Cryptography

Questions tagged [secp256k1]

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

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On an Elliptic Curve is that possible that from $P$ we can tell if $a$ is quadratic residue modulo $N$?

Imagine that, On an Elliptic Curve cryptography scheme where $P=a\times G$, Bob shares his public key $P$ with Eve (the devil who wants to know secrets he is not supposed to). Bob has also revealed a ...
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1answer
58 views

The better algorithm for Modular Exponentiation on secp256k1/r1

I know Modular Exponentiation ($r = b^e \bmod m$) is important for RSA, and I can find some algorithm that if e is expressed in binary form (for exp: )--in such way for a n-bit long e, one can expect ~...
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How to calculate a valid signature? [migrated]

I am trying to create a signature that is valid on https://etherscan.io/verifySig, but it shows always that my signature is invalid: I created a random private and public key: ...
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1answer
54 views

Chinese remainder theorem in ECDSA for parameters in secp256k1?

It is known that it is possible to apply the Chinese remainder theorem and attack RSA under precise conditions. https://tls.mbed.org/public/WSchindler-...
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0answers
36 views

Is it safe to implement elliptic curve Diffie Hellman with secp256k1

I need to implement X3DH Key Agreement Protocol according to Signal specification, in the document they suggest using either X25519 or X448 curves. I assume those curves have been chosen for this ...
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1answer
89 views

How to calculate the order of secp256k1?

The elliptic curve secp256k1 is defined as $y^2 = x^3 + 7$. The prime for the field is set to: ...
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1answer
111 views

ECC Point Addition on Jacob coordinate -- Not Commutative?

I have a python script that does the ECC point addition (code paste below), it simply performs the P =Q1+Q2 on Jacob coordination. However, when doing some regression tests, I found that if I exchange ...
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1answer
64 views

Is it possible to calculate and unknown point on an EC

I aim to find the answer to what is $X$ on an EC over a finite field where $A + X = B$ and $A$ and $B$ are known. I’m currently learning with secp256k1 so the simplified equation for the curve is $y^2 ...
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1answer
163 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 ...
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1answer
86 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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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 ...
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1answer
71 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 ...
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718 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?
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61 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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46 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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210 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 ...
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0answers
201 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 ...
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1answer
97 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
291 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 ...
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1answer
147 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: ...
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1answer
161 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&...
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2answers
528 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 ...
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93 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. ...

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