diff --git a/py-scripts/speedup_curvemult.py b/py-scripts/speedup_curvemult.py
index 1589a40..18d48af 100644
--- a/py-scripts/speedup_curvemult.py
+++ b/py-scripts/speedup_curvemult.py
@@ -11,21 +11,21 @@
 import random
 import time
 
-from btclib.ecc.curve import secp256k1 as ec
-from btclib.curvegroup import (
+from btclib.ec.curve import secp256k1 as ec
+from btclib.ec.curve_group import (
     _mult,
-    _mult_base_3,
-    _mult_fixed_window,
-    _mult_fixed_window_cached,
-    _mult_jac,
-    _mult_mont_ladder,
+    mult_base_3,
+    mult_fixed_window,
+    mult_fixed_window_cached,
+    mult_jac,
+    mult_mont_ladder,
     cached_multiples,
     cached_multiples_fixwind,
 )
-from btclib.curvegroup2 import (
-    _mult_endomorphism_secp256k1,
-    _mult_sliding_window,
-    _mult_w_NAF,
+from btclib.ec.curve_group_2 import (
+    mult_endomorphism_secp256k1,
+    mult_sliding_window,
+    mult_w_NAF,
 )
 
 # setup
@@ -47,14 +47,14 @@
 T = ec.GJ
 start = time.time()
 for q in qs:
-    T = _mult_jac(q, ec.GJ, ec) if gen_only else _mult_jac(q, T, ec)
+    T = mult_jac(q, ec.GJ, ec) if gen_only else mult_jac(q, T, ec)
 double_and_add = time.time() - start
 print(f"Double & add     : {double_and_add / benchmark:.0%}")
 
 T = ec.GJ
 start = time.time()
 for q in qs:
-    T = _mult_mont_ladder(q, ec.GJ, ec) if gen_only else _mult_mont_ladder(q, T, ec)
+    T = mult_mont_ladder(q, ec.GJ, ec) if gen_only else mult_mont_ladder(q, T, ec)
 montgomery = time.time() - start
 print(f"Montgomery ladder: {montgomery / benchmark:.0%}")
 
@@ -63,7 +63,7 @@
 T = ec.GJ
 start = time.time()
 for q in qs:
-    T = _mult_base_3(q, ec.GJ, ec) if gen_only else _mult_base_3(q, T, ec)
+    T = mult_base_3(q, ec.GJ, ec) if gen_only else mult_base_3(q, T, ec)
 base3 = time.time() - start
 print(f"Base 3           : {base3 / benchmark:.0%}", cached_multiples.cache_info())
 
@@ -75,9 +75,9 @@
 start = time.time()
 for q in qs:
     T = (
-        _mult_fixed_window(q, ec.GJ, ec, w, cached)
+        mult_fixed_window(q, ec.GJ, ec, w, cached)
         if gen_only
-        else _mult_fixed_window(q, T, ec, w, cached)
+        else mult_fixed_window(q, T, ec, w, cached)
     )
 fixed_window_4 = time.time() - start
 print(
@@ -93,9 +93,9 @@
 start = time.time()
 for q in qs:
     T = (
-        _mult_fixed_window(q, ec.GJ, ec, w, cached)
+        mult_fixed_window(q, ec.GJ, ec, w, cached)
         if gen_only
-        else _mult_fixed_window(q, T, ec, w, cached)
+        else mult_fixed_window(q, T, ec, w, cached)
     )
 fixed_window_5 = time.time() - start
 print(
@@ -111,9 +111,9 @@
 start = time.time()
 for q in qs:
     T = (
-        _mult_fixed_window(q, ec.GJ, ec, w, cached)
+        mult_fixed_window(q, ec.GJ, ec, w, cached)
         if gen_only
-        else _mult_fixed_window(q, T, ec, w, cached)
+        else mult_fixed_window(q, T, ec, w, cached)
     )
 fixed_window_4_ca = time.time() - start
 print(
@@ -129,9 +129,9 @@
 start = time.time()
 for q in qs:
     T = (
-        _mult_fixed_window(q, ec.GJ, ec, w, cached)
+        mult_fixed_window(q, ec.GJ, ec, w, cached)
         if gen_only
-        else _mult_fixed_window(q, T, ec, w, cached)
+        else mult_fixed_window(q, T, ec, w, cached)
     )
 fixed_window_5_ca = time.time() - start
 print(
@@ -145,9 +145,9 @@
 start = time.time()
 for q in qs:
     T = (
-        _mult_fixed_window_cached(q, ec.GJ, ec)
+        mult_fixed_window_cached(q, ec.GJ, ec)
         if gen_only
-        else _mult_fixed_window_cached(q, T, ec)
+        else mult_fixed_window_cached(q, T, ec)
     )
 fixed_window_cached = time.time() - start
 print(
@@ -162,9 +162,9 @@
 start = time.time()
 for q in qs:
     T = (
-        _mult_sliding_window(q, ec.GJ, ec, 5)
+        mult_sliding_window(q, ec.GJ, ec, 5)
         if gen_only
-        else _mult_sliding_window(q, T, ec, w)
+        else mult_sliding_window(q, T, ec, w)
     )
 sliding_window_4 = time.time() - start
 print(
@@ -179,9 +179,9 @@
 start = time.time()
 for q in qs:
     T = (
-        _mult_sliding_window(q, ec.GJ, ec, 5)
+        mult_sliding_window(q, ec.GJ, ec, 5)
         if gen_only
-        else _mult_sliding_window(q, T, ec, w)
+        else mult_sliding_window(q, T, ec, w)
     )
 sliding_window_5 = time.time() - start
 print(
@@ -195,7 +195,7 @@
 w = 4
 start = time.time()
 for q in qs:
-    T = _mult_w_NAF(q, ec.GJ, ec, 4) if gen_only else _mult_w_NAF(q, T, ec, w)
+    T = mult_w_NAF(q, ec.GJ, ec, 4) if gen_only else _mult_w_NAF(q, T, ec, w)
 wNAF_4 = time.time() - start
 print(f"wNAF 4           : {wNAF_4 / benchmark:.0%}", cached_multiples.cache_info())
 
