Small improvements

kryptools/dlp.py

@@ -43,7 +43,7 @@ def _dlog_switch(a: int, b: int, n: int, m: int, verbose: int = 0) -> int:
     # compare the theoreticaly expected running times ob bsgs and ic; the constant 6 is determined experimentally
     if log(m) - 6 < 2 * sqrt(log(n) * log(log(n))):
         if verbose > 1:
-            print(f"BS GS: {a}^x == {b} (order={m})")
+            print(f"BS GS: {a}^x = {b} (order={m})")
         return dlog_bsgs(a, b, n, m, verbose=max(0, verbose - 1))
     if verbose > 1:
         print(f"Quadratic sieve: {a}^x == {b} (order={m})")

kryptools/dlp_bsgs.py

@@ -43,7 +43,7 @@ def dlog_bsgs(a: int, b: int, n: int, m: int = None, verbose: int = 0) -> int:
     giant_step = b
     for l in range(1, mm):
         giant_step = (giant_step * giant_stride) % n
-        if show and not k % show and k:
+        if show and not l % show and l:
             print(".", end="")
         if giant_step in baby_steps:
             if verbose:

kryptools/factor_ecm.py

@@ -115,7 +115,7 @@ def factor_ecm(n: int, B1: int | None = None, B2: int | None = None, curves: int
         v = (4 * sigma) % n
         try:
             c = (pow(v - u, 3, n) * (3 * u + v) * pow(4 * u**3 * v, -1, n) - 2) % n
-        except:
+        except ValueError:
             if verbose > 1:
                 print("\nFactor found.")
             m = gcd(u, n)

kryptools/la.py

@@ -127,15 +127,10 @@ def applyfunc(self, func):
         tmp.map(func)
         return tmp
 
-    def _guess_ring(self):
+    def _guess_zero(self):
         zero = 0 * self.matrix[0][0]
-        try:
-            ring = type(zero)
-            one = ring(1)
-        except:
-            ring = None
-            one = zero**0
-        return zero, one, ring
+        one = zero**0
+        return zero, one
 
     def norm2(self) -> float:
         "Squared Frobenius/Euclidean norm."
@@ -213,7 +208,7 @@ def __rmul__(self, other) -> "Matrix":
 
     def rref(self) -> "Matrix":
         "Compute the reduced echelon form of a matrix M."
-        zero, one = self._guess_ring()[:2]
+        zero, one = self._guess_zero()
         n, m = self.cols, self.rows
         R = self[:, :]
         i = 0
@@ -239,7 +234,7 @@ def rref(self) -> "Matrix":
 
     def det(self) -> int:
         "Compute the determinant of a matrix M."
-        zero, one = self._guess_ring()[:2]
+        zero, one = self._guess_zero()
         if self.rows != self.cols:
             raise ValueError("Matrix must be square!")
         n, m = self.cols, self.rows
@@ -270,7 +265,7 @@ def inv(self) -> "Matrix":
         "Compute the inverse of a square matrix M."
         if self.rows != self.cols:
             raise ValueError("Matrix must be square!")
-        zero, one = self._guess_ring()[:2]
+        zero, one = self._guess_zero()
         n = self.cols
         MM = self.__class__([[zero for _ in range(2*n)] for _ in range(n)])
         for i in range(n):
@@ -298,7 +293,7 @@ def zeros(self, m: int = None, n: int = None):
             n, m = self.cols, self.rows
         elif not n:
             n = m
-        zero = self._guess_ring()[0]
+        zero = self._guess_zero()[0]
         return self.__class__([[zero for j in range(n)] for i in range(m)])
 
     def eye(self, m: int = None, n: int = None):
@@ -311,7 +306,7 @@ def delta(i, j):
             n, m = self.cols, self.rows
         elif not n:
             n = m
-        zero, one = self._guess_ring()[:2]
+        zero, one = self._guess_zero()
         return self.__class__([[delta(i, j) for j in range(n)] for i in range(m)])
 
 

kryptools/poly.py

@@ -114,15 +114,10 @@ def applyfunc(self, func) -> "Poly":
     def _check_type(self, other):
         return isinstance(other, int) or (isinstance(other, Number) and isinstance(self.coeff[0], Number)) or type(other) == type(self.coeff[0])
 
-    def _guess_ring(self):
+    def _guess_zero(self):
         zero = 0 * self.coeff[0]
-        try:
-            ring = type(zero)
-            one = ring(1)
-        except:
-            ring = None
-            one = zero**0
-        return zero, one, ring
+        one = zero**0
+        return zero, one
 
     def __add__(self, other: "Poly") -> "Poly":
         zero = 0 * self.coeff[0]
@@ -230,9 +225,9 @@ def __mod__(self, other: "Poly") -> "Poly":
 
     def divmod(self, other: "Poly") -> ("Poly", "Poly"):
         "Polynom division with remainder."
-        zero, one, ring = self._guess_ring()
+        zero, one = self._guess_zero()
         if isinstance(other, list):
-            other = self.__class__(other, ring=ring)
+            other = self.__class__(other)
         elif not isinstance(other, self.__class__):
             raise NotImplementedError(f"Cannot divide {self} and {other}.")
         if not other:
@@ -260,9 +255,9 @@ def divmod(self, other: "Poly") -> ("Poly", "Poly"):
 
     def mod(self, other: "Poly") -> None:
         "Reduce with respect to a given polynomial."
-        one, ring = self._guess_ring()[1:]
+        one = self._guess_zero()[1]
         if isinstance(other, list):
-            other = self.__class__(other, ring=ring)
+            other = self.__class__(other)
         elif not isinstance(other, self.__class__):
             raise NotImplementedError(f"Cannot divide {self} and {other}.")
         if not other:
@@ -289,9 +284,9 @@ def inv(self, other: "Poly" = None) -> "Poly":
         "Inverse modulo a given polynomial."
         if not other:
             other = self.modulus
-        zero, one, ring = self._guess_ring()
+        zero, one = self._guess_zero()
         if isinstance(other, list):
-            other = self.__class__(other, ring=ring)
+            other = self.__class__(other)
         elif not isinstance(other, self.__class__):
             raise NotImplementedError(f"Cannot invert {self} modulo {other}.")
         if not other:

tests/test_primes.py

@@ -75,13 +75,29 @@ def test_is_prime():
         assert is_prime(n) == prime_test[n]
 
 
+# https://oeis.org/A000043
+OEIS_A000043 = [2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281,
+                 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243,
+                 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221,
+                 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457,
+                 32582657, 37156667, 42643801, 43112609, 57885161]
+
+
+def test_mersenne_prime():
+    for p in range(1000):
+        if not prime_test[p]:
+            continue
+        if p > OEIS_A000043[-1]:
+            break
+        assert is_prime(2**p - 1) == (p in OEIS_A000043)
+
+
 # https://oeis.org/A005385
 OEIS_A005385 = [5, 7, 11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383, 467,
                 479, 503, 563, 587, 719, 839, 863, 887, 983, 1019, 1187, 1283, 1307, 1319, 1367, 1439,
                 1487, 1523, 1619, 1823, 1907, 2027, 2039, 2063, 2099, 2207, 2447, 2459, 2579, 2819,
                 2879, 2903, 2963]
 
-
 def test_is_safeprime():
     for n in range(OEIS_A005385[-1]+1):
         assert is_safeprime(n) == (n in OEIS_A005385)