty of the solution and the decomposition of large numbers equivalent to the difficulty of questions.3.Give a signature program,which is not based on decomposition of large numbers of difficult questions,but difficult questions and break down the equivalent of large numbers.4.Give the factorization of a new research method.5.Set up the decomposition of large numbers and a small number of contact between the circle and to get a new factorization algorithm.