bquast

import numpy as np
from numpy.polynomial import Polynomial

def polynomial_modulo(polynomial, mod):
    q, r = divmod(polynomial, mod)
    return r

def mod_on_coefficients(polynomial, modulo):
    coefs = polynomial.coef
    mod_coefs = [c % modulo for c in coefs]

bquast

## ----setup----
library(polynom)
library(HEtools)

## ----params----
d  =   4
n  =   2^d
p  =   (n/2)-1
t  =   p
q  = 868

bquast

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bquast

import numpy as np
from numpy.polynomial import Polynomial

def polynomial_modulo(polynomial, mod):
    """
    Perform polynomial modulo operation using divmod.
    """
    q, r = divmod(polynomial, mod)
    return r

bquast

import numpy as np
from numpy.polynomial import Polynomial

def polynomial_modulo(polynomial, mod):
    """
    Perform polynomial modulo operation using divmod.
    """
    q, r = divmod(polynomial, mod)
    return r

bquast

library(polynom)

M <- 8
N <- M %/% 2
scale <- 64
xi <- complex(real = cos(2 * pi / M), imaginary = sin(2 * pi / M))

vandermonde <- function(xi, M) {
  N <- M %/% 2
  # Initialize an empty matrix with complex data type

bquast

import numpy as np
from numpy.polynomial import Polynomial

# Set the parameters
M = 8
N = M // 2
scale = 64
xi = np.exp(2 * np.pi * 1j / M)

def vandermonde(xi: np.complex128, M: int) -> np.array:

bquast

library(matrixStats)

# Softmax function
softmax <- function(x) {
  exp_x <- exp(x - max(x))
  exp_x / sum(exp_x)
}

# Scaled dot product attention
scaled_dot_product_attention <- function(Q, K, V, mask = NULL) {

bquast

# HE illustrated primer

# define some parameters (small as an example)
# N.B. these parameters are not secure, they are completely insecure
d =   4
n =   2^d
t =   (n/2)-1
q = 874

# load library to create polynomials

bquast

# HE illustrated primer

# define some parameters (small as an example)
# N.B. these parameters are not secure, they are completely insecure
n =   4
d =   2^n
t =   7
q = 874

# load library to create polynomials