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Questions tagged [secp256k1]

This tag should be used for anything related to the secp256k1 algorithm used for Bitcoin's public key cryptography.

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1answer
102 views

Problem with point addition about [n-1]+[2]G and [n-1]+G on on Secp256k1

I apologize in advance for my question. I am trying to make my own simple Secp256k1 calculator, just addition and subtraction, and one thing keeps confusing me. When I add 2 points, and I know what ...
1
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1answer
27 views

Verify that x, y coordinates given as hex string are valid points on an Elliptic Curve [duplicate]

Given the following information: "curve": "P-256", "qx": "729C51D177EBE2079A0FB7B0B3C2145159CF81EC61960E642A1744719AA9F913", "qy": "...
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0answers
13 views

h(e) -> hash message diggest when inputs is more than one - secp256k crypto

Please help Dear all How to perform calculation "Z" as message hash diggest h(e) for input 1 and input 2 - when we have more than one input in transaction? here is transaction with 2 inputs ...
0
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1answer
59 views

Fully understanding bitcoin transcation verifying and secp256k1

Hello fellow cryptographers. I have spent last few days trying to understand and find a way to generate secp256k1 private and public keys from scratch, but i failed. I have seen tons of videos and ...
4
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3answers
669 views

secp256k1: is it theoretically possible to generate same signature with different key, message hash and k?

For a given private key $d$, random $k$ and message hash $h$ is it possible that there exists a different set of $d$, $k$ and $h$ which produces the same signature using $\text{secp256k1}$ curve?
0
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1answer
59 views

substract points on secp256k - result as moved to N-1

I must perform calculate of substract two points: Let $G$ be the generator point and; $P_1 =[1]G = (x_1,y_1)$ $P_2 = [2]G = (x_2,y_2)$, When I will subtract $P_1 - P_2$ -> I will move Point to N-1 ...
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0answers
42 views

Security of SecretKey addition and PublicKey multiplication in secp256k1

I understand that: $[a+b]G = [a]G + [b]G$ where $a$ and $b$ are secret keys. (See: Is there a relationship between the secp256k1 public key of the sum of two private keys, and the public keys of ...
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0answers
155 views

Bitcoin Key Recovery Without Nonce Re-Use

There are a lot of questions in these forums regarding the recovery of private keys. But I'm here to postulate on something unique to a specific piece of research that I looked into recently. The ...
4
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0answers
143 views

secp256k1 scalar decomposing and prime field arithmetic

I'm currently studying the elliptic curve secp256k1 implementation. In my understanding, it has efficiently computable endomorphisms: We can find out a pair of number $\lambda$ and $\beta$ from the ...
0
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1answer
57 views

Deterministic Key using a seed for ECNamedCurve

I am trying to generate deterministic keys using EC curve secp521r1 in java. I went through KDF but, couldn't find any references to use it with EC curves. I would appreciate if someone could point me ...
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3answers
197 views

secp256k1 prime modulus vs order

For curve secp256k1 prime modulus is $2^{256}-2^{32}-977$ and order is smaller number but has near half of starting bits set. If I draw number to be private key, it must be less than order. All field ...
0
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1answer
106 views

How to choose secp256k1 private key?

The private key is any random 256 bit (but smaller than prime p) number or must be prime or other condition? For selected $x$ can be found $y$ - decompressing key: ...
1
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1answer
139 views

Is it acceptable to use a HMAC-SHA256 hash as a secp256k1 private key?

Say I want to generate a deterministic private key related to some data, for instance to a domain name. The easiest way I can think of is: take a secret material which will work as "generator&...
2
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2answers
378 views

Is there a relationship between the secp256k1 public key of the sum of two private keys, and the public keys of those original two private keys?

If I have two secp256k1 private keys and add them together, can I derive the public key for the sum, if I only know the public keys for the two original private keys? (I think this may be the core of ...
0
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0answers
78 views

Is there a relation between the private keys of secp256k1 public keys of opposite parities?

From observation, 32 bit public key values of opposite parities are either both valid, or both invalid. ...