| Summary: | 碩士 === 東海大學 === 資訊工程與科學系碩士在職專班 === 92 === There are many businesses using RSA algorithm to protect important messages such as e-commerce, financial institution and many others. This paper discussed the singular points in RSA. B.Blakley, G.R.Blakley and I.Borosh had shown that the number message of plaintext cannot be concealed in RSA to at least 9 cases. The number message X is a singular point if X^PK (mod N) ≡X. Based on my experiment there are at least 9 singular points in RSA system for smaller numbers of p,q , PK and very big prime numbers. One interesting result I discovered is that the cipher text of RSA can be exist only as pairs. Hence, there are merely (N/2) availability cipher spaces of RSA. From our research, We can conclude the followings (1) X is a singular point, if X^3 (mod N)≡X. (2) If X is a singular point, either X-1 or X+1 is also a singular point. (3)There are two singular points satisfying X^2(mod N)≡ X^3(mod N)≡X^4(mod N)≡……………… ≡X ^PK(mod N)≡X. (4) We can find the other singular points from (X^2(mod N), X^3(mod N) , X^4(mod N),…………,X^PK (mod N) ), if X is singular point.
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