@@ -205,7 +205,7 @@
 w = 5
 start = time.time()
 for q in qs:
-    T = _mult_w_NAF(q, ec.GJ, ec, 4) if gen_only else _mult_w_NAF(q, T, ec, w)
+    T = mult_w_NAF(q, ec.GJ, ec, 4) if gen_only else mult_w_NAF(q, T, ec, w)
 wNAF_5 = time.time() - start
 print(f"wNAF 5           : {wNAF_5 / benchmark:.0%}", cached_multiples.cache_info())
 
@@ -214,7 +214,7 @@
 start = time.time()
 for q in qs:
     T = (
-        _mult_endomorphism_secp256k1(q, ec.GJ, ec)
+        mult_endomorphism_secp256k1(q, ec.GJ, ec)
         if gen_only
         else _mult_endomorphism_secp256k1(q, T, ec)
     )
diff --git a/py-scripts/speedup_doubleandadd.py b/py-scripts/speedup_doubleandadd.py
index e22fb6b..3c05a13 100644
--- a/py-scripts/speedup_doubleandadd.py
+++ b/py-scripts/speedup_doubleandadd.py
@@ -11,45 +11,45 @@
 import random
 import time
 
-from btclib.ecc.curve import secp256k1 as ec
-from btclib.curvegroup import (
-    _mult_aff,
-    _mult_jac,
-    _mult_recursive_aff,
-    _mult_recursive_jac,
+from btclib.ec.curve import secp256k1 as ec
+from btclib.ec.curve_group import (
+    mult_aff,
+    mult_jac,
+    mult_recursive_aff,
+    mult_recursive_jac,
 )
 
 # setup
-random.seed(42)
+random.seed(350746)
 qs = [random.getrandbits(ec.nlen) % ec.n for _ in range(100)]
 
 start = time.time()
 for q in qs:
     # starts from affine coordinates, ends with affine coordinates
-    ec._aff_from_jac(_mult_jac(q, ec.GJ, ec))
+    ec.aff_from_jac(mult_jac(q, ec.GJ, ec))
 benchmark = time.time() - start
 print("Benchmark completed")
 
 start = time.time()
 for q in qs:
-    _mult_recursive_aff(q, ec.G, ec)
+    mult_recursive_aff(q, ec.G, ec)
 recursive_aff = time.time() - start
 print(f"Recursive aff       : {recursive_aff / benchmark:.0%}")
 
 start = time.time()
 for q in qs:
-    ec._aff_from_jac(_mult_recursive_jac(q, ec.GJ, ec))
+    ec.aff_from_jac(mult_recursive_jac(q, ec.GJ, ec))
 recursive_jac = time.time() - start
 print(f"Recursive jac       : {recursive_jac / benchmark:.0%}")
 
 start = time.time()
 for q in qs:
-    _mult_aff(q, ec.G, ec)
+    mult_aff(q, ec.G, ec)
 double_add_aff = time.time() - start
 print(f"Double and add aff  : {double_add_aff / benchmark:.0%}")
 
 start = time.time()
 for q in qs:
-    ec._aff_from_jac(_mult_jac(q, ec.GJ, ec))
+    ec.aff_from_jac(mult_jac(q, ec.GJ, ec))
 double_add_jac = time.time() - start
 print(f"Double and add jac  : {double_add_jac / benchmark:.0%}")
diff --git a/py-scripts/speedup_fixwind.py b/py-scripts/speedup_fixwind.py
index 06d780b..21f92d3 100644
--- a/py-scripts/speedup_fixwind.py
+++ b/py-scripts/speedup_fixwind.py
@@ -11,12 +11,12 @@
 import random
 import time
 
