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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 ...
• 141k

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 ...
• 22.5k

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 ...

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 ...
• 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 ...
• 13k
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 ...
• 13k
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 $s \in \mathbb{F}_{\... • 147k 2 votes Accepted Is there any reference about the half-trace when m is even in F(2^m) Good reference for this include section II.2.4 of Elliptic Curves in Cryptography (Blake, Seroussi, Smart) or section 11.2.6 of the Handbook of elliptic and hyperelliptic curve cryptography (Cohen and ... • 23.8k 3 votes Is it possible to generate an elliptic curve (with the hard discrete logarithm problem) by iterating only a finite field, but not its$j$-invariant? Yes, this is straightforward enough. Write down you elliptic curve with coefficients in$\mathbb Q$. For any$p$you can then use the same equation with the coefficients interpreted as elements of$\...
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 ...