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interesting solution, but it won’t work if only public keys are known, let's say there is a public key theoretically with private key 1, how to divide the public key by 10 to get public key with 0.1 without knowing the private keys?
i think that not all points have private key, maybe i am wrong
For example simple 7/5 it is (3ef1f322847965ee7f8d745af562e6507568fea5316b199f7349a2717021661d,b9a20bc3783777d2681f64d92740817f95b2c169c5db92ce0bab00efb36c0d74)
i don`t know if this result have private key.. (n+7)/5 give the same result as for ex. (n+3)/5 = 0x33333333333333333333333333333332f222f8faefdb533f265d461c29a47374
but 0x33333333333333333333333333333332f222f8faefdb533f265d461c29a47374 for (n+3)/5 is correct.
becouse if 1 have the same x-coordinate as n-1 so there only 2^255 points with unique x-coordinate. So there can be around 2^255 points that not have private key.(maybe
)
Mathematical working according to the rules of mathematics of public keys (addition, subtraction, division, multiplication), you will always get the coordinates (public key) at the output, which will have the corresponding private key.
Another thing is that one public key can have several private keys. But this collision has not yet been proven.
??