-from btclib.ecc.curve import secp256k1 as ec
-from btclib.curvegroup import (
-    _mult_base_3,
-    _mult_fixed_window,
-    _mult_jac,
-    _mult_mont_ladder,
+from btclib.ec.curve import secp256k1 as ec
+from btclib.ec.curve_group import (
+    mult_base_3,
+    mult_fixed_window,
+    mult_jac,
+    mult_mont_ladder,
 )
 
 # setup
@@ -27,28 +27,28 @@
 T = ec.GJ
 start = time.time()
 for q in qs:
-    T = _mult_jac(q, T, ec)
+    T = mult_jac(q, T, ec)
 benchmark = time.time() - start
 print("Benchmark completed")
 
 T = ec.GJ
 start = time.time()
 for q in qs:
-    T = _mult_jac(q, T, ec)
+    T = mult_jac(q, T, ec)
 double_and_add = time.time() - start
 print(f"Double & add     : {double_and_add / benchmark:.0%}")
 
 T = ec.GJ
 start = time.time()
 for q in qs:
-    T = _mult_mont_ladder(q, T, ec)
+    T = mult_mont_ladder(q, T, ec)
 montgomery = time.time() - start
 print(f"Montgomery ladder: {montgomery / benchmark:.0%}")
 
 T = ec.GJ
 start = time.time()
 for q in qs:
-    T = _mult_base_3(q, T, ec)
+    T = mult_base_3(q, T, ec)
 base3 = time.time() - start
 print(f"Base 3           : {base3 / benchmark:.0%}")
 
@@ -56,7 +56,7 @@
 w = 4
 start = time.time()
 for q in qs:
-    T = _mult_fixed_window(q, T, ec, w)
+    T = mult_fixed_window(q, T, ec, w)
 fixed_window_4 = time.time() - start
 print(f"Fixed window 4   : {fixed_window_4 / benchmark:.0%}")
 
@@ -64,6 +64,6 @@
 w = 5
 start = time.time()
 for q in qs:
-    T = _mult_fixed_window(q, T, ec, w)
+    T = mult_fixed_window(q, T, ec, w)
 fixed_window_5 = time.time() - start
 print(f"Fixed window 5   : {fixed_window_5 / benchmark:.0%}")
diff --git a/py-scripts/speedup_jacobian.py b/py-scripts/speedup_jacobian.py
index 40a1233..cbae549 100644
--- a/py-scripts/speedup_jacobian.py
+++ b/py-scripts/speedup_jacobian.py
@@ -11,8 +11,8 @@
 import random
 import time
 
-from btclib.ecc.curve import secp256k1 as ec
-from btclib.curvegroup import _mult_aff, _mult_jac
+from btclib.ec.curve import secp256k1 as ec
+from btclib.ec.curve_group import mult_aff, mult_jac
 
 random.seed(42)
 
@@ -20,13 +20,13 @@
 qs = [random.getrandbits(ec.nlen) % ec.n for _ in range(50)]
 start = time.time()
 for q in qs:
-    _mult_aff(q, ec.G, ec)
+    mult_aff(q, ec.G, ec)
 elapsed1 = time.time() - start
 
 start = time.time()
 for q in qs:
     # starts from affine coordinates, ends with affine coordinates
-    ec._aff_from_jac(_mult_jac(q, ec.GJ, ec))
+    ec.aff_from_jac(mult_jac(q, ec.GJ, ec))
 elapsed2 = time.time() - start
 
 print(elapsed2 / elapsed1)
diff --git a/py-scripts/speedup_shamir.py b/py-scripts/speedup_shamir.py
index 1b6d47a..f688b45 100644
--- a/py-scripts/speedup_shamir.py
+++ b/py-scripts/speedup_shamir.py
@@ -11,8 +11,9 @@
 import random
 import time
 
-from btclib.ecc.curve import secp256k1 as ec
-from btclib.curvegroup import _double_mult, _mult
+from btclib.ec.curve import secp256k1 as ec
+from btclib.ec.curve_group import _mult, _double_mult
+from btclib.ec.curve import mult, double_mult
 
 random.seed(42)
 
@@ -35,7 +36,7 @@
 
 start = time.time()
 for u, v, QJ in zip(us, vs, QJs):
-    ec._add_jac(_mult(u, ec.GJ, ec), _mult(v, QJ, ec))
+    ec.add_jac(_mult(u, ec.GJ, ec), _mult(v, QJ, ec))
 elapsed1 = time.time() - start
 
 start = time.time()