KRzA/2-lab/modul1.rb

#!/usr/bin/ruby

#####################################
#
# Marcin Woźniak
# s434812
#
# Last edit: 27-10-2020
#
#####################################

#!/usr/bin/ruby

require 'prime'
require 'openssl'
require 'securerandom'
require 'prime'

def extended_euklides(a, b)
  return 1, 0 if b == 0

  q, r = a.divmod b
  s, t = extended_euklides(b, r)

  return t, s - q * t
end

## Zad. 1.1
def random_gen_Zn(n,k)
  if 2**(k-1) < n && k > 0 then
    if k == 1 then
      min = 0
      max = 1
    else
      min = 2**(k-1)
      max = (2**k)-1
    end
  end

  while true do
    r = rand(min..max)
      if r < n then
        break
      end
  end

    return ra

end

## Zad. 1.2
def reciprocal_Phi_p(n,p)
  # n mod p
  u = extended_euklides(n,p)[0]
  v = extended_euklides(n,p)[1]

  if u * n % p == 1
    puts u
  else
    puts v
  end
end

## Zad. 1.3
def betterExponentiation(x,k,n)
  b = k.to_s(2).reverse
  l = b.count "[0-1]"
  y = 1
  i = l - 1

  while i >= 0
    y = y**2 % n
    if b[i]=="1" then
      y = y * x % n
    end
    i = i - 1
  end
  return y
end

## Zad. 1.4
def remSqEuler(a,p)
  ans = betterExponentiation(a,(p-1)/2,p)

  if ans == 1 && Prime.prime?(p) then
    return true
  else
    return false
  end
end

## Zad. 1.5
def squareRootFp(p,b)
  if p % 4 == 3 && remSqEuler(p,b) == true then
    for i in 1..p
      a = betterExponentiation(i, (p+1)/4, p)
      #puts i.inspect + " " + a.inspect + "=" + b.inspect
      if a == b then
        puts i
        break
      end
    end
  end
end

## Zad. 1.6
def primalityTest(n)
  if n == 1 then
    return false
  end

  if n == 2 || n == 3 then
    return true
  end

  counter = rand(3..n)
  while (counter != 0) do
    b = rand(2..n-2) # Tez dziala n-1
      if betterExponentiation(b,n-1,n) != 1 then
        return false
      end
      counter = counter - 1
  end
  return true
end

#1 puts random_gen_Zn(50,3)
#2 puts reciprocal_Phi_p(5,7)
#3 puts betterExponentiation(24637864786278436723,10,3)
#4 puts remSqEuler(5,13)
#5 puts squareRootFp(7,2)
#6 puts primalityTest(13)