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Signed-off-by: Luong Duc Anh <[email protected]>
2026-01-24 18:02:44 +07:00
1 parent 0cf70e272b
commit 54d82ac660
@@ -0,0 +1,196 @@
+from math import gcd as mathgcd
+from itertools import combinations
+from functools import wraps
+import random
+
+
+# home grown gcd
+def gcd(a, b):
+    return a if b == 0 else gcd(b, a % b)
+
+
+def cooked(s: set[int]):
+    for a, b in combinations(s, 2):
+        if mathgcd(a, b) == 1:
+            yield a, b
+
+
+printingTs = False
+
+
+def printTs(f):
+    @wraps(f)
+    def ff(*a, **kw):
+        if printingTs:
+            if a:
+                print(*a)
+            if kw:
+                print(*kw.items())
+        r = f(*a, *kw)
+        if printingTs:
+            print(r)
+        return r
+
+    return ff
+
+
+@printTs
+def smx(x, e, n, r=1):  # this is not it cuh
+    return (
+        smx(inv(x, n), -e, n, r)
+        if e < 0
+        else r
+        if e == 0
+        else smx(x * x % n, e >> 1, n, r * x % n if e & 1 else r)
+    )
+
+
+def realsmx(x, e, n):
+    r = x
+    for bro in map(int, bin(e)[3:]):
+        r = (r * r) % n
+        if bro:
+            r = (r * x) % n
+    return r
+
+
+@printTs
+def theREALsmx(x, e, n):
+    "locked in"
+    return (
+        theREALsmx(inv(x, n), -e, n)
+        if e < 0
+        else x**e
+        if e <= 1
+        else theREALsmx(x, e >> 1, n) ** 2 % n
+        if not e & 1
+        else (x * theREALsmx(x, e & ~1, n)) % n
+    )
+
+
+def realest(x=None, y=None, n=None):
+    x = x or random.randint(-10e9, 10e9)
+    y = y or random.randint(-10e9, 10e9)
+    n = n or random.randint(2, 10e9)
+    # print(x, y, n)
+    if y < 0:
+        try:
+            p = pow(x, -1, n)
+        except ValueError:
+            p = None
+        else:
+            assert (p * x) % n == 1, f"{p = }, {(p*x)%n = }"
+        try:
+            i = inv(x, n)
+        except ValueError:
+            i = None
+        else:
+            assert (i * x) % n == 1, f"{i = }, {(i*x)%n = }"
+
+        assert i == p, f"{i = }, {p = }"
+        if gcd(x, n) != 1:
+            return  # not doing ts
+
+    p = pow(x, y, n)
+    s = smx(x, y, n)
+    t = theREALsmx(x, y, n)
+    assert p == s == t, f"{p = }, {s = }, {t = }"
+
+
+def xgcd(a, b) -> tuple[int, tuple[int, int]]:
+    "answer at index 0, wiki ripoff"
+    s, ps, r, pr = 0, 1, b, a
+    # shit = 0
+    while r != 0:
+        # shit += 1
+        # if shit > 1000:
+        # raise RecursionError("SHIT")
+        q = pr // r
+        pr, r = r, (pr - q * r)
+        ps, s = s, (ps - q * s)
+    bt = 0 if b == 0 else (pr - ps * a) % b
+    return (pr, (ps, bt))
+
+
+def inv(a, n):
+    "also wiki ripoff"
+    t, nt, r, nr = 0, 1, n, a % n
+    # shit = 0
+    while nr != 0:
+        # shit += 1
+        # if shit > 1000:
+        #    raise RecursionError("SHIT")
+        q = r // nr
+        r, nr = nr, (r - q * nr)
+        t, nt = nt, (t - q * nt)
+        # print(t, nt, r, nr)
+    if r > 1:
+        raise ValueError("base is not invertible for the given modulus")
+    if t < 0:
+        return t + n
+    return t
+
+
+def fahhh(x, e, n):
+    "only works for this specific thing"
+    eb = f"{e:b}"
+    print(f"x^H mod n = {x}^{e} mod {n}")
+    print()
+    print(f"H = {e}_10 = {eb}_2")
+    print(
+        ",\n".join(reversed([f"h_{i} = {ie}_2" for i, ie in enumerate(reversed(eb))]))
+    )
+    r = x
+    ee = 1
+    print()
+    print(f"x = x^{{{eb[0]}_2}}")
+    print(f"h_{len(eb)-1} = {eb[0]}")
+    print()
+    print(f"r <- {x = }")
+    print()
+    for ie, i in zip(range(len(eb) - 2, -1, -1), eb[1:]):
+        print(f"(x^{ee})^2 = x^{2*ee} = x^{{{2*ee:b}_2}}")
+        print(f"SQ, h_{ie}")
+        print()
+        ee *= 2
+        r *= r
+        print(f"r <- r*r = {r}")
+        print(f"r <- r mod n = {r%n}")
+        r %= n
+        print()
+        if int(i):
+            print(f"x^{ee}*x = x^{ee+1} = x^{{{ee+1:b}_2}}")
+            print(f"MUL, h_{ie} = 1")
+            print()
+            ee += 1
+            r *= x
+            print(f"r <- r * x = {r}")
+            print(f"r <- r mod n = {r%n}")
+            r %= n
+        else:
+            print(f"h_{ie} = 0")
+        print()
+    print(f"x^H mod n = {x}^{e} mod {n} = {r}")
+    return r
+
+
+if __name__ == "__main__":
+    print("#1:", f"{gcd(52698, 61430) = }")
+    E2 = {
+        290345,
+        218585,
+        143231,
+        164172,
+        155768,
+        423151,
+        239707,
+        153544,
+        287390,
+        480837,
+    }
+    print("#2:", *(f"gcd({m}, {n}) = {gcd(m,n)}" for m, n in cooked(E2)), sep="\n")
+    print("#3:")
+    fahhh(856, 25, 7)
+    print(f"{pow(856, 25, 7) = }")
+    print("#4:", f"{inv(65537, 35256) = }")
+