Added version 1

Signed-off-by: Marcin Woźniak <y0rune@aol.com>

2-lab/modul1.rb

@@ -0,0 +1,122 @@
+#!/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)