# Questions tagged [elliptic-curve-generation]

ECC is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide equivalent security. Elliptic curves are applicable for key agreement, digital signatures, pseudorandom generators, and other tasks. they can be used for encryption by combining the key agreement with an asymmetric encryption scheme.

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### Generating pseudorandom numbers using Dual_EC_DRBG

I am currently learning about the Dual_EC_DRBG protocol and I am stuck at the calculation of the initial state with the point P. For context, I am using the secp256k1 curve with a = 0 and b = 7. I ...
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### Standard Montgomery curves over prime field

Is there some source of standard, vetted, efficient Montgomery elliptic curves over prime field? I'm looking for curves $B\,y^2\equiv x^3+A\,x^2+x\pmod p$ engineered for efficient computation of ...
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### Generating a new curve using an existing curve and new prime

Can you take a curve equation from https://safecurves.cr.yp.to and a large safe prime from existing DH parameters (for example openssl dhparam 9000), combine them, ...
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### EC public key with leading zeros

Let us take example of secp256k1 curve. The current known public key with most leading zero (in x cordinate) is: ...
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### Practical deployments of ECC with cofactor of elliptic curves $4$ or $8$?

Are cofactor $4$ and $8$ ECC schemes widely used in practical deployments such as those in cryptocurrencies? Can you name some practical settings where there curves are used and cryptocurrencies where ...
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### Non-interactive EC DKG (Distributed Key Generation) question

Normally, when computing an EC threshold DKG, I have all parties reveal a commitment to the public key, and only reveal their own public key after verifying the commitments. Otherwise it's trivial ...
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1 vote
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### How to generate a random point on an elliptic curve without knowing it's corresponding scalar private key

Given an elliptic curve with generator $G$, is it possible to generate a random point on the curve $Q = a \cdot G$ without knowing the secret value $a$ that generated it? Note that just using an $a$ ...
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### In The Ristretto Group, do all points sampled with Elligator have the same order?

Assume the Hash-to-ristretto255 function Elligator as laid out here. Assume a random hash that is then mapped to a point in the <...
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### 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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### Diffie Hellman groups

I saw that non-negative integers with the addition operation cannot be the Diffie Hellman group. I'm having trouble understanding why it cannot be the DHKE group. To be DHKE group, there are five ...
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### Elliptic curve subgroup with $p$ elements in field of characteristic $p$

Are there any elliptic curves defined over a finite field $\mathrm{GF}(p^k)$ with a subgroup of order $p$ where the discrete log (and preferably DDH) problem is hard? Elliptic curve with prime ...
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### How to convert coordinates o a point from y^2=x^3+7 to y^2=x^3+4? [closed]

To moderator, this my question is not off topic !!! Please OPEN MY QUESTION. If for this place elliptic curves was off topic this so world is crazy. ...
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