<blockquote>
<p><strong>I need to solidify the meanings of a few symbols.</strong></p>
</blockquote>
<p>Well, so long as we regard solidification as a process. One in which even a small further step along the way is helpful ...</p>
<blockquote>
<p>Q, k I don’t know what these represent.</p>
</blockquote>
<p>Your link says <em>&quot;to find the public key Q corresponding to a private key k, ...|&quot;</em></p>
<p>I guess you know about public-key cryptography and that keys are just integers. Usually large ones. Ones that have a useful relationship.</p>
<blockquote>
<p>P: upper case, I don’t know</p>
</blockquote>
<p>Your link says <em>&quot;P = 2<sup>256</sup> - 2<sup>32</sup> - 2<sup>9</sup> - 2<sup>8</sup> - 2<sup>7</sup> - 2<sup>6</sup> - 2<sup>4</sup> - 1.&quot;</em> so P is a constant.</p>
<blockquote>
<p>Looks like G is our originating point on the ecliptic curve. Is this correct.</p>
</blockquote>
<p>Your link says <em>&quot;starting with its base point G&quot;</em>. I believe this starting point is called the generator, hence &quot;G&quot;</p>
<hr />
<p>Related questions</p>
<ul>
<li><a href="https://bitcoin.stackexchange.com/q/29904/13866">What exactly is generator G in Bitcoin&#39;s elliptical curve algorithm?</a></li>
<li><a href="https://bitcoin.stackexchange.com/q/113116/13866">How is the generator point G chosen in the secp256k1 curve used in Bitcoin?</a></li>
</ul>
<p>Some external web pages that might potentially be useful?</p>
<ul>
<li><a href="https://blog.cloudflare.com/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/" rel="nofollow noreferrer">https://blog.cloudflare.com/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/</a></li>
</ul>

CC BY-SA 4.0
2024-11-11T01:15:44.993Z
P is a carefully selected constant.  It is a bit below the max value for a 256 bit number.  When calculating Q, the public key, and when the calculated numbers get too bit, we divide by <something, maybe P itself?> and the remainder becomes the number with which we continue the calculations.

If I save my private key, and have to move to a new wallet, and can provide the new wallet with nothing but that private key, will that private key give me access to everything that has been put in its Q, the public key?
Thank you very much for your time and patience with me.
Bryan Kelly
CC BY-SA 4.0
2024-11-11T01:23:29.710Z
Is there a way to put line breaks, carriage returns, in a comment for readability?
Bryan Kelly
CC BY-SA 4.0
2024-11-11T09:36:11.767Z
Comments have limited formatting. They are intended to be disposable. They are intended mainly to suggest improvements to a question oranswer. Or to seek clarification. You may prefer to edit your question.
RedGrittyBrick
CC BY-SA 4.0
2024-11-11T09:38:11.723Z
And yes, private keys suffice. Along with any relevant derivation paths for child keys if BIP-32 has been used to derive them.
RedGrittyBrick
CC BY-SA 4.0
2024-11-11T17:13:39.013Z
Cool.  Both of your comments help and are appreciated. Thank you.
Bryan Kelly
CC BY-SA 4.0
2024-11-10T22:09:50.087Z
2024-11-10T22:35:27.537Z
2024-11-10T22:35:27.537Z
RedGrittyBrick
<p>(Note, please see EDIT below.)
I title this with “arithmetic” because “mathematics” is an abstraction for arithmetic and a mathematical function can be broken down into arithmetic.  I need the arithmetic.</p>
<p>The top level question / goal:  I am trying to understand the arithmetic in how a private key is translated into a public key.  Presume my wallet has generated a private key for me.  What are the steps the wallet (and/or the bitcoin nodes) use to create the public key that it uses to deposit coins into?</p>
<p>I have found and read multiple articles, but am not recognizing the steps.  But before going there, I need to solidify the meanings of a few symbols.  Start with this post found from a search:  <a href="https://bitcoin.stackexchange.com/questions/102940/what-is-the-math-behind-bitcoins-elliptic-curve">What is the math behind Bitcoin&#39;s elliptic curve?</a></p>
<p>Q, k        I don’t know what these represent.</p>
<p>G   from another post I find this:  “The generator point G, or a ECDSA public key, is a pair of coordinates x and y, for which the above equation holds.”   I presume this mean some specific point on the curve, which is composed of the x and y value.  Is this correct?  What is intended by “generator point?”</p>
<p>n   is a variable, often meaning repeat some operation this many times.</p>
<p>From other places I find these items along with what I suspect they mean.  Please correct me where I am wrong.</p>
<p>X:    upper case, the private key</p>
<p>x,y:    lower case  a point on the curve,</p>
<p>p:    lower case, the largest prime smaller than 2^^256</p>
<p>P:    upper case, I don’t know</p>
<p>Thank you for your time and patience.</p>
<p>Edit: found this site:  <a href="https://bitcoin.stackexchange.com/questions/25024/how-do-you-get-a-bitcoin-public-key-from-a-private-key#29880">How do you get a Bitcoin Public Key from a Private Key</a></p>
<p>It looks pretty good.  Looks like G is our originating point on the ecliptic curve.  Is this correct.</p>
<p>If is save my private key, on a thumb drive or somewhere else, and my cold storage wallet (is that a correct name?) completely fails, and I put my private key into a new wallet, will it be able to access all the coin I put into the account used by my failed wallet?</p>

