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Results tagged with elliptic-curve-generation
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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.
14
votes
Accepted
What's wrong with this curve (generation algorithm)?
As a lone curve, yours is not bad. But Barreto's proposal offers an extra property, which is that the quadratic twist also has prime order.
In general, in a given finite field $K$, if you have a non- …
- 87.8k
9
votes
What is necessary for generating an elliptic curve?
Let's suppose that you want to generate a classic $n$-bit curve in a prime field, with the complete curve order being prime. The process goes about thus:
Get a prime $p$ of size $n$ bits. The curve …
- 87.8k
13
votes
Accepted
Security of elliptic curves
Mathematically speaking, we cannot. There is no proof that elliptic curves are actually "secure". But the same apply to about all other cryptographic algorithms, so we have to make do with the next be …
- 87.8k
23
votes
Accepted
What is the curve type of SECP256K1?
There are curve types, and equation types.
As algebraic objects, all curves can be expressed with a "Weierstraß equation". Through some changes of variables, that equation can be simplified into a "s …
- 87.8k
7
votes
Accepted
Is there a theorem to determine the elliptic curve parameters based on the group order?
There is a method known as "Complex Multiplication". However, it is not simple at all, and tends to be overly expensive for most target orders. See this article for some details. There is also the (th …
- 87.8k