A Note on Fixed Points of a RSA System
Yu Xiu · Chinese Journal of Computers · 2001
Let n=p 1…p k, where p′ is are different primes, e be a positive integer satisfying (e,φ(n))=1, and φ(n)=(p 1-1)…(p k-1). By RSA(n,e) denote the RSA-ciphering system with n and e as its public keys. Using Sun Zi's theorem, a method to calculate the fixed point P′s of RSA(n,e), that (P,n)=1, is given. Let T(n,e,α) be the number of α-order fixed points P′s of RSA(n,e), that (P,n)=1, and S(n,e,K)=∏Kα=1T(n,e,α)1K, thenlog S(n,e,K)=ω(n)log2+1K∑p|n∑q|p-1∑rm|qlog rK(ind ge, r m-1(r-1))r m-1(r-1).where r is prime, g is a primitive root of mod rm, and [x] denote the integer part of x.