make elliptic curves available to solver.py

lib.py

@@ -7,6 +7,8 @@ import math
 def is_prime(num):
     if isinstance(num, str):
         num = int(num)
+    if num in [2, 3, 5]:
+        return True
     if num & 1 and num % 5 > 0:
         for i in range(2, math.floor(math.sqrt(num)) + 1):
             if i & 1 and (num % i) == 0:
@@ -24,3 +26,47 @@ def rev(num):  # or int(str(num)[::-1])
         revs = (revs * 10) + remainder
         num = num // 10
     return revs
+
+
+def power(x, y, p):
+    res = 1
+    x %= p
+    while (y > 0):
+        if (y & 1):
+            res = (res * x) % p
+        y = y >> 1
+        x = (x * x) % p
+    return res
+
+
+def sqrtNormal(n, p):
+    n %= p
+    for x in range(2, p):
+        if ((x * x) % p == n):
+            return x
+    return None
+
+
+# Assumption: p is of the form 3*i + 4 where i >= 1
+def sqrtFast(n, p):
+    if (p % 4 != 3):
+        # raise ValueError('Invalid Input')
+        return sqrtNormal(n, p)
+    # Try "+(n ^ ((p + 1)/4))"
+    n = n % p
+    x = power(n, (p + 1) // 4, p)
+    if ((x * x) % p == n):
+        return x
+    # Try "-(n ^ ((p + 1)/4))"
+    x = p - x
+    if ((x * x) % p == n):
+        return x
+    return None
+
+
+def elliptic_curve(x, a, b, r):
+    y2 = (x ** 3 + a * x + b) % r
+    y = sqrtFast(y2, r) if y2 > 0 else 0
+    if y is None:
+        return None, None
+    return y, -y % r