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### Difference in elliptic curve order and finite field size [duplicate]

Must the prime finite field, Fp, an elliptic curve is defined over always have a greater number of elements than the cardinality of an elliptic curve. For example, If I have ...
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### Summarize the mathematical problem at the heart of breaking a Curve25519 public key

It's pretty easy to generate a Curve25519 private key: generate 32 random bytes of data and then do: e[0] &= 248 e[31] &= 127 e[31] |= 64 You can then ...
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### What is an elliptic curve cofactor?

As the title says, I have some doubts about the term "cofactor" used to describe elliptic curves. AFAIK, it's a factor of the curve order, but why is it explicitly specified in some parameter lists ...
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### Generating a NIST P-256 private key

From the Curve25519 spec I learned that it possible to take a random 32 bytes and with a few operations make it on the curve: To generate a 32-byte Curve25519 secret key, start by generating 32 ...
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### EC Key Compression

Using the secp256k1 curve, will the below yield the same result? Generate private key -> compress private key -> generate public key Generate private key -> generate public key -> compress public key ...
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### Can you tell me why doing scalar multiplication of a point on a Elliptic curve over a finite field gets to a point at infinity?

I am reading Programming Bitcoin. The author said: Another property of scalar multiplication is that at a certain multiple, we get to the point at infinity (remember, the point at infinity is the ...
1k views

### What is the difference between: ecdsap, ecdsak, and ecdsab in the output of "openssl speed"? What do the letters P/K/B refer to?

openssl speed tests the speed of different protocols on your computer: ...
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### How are Elliptic Curve private and public keys actually used to encrypt or sign data?

I've read article after article about curve parameters, generator points, the dot operation, and how you dot the generator point priv times to get the ...
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### Ed25519 and hierarchical deterministic wallet

I'm building a solution based on the stellar codebase and using the Ed25519 curve for the signatures. One of the features I've been adding to the system is a support for hierarchical deterministic ...
1 vote
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### ECC with 512bit compatible curves

I understand that given solutions for solving a discrete logarithm problem are on the order of 𝑂(2𝑛/2), ergo, 256bit private keys based on 25519 or secp256k1 have an effective bit strength of ...
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Recently I've been studying the ECC with the Chinese SM2 standard. One question is on standard part 5, parameters definition, it only defines $p, a, b, n, XG,$ and $YG$, but not cofactor $h$. I found ...