46 views

### 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 ...
32 views

### ECC order and modulus in EC [duplicate]

This question came from security.stackexchange.com. I have an error in reasoning regarding to the calculations on elliptic curves. The basic group operations are all calculated mod p. Ok right. Then ...
954 views

### 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 ...
2k views

### 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 ...
2k views

### 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 ...
583 views

### 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 ...
388 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: ...
472 views

### 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 ...
243 views

### 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 ...
285 views

### 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 ...
445 views

### Key size and finite fields in ECC (References)

So somehow I know that the key size in ECC is defined over the number of elements in a finite field or that it is almost equivalent to that (Correct me if I am wrong). However, other than on Wikipedia ...
244 views

### Generating a random point on an elliptic curve over a finite field

I have coded an implementation of elliptic curves in order to apply some of the ECC algorithms. However, in most of them, Alice needs to choose a point P on a given curve. What is the general ...
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 ...