<p>As you pointed out, the identity is the point at infinity. It is also the only identity for addition over the elliptic curve.</p>
<p>But infinity is not a valid public key, for a number of reasons, and thus also not a valid input to combine.</p>

CC BY-SA 4.0
2022-10-29T12:42:55.813Z
2022-10-29T12:42:55.813Z
Pieter Wuille
<p>I am aware that the identity on elliptic curves is the infinity element.</p>
<p>Long shot (as it would be very useful to me): with that being said, does there exist a public key, <code>pk</code>, on secp256k1 such that, <code>combine(pk, x) = x for all x</code>?</p>
<p><code>combine</code> is via (<a href="https://github.com/bitcoin-core/secp256k1/blob/cd470333351bd6d90296352f2a957f38bbdaf014/src/secp256k1.c#L725" rel="nofollow noreferrer">https://github.com/bitcoin-core/secp256k1/blob/cd470333351bd6d90296352f2a957f38bbdaf014/src/secp256k1.c#L725</a>)</p>

<secp256k1><math>
Secp256k1: Does there exist an identity public key for combinations of public keys?
jet
# Secp256k1: Does there exist an identity public key for combinations of public keys?

(Asked by: username_0 on 2022-10-29)

I am aware that the identity on elliptic curves is the infinity element.

Long shot (as it would be very useful to me): with that being said, does there exist a public key, `pk`, on secp256k1 such that, `combine(pk, x) = x for all x`?

`combine` is via (<https://github.com/bitcoin-core/secp256k1/blob/cd470333351bd6d90296352f2a957f38bbdaf014/src/secp256k1.c#L725>)

**Tags:** secp256k1, math


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## 1 answers

### Answer by username_1 on 2022-10-29. Score: 2 | Accepted answer

As you pointed out, the identity is the point at infinity. It is also the only identity for addition over the elliptic curve.

But infinity is not a valid public key, for a number of reasons, and thus also not a valid input to combine.


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