Update

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

2-lab/modul1.rb

@@ -27,22 +27,6 @@ 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
@@ -52,43 +36,44 @@ def random_gen_Zn(n,k)
       max = (2**k)-1
     end
   end
+
+  while true do
     r = rand(min..max)
-    while true do
-      ra = rand(min..max)
-        if ra < n then
-          break
-        end
-    end
+      if r < 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]
+def reciprocal_Phi_p(n,p)
+  # n mod p
+  u = extended_euklides(n,p)[0]
+  v = extended_euklides(n,p)[1]
 
-  if v % n == 0 then
-    return v
+  if u * n % p == 1
+    puts u
   else
-    return u
+    puts v
   end
 end
 
 ## Zad. 1.3
-
 def betterExponentiation(x,k,n)
-  b = x.to_s(2)
+  b = k.to_s(2).reverse
   l = b.count "[0-1]"
   y = 1
   i = l - 1
 
-  for j in 1..i
+  while i >= 0
     y = y**2 % n
-    if b[-1*(j)]
-      y = y * x  % n
+    if b[i]=="1" then
+      y = y * x % n
     end
+    i = i - 1
   end
   return y
 end
@@ -97,7 +82,7 @@ end
 def remSqEuler(a,p)
   ans = betterExponentiation(a,(p-1)/2,p)
 
-  if ans > 0 && Prime.prime?(p) then
+  if ans == 1 && Prime.prime?(p) then
     return true
   else
     return false
@@ -105,18 +90,43 @@ def remSqEuler(a,p)
 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
+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
 
-#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)
+## Zad. 1.6
+def primalityTest(n)
+  if n == 1 then
+    return false
+  end
+
+  if n == 2 || n == 3 then
+    return true
+  end
+
+  counter = rand(n/2..n)
+  while (counter != 0) do
+    b = rand(2..n)
+      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(10)