Join Log in
Score:2
avatar Crypto

Linear approximation of modular addition of a constant?

np flag
Federico Lebrón

In Linear Approximations of Additions Modulo $2^n$, Wallén shows how to compute the correlation of the modular addition of two binary bit vectors. A simple recursive procedure was given by Schulte-Geers in On CCZ-equivalence of Addition mod $2^n$. However, these papers both assume that the summands are uniformly distributed random variables over $\mathbb{F}_2^n$.

Suppose one has $f: \mathbb{F}_2^n \to \mathbb{F}_2^n$, $f(x) = x \boxplus C$, where $C \in \mathbb{F}_2^n$ is fixed, and $\boxplus$ means modular addition. If $\alpha, \beta \in \mathbb{F}_2^n$ are bitmasks, and juxtaposition means bitwise $\operatorname{AND}$, what can one say about the bias of the approximation $\langle \alpha x, \beta f(x)\rangle = 0$?

52
0 + 0
arx
ธงชาติไทย
Elon Musk
I sit in a Tesla and translated this thread with Ai:

mangohost

Post an answer

Most people don’t grasp that asking a lot of questions unlocks learning and improves interpersonal bonding. In Alison’s studies, for example, though people could accurately recall how many questions had been asked in their conversations, they didn’t intuit the link between questions and liking. Across four studies, in which participants were engaged in conversations themselves or read transcripts of others’ conversations, people tended not to realize that question asking would influence—or had influenced—the level of amity between the conversationalists.