# y 좌표가 짝수인 공개 키가 n/2보다 작은 개인 키에 해당하고 그 반대의 경우도 마찬가지입니까? (Secp256k1) Related eBooks

The question is somewhat complex and directed to clearing thing out.

Suppose that `n` is the order of the cyclic group. It `n - 1` is the number of all private keys possible

``````n = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
``````

We also know that every private and public key has its modular inverse.
To get a modular inverse of a private key, we need to subtract the private key from `n`.

`n - privKey`

To get a modular inverse of a public key, we’ll have to multiply its `y` coordinate by `-1` and modulo by the `p` – order of the finite field.

``````x,y = x, -y % p
``````

A modular inversed public key has the same `x` coordinate as original public key, but different `y` coordinate, and the `y` coordinate is always different in its polarity.
If the original `y` was odd, in a modular inversed key it will be even, and vice versa.

If a compressed public key has `"02"` index at the biggining then it has even `y`. If it is `"03"` then it is odd.

The question is, if the `y` coordinate of a public key is even, does it mean that the corresponding private key is less than `n/2` by its value? If the `y` is odd, the private key is more than `n/2` ?

Is there any relationship between the eveness/oddness of the `y` (or `x`) coordinate and the value of the corresponding private key?

Is there any way to know that the private key is more or less than `n/2` while not knowing the private key itself?

Is there a way to find out the public key of an address that never sent Bitcoin but only received it?

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