CC BY-SA 4.0
2024-11-10T21:56:15.427Z
Welcome to bitcoin.stackexchange.com. Your final paragraph asks a completely separate second question. This site is designed to answer one question at a time. This is so future people with the same question can find existing answers without being put off by title and preamble that seem unrelated. Please consider editing your question and moving the final paragraph to a separate new question. One of the closure reasons offered here is "needs more focus", readers often click that.
RedGrittyBrick
<bitcoin-core>
Bitcoin arithmetic, symbol definitions, from private key to public address
Bryan Kelly
# Bitcoin arithmetic, symbol definitions, from private key to public address

(Asked by: username_0 on 2024-11-10)

(Note, please see EDIT below.)
I title this with “arithmetic” because “mathematics” is an abstraction for arithmetic and a mathematical function can be broken down into arithmetic. I need the arithmetic.

The top level question / goal: I am trying to understand the arithmetic in how a private key is translated into a public key. Presume my wallet has generated a private key for me. What are the steps the wallet (and/or the bitcoin nodes) use to create the public key that it uses to deposit coins into?

I have found and read multiple articles, but am not recognizing the steps. But before going there, I need to solidify the meanings of a few symbols. Start with this post found from a search: [What is the math behind Bitcoin's elliptic curve?](https://bitcoin.stackexchange.com/questions/102940/what-is-the-math-behind-bitcoins-elliptic-curve)

Q, k I don’t know what these represent.

G from another post I find this: “The generator point G, or a ECDSA public key, is a pair of coordinates x and y, for which the above equation holds.” I presume this mean some specific point on the curve, which is composed of the x and y value. Is this correct? What is intended by “generator point?”

n is a variable, often meaning repeat some operation this many times.

From other places I find these items along with what I suspect they mean. Please correct me where I am wrong.

X: upper case, the private key

x,y: lower case a point on the curve,

p: lower case, the largest prime smaller than 2^^256

P: upper case, I don’t know

Thank you for your time and patience.

Edit: found this site: [How do you get a Bitcoin Public Key from a Private Key](https://bitcoin.stackexchange.com/questions/25024/how-do-you-get-a-bitcoin-public-key-from-a-private-key#29880)

It looks pretty good. Looks like G is our originating point on the ecliptic curve. Is this correct.

If is save my private key, on a thumb drive or somewhere else, and my cold storage wallet (is that a correct name?) completely fails, and I put my private key into a new wallet, will it be able to access all the coin I put into the account used by my failed wallet?

**Tags:** bitcoin-core

> **Comments:**
> **username_1**: Welcome to bitcoin.stackexchange.com. Your final paragraph asks a completely separate second question. This site is designed to answer one question at a time. This is so future people with the same question can find existing answers without being put off by title and preamble that seem unrelated. Please consider editing your question and moving the final paragraph to a separate new question. One of the closure reasons offered here is "needs more focus", readers often click that.  

---

## 1 answers

### Answer by username_1 on 2024-11-10. Score: 0

> **I need to solidify the meanings of a few symbols.**

Well, so long as we regard solidification as a process. One in which even a small further step along the way is helpful ...

> Q, k I don’t know what these represent.

Your link says *"to find the public key Q corresponding to a private key k, ...|"*

I guess you know about public-key cryptography and that keys are just integers. Usually large ones. Ones that have a useful relationship.

> P: upper case, I don’t know

Your link says *"P = 2256 - 232 - 29 - 28 - 27 - 26 - 24 - 1."* so P is a constant.

> Looks like G is our originating point on the ecliptic curve. Is this correct.

Your link says *"starting with its base point G"*. I believe this starting point is called the generator, hence "G"

---

Related questions

* [What exactly is generator G in Bitcoin's elliptical curve algorithm?](https://bitcoin.stackexchange.com/q/29904/13866)
* [How is the generator point G chosen in the secp256k1 curve used in Bitcoin?](https://bitcoin.stackexchange.com/q/113116/13866)

Some external web pages that might potentially be useful?

* <https://blog.cloudflare.com/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/>

> **Comments:**
> **username_0**: P is a carefully selected constant.  It is a bit below the max value for a 256 bit number.  When calculating Q, the public key, and when the calculated numbers get too bit, we divide by <something, maybe P itself?> and the remainder becomes the number with which we continue the calculations.  If I save my private key, and have to move to a new wallet, and can provide the new wallet with nothing but that private key, will that private key give me access to everything that has been put in its Q, the public key? Thank you very much for your time and patience with me.  
> **username_0**: Is there a way to put line breaks, carriage returns, in a comment for readability?  
> **username_1**: Comments have limited formatting. They are intended to be disposable. They are intended mainly to suggest improvements to a question oranswer. Or to seek clarification. You may prefer to edit your question.  
> **username_1**: And yes, private keys suffice. Along with any relevant derivation paths for child keys if BIP-32 has been used to derive them.  
> **username_0**: Cool.  Both of your comments help and are appreciated. Thank you.  

---

