New answers tagged

7 votes

When incrementing a private key by 1, by how much is the public key Incremented?

If you have a secp256k1 keypair and you increment the private key by 1, what's a fast way to compute the new public key? Using notation close to sec1 and the parameters of secp256k1, if the private ...
fgrieu's user avatar
  • 141k
0 votes

wrting algorithm for torsion group elements

It is absolutely your lecturer's/professor's responsibility to give feedback on what's wrong with your answer. We don't know what is the assumed knowledge for the course, what level of pseudocode is ...
kodlu's user avatar
  • 22.5k
0 votes

Providing a bound on the field-trace of a specific kind of polynomial to solve the finite-field isomorphism decisional problem

When f(x) is (half) sparse and ternary, we have a very special form of the traces of the powers of x (Lemma 1). However, as the sparsity decreases, the traces of the powers of x increase. This is ...
Das Dipayan's user avatar
2 votes

How to know if an ECC public key is y or -y

Straightening the question's vocabulary: on secp256k1 every point $Q$ has an opposite point (or additive inverse point) noted $-Q$. For the $n-1$ points $Q$, the opposite $Q'=-Q$ of $Q$ has the ...
fgrieu's user avatar
  • 141k
1 vote

Providing a bound on the field-trace of a specific kind of polynomial to solve the finite-field isomorphism decisional problem

First, I have been unable to find any resources that relate the trace to the specific coefficients in the polynomials This is expected. The trace of a field element is independent of the particular ...
Mark Schultz-Wu's user avatar
1 vote
Accepted

Probabilistic proof of multiplying two elements from non-prime finite field

I'll only address your comment And in the paper they use $n=2^k$ and $q−1=2n$, which makes $\alpha^n+1$ the cyclotomic polynomial $\Phi_{2n}(\alpha)$ (which makes polynomial multiplication more ...
Mark Schultz-Wu's user avatar
0 votes

Probabilistic proof of multiplying two elements from non-prime finite field

But then I am thinking, since any element $X \in \mathbb{F}_{\large p^{\Large n}}$ can be thought of as a polynomial, can you "evaluate" that polynomial at some point $s \in \mathbb{F}_{\...
poncho's user avatar
  • 147k
2 votes
Accepted

Is there any reference about the half-trace when m is even in F(2^m)

Good reference for this include section II.2.4 of Elliptic Curves in Cryptography (Blake, Seroussi, Smart) or section 11.2.6 of the Handbook of elliptic and hyperelliptic curve cryptography (Cohen and ...
Daniel S's user avatar
  • 23.8k
3 votes

Is it possible to generate an elliptic curve (with the hard discrete logarithm problem) by iterating only a finite field, but not its $j$-invariant?

Yes, this is straightforward enough. Write down you elliptic curve with coefficients in $\mathbb Q$. For any $p$ you can then use the same equation with the coefficients interpreted as elements of $\...
Daniel S's user avatar
  • 23.8k
0 votes

Finite Field Arithmetic _ Montgomery reduction

Montgomery arithmetic is a technique for modular computation modulo some integer $m$. It centers on Montgomery reduction, an alternative to reduction modulo $m$ by Euclidean division. Montgomery ...
fgrieu's user avatar
  • 141k

Top 50 recent answers are included