Data commit

Task/Tonelli-Shanks-algorithm/Visual-Basic-.NET/tonelli-shanks-algorithm.vb

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+Imports System.Numerics
+
+Module Module1
+
+    Class Solution
+        ReadOnly root1 As BigInteger
+        ReadOnly root2 As BigInteger
+        ReadOnly exists As Boolean
+
+        Sub New(r1 As BigInteger, r2 As BigInteger, e As Boolean)
+            root1 = r1
+            root2 = r2
+            exists = e
+        End Sub
+
+        Public Function GetRoot1() As BigInteger
+            Return root1
+        End Function
+
+        Public Function GetRoot2() As BigInteger
+            Return root2
+        End Function
+
+        Public Function GetExists() As Boolean
+            Return exists
+        End Function
+    End Class
+
+    Function Ts(n As BigInteger, p As BigInteger) As Solution
+        If BigInteger.ModPow(n, (p - 1) / 2, p) <> 1 Then
+            Return New Solution(0, 0, False)
+        End If
+
+        Dim q As BigInteger = p - 1
+        Dim ss = BigInteger.Zero
+        While (q Mod 2) = 0
+            ss += 1
+            q >>= 1
+        End While
+
+        If ss = 1 Then
+            Dim r1 = BigInteger.ModPow(n, (p + 1) / 4, p)
+            Return New Solution(r1, p - r1, True)
+        End If
+
+        Dim z As BigInteger = 2
+        While BigInteger.ModPow(z, (p - 1) / 2, p) <> p - 1
+            z += 1
+        End While
+        Dim c = BigInteger.ModPow(z, q, p)
+        Dim r = BigInteger.ModPow(n, (q + 1) / 2, p)
+        Dim t = BigInteger.ModPow(n, q, p)
+        Dim m = ss
+
+        Do
+            If t = 1 Then
+                Return New Solution(r, p - r, True)
+            End If
+            Dim i = BigInteger.Zero
+            Dim zz = t
+            While zz <> 1 AndAlso i < (m - 1)
+                zz = zz * zz Mod p
+                i += 1
+            End While
+            Dim b = c
+            Dim e = m - i - 1
+            While e > 0
+                b = b * b Mod p
+                e = e - 1
+            End While
+            r = r * b Mod p
+            c = b * b Mod p
+            t = t * c Mod p
+            m = i
+        Loop
+    End Function
+
+    Sub Main()
+        Dim pairs = New List(Of Tuple(Of Long, Long)) From {
+            New Tuple(Of Long, Long)(10, 13),
+            New Tuple(Of Long, Long)(56, 101),
+            New Tuple(Of Long, Long)(1030, 10009),
+            New Tuple(Of Long, Long)(1032, 10009),
+            New Tuple(Of Long, Long)(44402, 100049),
+            New Tuple(Of Long, Long)(665820697, 1000000009),
+            New Tuple(Of Long, Long)(881398088036, 1000000000039)
+        }
+
+        For Each pair In pairs
+            Dim sol = Ts(pair.Item1, pair.Item2)
+            Console.WriteLine("n = {0}", pair.Item1)
+            Console.WriteLine("p = {0}", pair.Item2)
+            If sol.GetExists() Then
+                Console.WriteLine("root1 = {0}", sol.GetRoot1())
+                Console.WriteLine("root2 = {0}", sol.GetRoot2())
+            Else
+                Console.WriteLine("No solution exists")
+            End If
+            Console.WriteLine()
+        Next
+
+        Dim bn = BigInteger.Parse("41660815127637347468140745042827704103445750172002")
+        Dim bp = BigInteger.Pow(10, 50) + 577
+        Dim bsol = Ts(bn, bp)
+        Console.WriteLine("n = {0}", bn)
+        Console.WriteLine("p = {0}", bp)
+        If bsol.GetExists() Then
+            Console.WriteLine("root1 = {0}", bsol.GetRoot1())
+            Console.WriteLine("root2 = {0}", bsol.GetRoot2())
+        Else
+            Console.WriteLine("No solution exists")
+        End If
+    End Sub
+
+End Module