Assume the following scenario:
Alice has access to 32 bytes of true randomness $s$.
Alice hashes $s$ with SHA-512, and uses the resulting hash as the secret $d_{A}$ for Ed25519. Assume number-clamping and so on are correctly implemented.
Alice hashes $s$ with a different hash function, say BLAKE...
Consider a service S which receives hashes of documents from a number of providers. If two hashes match, it notifies the providers. We do not want anyone at the service to be able to identify the documents. However the document space is actually quite small (~billions) so a dictionary attack is p...
I'm finding the algebra behind cyclic codes somewhat tricky. The starting point is easy enough: $C\subseteq \mathbb F_q^n$ is cyclic if any cyclic shift of a codeword $c\in \mathbb F_q^n$ is still in $C$. Then I got hit with this: cyclic codes correspond to the ideals of
$$\mathbb F_q[x]/(x^n-1)....
To carry out Elliptic Curve Cryptography between parties, are all elliptic curve equations considered to be in the form $\bmod p$?
For example, the $secp256k1$ Bitcoin curve of the equation $y^2=x^3+7$ uses $\bmod p$, where $p=2^{256}-2^{32}-977$.
To carry out Elliptic Curve Cryptography between parties, are all elliptic curve equations considered to be in the form $\bmod p$?
For example, the $secp256k1$ Bitcoin curve of the equation $y^2=x^3+7$ uses $\bmod p$, where $p=2^{256}-2^{32}-977$.
