RSA fixed points


An RSA cryptosystem has at least nine fixed points: numbers M such
that M^e mod n == M. Of course, 0, 1, and n-1 are fixed points. The
others should be kept secret, they say: if you know all of them, you
can factor n. What if you know only one non-trivial fixed point?

Let's say n=34218 8568105535 9528256603 0192918127 8953688137
8512790785 3018868346 8393435582 7161134410 8451194470
1958932539 1996386382 3514735146 0678619426 4890846769
and e=5; so 22886 0631108311 1719157164 9934177112 3347070183
0850799264 0438508169 2244820242 1483007861 2306917436
1618283935 4170516961 3070891230 4148270705 6047605625
is a fixed point. Can you factor n?

--
Don Reble djr@xxxxx

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