master > master: code py - pollard rho mit 2 modi

code/python/models/commands-schema.yaml

@@ -235,6 +235,7 @@ components:
       type: object
       required:
         - name
+        - growth
         - number
       properties:
         name:
@@ -242,6 +243,8 @@ components:
         number:
           type: integer
           exclusiveMinimum: 0
+        growth:
+          $ref: '#/components/schemas/EnumPollardGrowthRate'
         x-init:
           type: integer
           default: 2
@@ -327,6 +330,21 @@ components:
         - GREEDY
         - BRANCH-AND-BOUND
     # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+    # Enum Type for choice of growth rate in Pollard Algorithm
+    # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+    EnumPollardGrowthRate:
+      description: |-
+        Via the 'tail-chasing' period finding method in Pollard's rho algorithm,
+        the difference between the indexes of the pseudo-random sequence
+        can be chosen to growth according to different rates, e.g.
+
+        - `LINEAR` - choose `x[k]` and `x[2k]`
+        - `EXPONENTIAL` - choose `x[k]` and `x[2^{k}]`
+      type: string
+      enum:
+        - LINEAR
+        - EXPONENTIAL
+    # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
     # Enum Type of walk mode for fitness walk algorithm
     # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
     EnumWalkMode:

code/python/src/algorithms/pollard_rho/__init__.py

@@ -12,5 +12,6 @@ from src.algorithms.pollard_rho.algorithms import *;
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 __all__ = [
-    'pollard_rho_algorithm',
+    'pollard_rho_algorithm_linear',
+    'pollard_rho_algorithm_exponential',
 ];

code/python/src/algorithms/pollard_rho/algorithms.py

@@ -18,14 +18,71 @@ from src.algorithms.pollard_rho.display import *;
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 __all__ = [
-    'pollard_rho_algorithm',
+    'pollard_rho_algorithm_linear',
+    'pollard_rho_algorithm_exponential',
 ];
 
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-# METHOD pollard's rho algorithm
+# METHOD pollard's rho algorithm - with linear grwoth
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
-def pollard_rho_algorithm(
+def pollard_rho_algorithm_linear(
+    n: int,
+    x_init: int = 2,
+    verbose: bool = False,
+):
+    steps = [];
+    success = False;
+    f = lambda _: fct(_, n=n);
+
+    d = 1;
+    x = y = x_init;
+    steps.append(Step(x=x));
+    k = 0;
+    k_next = 1;
+
+    while True:
+        # aktualisiere x: x = f(x_prev):
+        x = f(x);
+        # aktualisiere y: y = f(f(y_prev)):
+        y = f(f(y));
+
+        # ggT berechnen:
+        d = math.gcd(abs(x-y), n);
+        steps.append(Step(x=x, y=y, d=d));
+
+        # Abbruchkriterien prüfen:
+        if d == 1: # weitermachen, solange d == 1
+            k += 1;
+            continue;
+        elif d == n: # versagt
+            success = False;
+            break;
+        else:
+            success = True;
+            break;
+
+    if verbose:
+        repr = display_table_linear(steps=steps);
+        print('');
+        print('\x1b[1mEuklidescher Algorithmus\x1b[0m');
+        print('');
+        print(repr);
+        print('');
+        if success:
+            print('\x1b[1mBerechneter Faktor:\x1b[0m');
+            print('');
+            print(f'd = \x1b[1m{d}\x1b[0m.');
+        else:
+            print('\x1b[91mKein (Prim)faktor erkannt!\x1b[0m');
+        print('');
+    return d;
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# METHOD pollard's rho algorithm - with exponential grwoth
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+def pollard_rho_algorithm_exponential(
     n: int,
     x_init: int = 2,
     verbose: bool = False,
@@ -64,7 +121,7 @@ def pollard_rho_algorithm(
             break;
 
     if verbose:
-        repr = display_table(steps=steps);
+        repr = display_table_exponential(steps=steps);
         print('');
         print('\x1b[1mEuklidescher Algorithmus\x1b[0m');
         print('');

code/python/src/algorithms/pollard_rho/display.py

@@ -16,14 +16,37 @@ from src.models.pollard_rho import *;
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 __all__ = [
-    'display_table',
+    'display_table_linear',
+    'display_table_exponential',
 ];
 
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-# METHOD display table
+# METHOD display table - linear
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
-def display_table(steps: List[Step]) -> str:
+def display_table_linear(steps: List[Step]) -> str:
+    table = pd.DataFrame({
+        'i':  [i for i in range(len(steps))],
+        'x':  [step.x for step in steps],
+        'y':  [step.y or '-' for step in steps],
+        'd':  [step.d or '-' for step in steps],
+    }) \
+    .reset_index(drop=True);
+    # benutze pandas-Dataframe + tabulate, um schöner darzustellen:
+    repr = tabulate(
+        table,
+        headers=['i', 'x(i)', 'y(i) = x(2i)', 'gcd(|x - y|,n)'],
+        showindex=False,
+        colalign=('right', 'right', 'right', 'center'),
+        tablefmt='simple',
+    );
+    return repr;
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# METHOD display table - exponential
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+def display_table_exponential(steps: List[Step]) -> str:
     table = pd.DataFrame({
         'i':  [i for i in range(len(steps))],
         'x':  [step.x for step in steps],

code/python/src/endpoints/ep_algorithm_pollard_rho.py

@@ -26,9 +26,21 @@ __all__ = [
 
 @run_safely()
 def endpoint_pollard_rho(command: CommandPollard) -> Result[CallResult, CallError]:
-    result = pollard_rho_algorithm(
+    match command.growth:
-        n = command.number,
+        case EnumPollardGrowthRate.linear:
-        x_init = command.x_init,
+            result = pollard_rho_algorithm_linear(
-        verbose = config.OPTIONS.pollard_rho.verbose,
+                n = command.number,
-    );
+                x_init = command.x_init,
+                verbose = config.OPTIONS.pollard_rho.verbose,
+            );
+            pass;
+        case EnumPollardGrowthRate.exponential:
+            result = pollard_rho_algorithm_exponential(
+                n = command.number,
+                x_init = command.x_init,
+                verbose = config.OPTIONS.pollard_rho.verbose,
+            );
+            pass;
+        case _ as growth:
+            raise Exception(f'No algorithm implemented for \x1b[1m{growth.value}\x1b[0m as growth rate.');
     return Ok(CallResult(action_taken=True, message=result));