#!/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)

  #b = k.to_s(2).count "[0-1]"

  #r = SecureRandom.random_number(n)
  #x = r.to_s(2).count "[0-1]"

  #until x != b do
  #  #if r < n then
  #    r = SecureRandom.random_number(n)
  #    x = r.to_s(2).count "[0-1]"
  #    puts r
  #    puts x
  #  #end
  #end
  #return r

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

    return ra

end

## Zad. 1.2
def reciprocal_Phi_n(n,b)
  u = extended_euklides(n,b)[0]
  v = extended_euklides(n,b)[1]

  if v % n == 0 then
    return v
  else
    return u
  end
end

## Zad. 1.3

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

  for j in 1..i
    y = y**2 % n
    if b[-1*(j)]
      y = y * x  % n
    end
  end
  return y
end

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

  if ans > 0 && Prime.prime?(p) then
    return true
  else
    return false
  end
end

## Zad. 1.5
def squareRootFp(a)
  p = 3 % 4
  if remSqEuler(a,p) then
     bp = betterExponentiation(a,(p+1)/4,4) % 4
     bm = -1 * bp
     return bp,bm
  end
end

#puts extended_euklides(10,13)
puts random_gen_Zn(50,3)
#puts reciprocal_Phi_n(10,13)
#puts betterExponentiation(112218876,2,10)
#puts remSqEuler(3,13)
#puts squareRootFp(13)