diff --git a/plutus-conformance/agda/Spec.hs b/plutus-conformance/agda/Spec.hs
index b64664904c6..e8008b9159f 100644
--- a/plutus-conformance/agda/Spec.hs
+++ b/plutus-conformance/agda/Spec.hs
@@ -62,15 +62,19 @@ failingTests = [
      , "bls12_381_G1_equal/equal-false"
      , "bls12_381_G1_equal/equal-true"
      , "bls12_381_G1_hashToCurve/hash"
-     , "bls12_381_G1_mul/mul0"
-     , "bls12_381_G1_mul/mul4x11"
-     , "bls12_381_G1_mul/muladd"
-     , "bls12_381_G1_mul/mul1"
-     , "bls12_381_G1_mul/mul44"
-     , "bls12_381_G1_mul/addmul"
-     , "bls12_381_G1_mul/mulneg44"
-     , "bls12_381_G1_mul/mul19+25"
-     , "bls12_381_G1_mul/mulneg1"
+     , "bls12_381_G1_scalarMul/mul0"
+     , "bls12_381_G1_scalarMul/mul4x11"
+     , "bls12_381_G1_scalarMul/muladd"
+     , "bls12_381_G1_scalarMul/mul1"
+     , "bls12_381_G1_scalarMul/mul44"
+     , "bls12_381_G1_scalarMul/addmul"
+     , "bls12_381_G1_scalarMul/mulneg44"
+     , "bls12_381_G1_scalarMul/mul19+25"
+     , "bls12_381_G1_scalarMul/mulneg1"
+     , "bls12_381_G1_scalarMul/mulperiodic1"
+     , "bls12_381_G1_scalarMul/mulperiodic2"
+     , "bls12_381_G1_scalarMul/mulperiodic3"
+     , "bls12_381_G1_scalarMul/mulperiodic4"
      , "bls12_381_G1_neg/neg"
      , "bls12_381_G1_neg/add-neg"
      , "bls12_381_G1_neg/neg-zero"
@@ -93,15 +97,19 @@ failingTests = [
      , "bls12_381_G2_equal/equal-false"
      , "bls12_381_G2_equal/equal-true"
      , "bls12_381_G2_hashToCurve/hash"
-     , "bls12_381_G2_mul/mul0"
-     , "bls12_381_G2_mul/mul4x11"
-     , "bls12_381_G2_mul/muladd"
-     , "bls12_381_G2_mul/mul1"
-     , "bls12_381_G2_mul/mul44"
-     , "bls12_381_G2_mul/addmul"
-     , "bls12_381_G2_mul/mulneg44"
-     , "bls12_381_G2_mul/mul19+25"
-     , "bls12_381_G2_mul/mulneg1"
+     , "bls12_381_G2_scalarMul/mul0"
+     , "bls12_381_G2_scalarMul/mul4x11"
+     , "bls12_381_G2_scalarMul/muladd"
+     , "bls12_381_G2_scalarMul/mul1"
+     , "bls12_381_G2_scalarMul/mul44"
+     , "bls12_381_G2_scalarMul/addmul"
+     , "bls12_381_G2_scalarMul/mulneg44"
+     , "bls12_381_G2_scalarMul/mul19+25"
+     , "bls12_381_G2_scalarMul/mulneg1"
+     , "bls12_381_G2_scalarMul/mulperiodic1"
+     , "bls12_381_G2_scalarMul/mulperiodic2"
+     , "bls12_381_G2_scalarMul/mulperiodic3"
+     , "bls12_381_G2_scalarMul/mulperiodic4"
      , "bls12_381_G2_neg/neg"
      , "bls12_381_G2_neg/add-neg"
      , "bls12_381_G2_neg/neg-zero"
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/addmul/addmul.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/addmul/addmul.uplc
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/addmul/addmul.uplc
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/addmul/addmul.uplc
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/addmul/addmul.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/addmul/addmul.uplc.expected
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/addmul/addmul.uplc.expected
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/addmul/addmul.uplc.expected
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mul0/mul0.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mul0/mul0.uplc
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mul0/mul0.uplc
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mul0/mul0.uplc
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mul0/mul0.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mul0/mul0.uplc.expected
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mul0/mul0.uplc.expected
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mul0/mul0.uplc.expected
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mul1/mul1.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mul1/mul1.uplc
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mul1/mul1.uplc
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mul1/mul1.uplc
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mul1/mul1.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mul1/mul1.uplc.expected
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mul1/mul1.uplc.expected
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mul1/mul1.uplc.expected
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mul19+25/mul19+25.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mul19+25/mul19+25.uplc
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mul19+25/mul19+25.uplc
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mul19+25/mul19+25.uplc
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mul19+25/mul19+25.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mul19+25/mul19+25.uplc.expected
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mul19+25/mul19+25.uplc.expected
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mul19+25/mul19+25.uplc.expected
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mul44/mul44.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mul44/mul44.uplc
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mul44/mul44.uplc
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mul44/mul44.uplc
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mul44/mul44.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mul44/mul44.uplc.expected
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mul44/mul44.uplc.expected
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mul44/mul44.uplc.expected
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mul4x11/mul4x11.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mul4x11/mul4x11.uplc
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mul4x11/mul4x11.uplc
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mul4x11/mul4x11.uplc
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mul4x11/mul4x11.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mul4x11/mul4x11.uplc.expected
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mul4x11/mul4x11.uplc.expected
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mul4x11/mul4x11.uplc.expected
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/muladd/muladd.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/muladd/muladd.uplc
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/muladd/muladd.uplc
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/muladd/muladd.uplc
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/muladd/muladd.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/muladd/muladd.uplc.expected
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/muladd/muladd.uplc.expected
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/muladd/muladd.uplc.expected
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mulneg1/mulneg1.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulneg1/mulneg1.uplc
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mulneg1/mulneg1.uplc
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulneg1/mulneg1.uplc
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mulneg1/mulneg1.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulneg1/mulneg1.uplc.expected
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mulneg1/mulneg1.uplc.expected
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulneg1/mulneg1.uplc.expected
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mulneg44/mulneg44.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulneg44/mulneg44.uplc
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mulneg44/mulneg44.uplc
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulneg44/mulneg44.uplc
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mulneg44/mulneg44.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulneg44/mulneg44.uplc.expected
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_mul/mulneg44/mulneg44.uplc.expected
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulneg44/mulneg44.uplc.expected
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic1/mulperiodic1.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic1/mulperiodic1.uplc
new file mode 100644
index 00000000000..974dc102591
--- /dev/null
+++ b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic1/mulperiodic1.uplc
@@ -0,0 +1,13 @@
+-- Scalar multiplication by the group size should give you the zero element of the group.
+(program 1.0.0
+[
+ [ (builtin bls12_381_G1_equal)
+  [
+   (builtin bls12_381_G1_scalarMul)
+   (con integer 52435875175126190479447740508185965837690552500527637822603658699938581184513 )
+   (con bls12_381_G1_element 0xabd61864f519748032551e42e0ac417fd828f079454e3e3c9891c5c29ed7f10bdecc046854e3931cb7002779bd76d71f)
+  ]
+ ]
+ (con bls12_381_G1_element 0xc00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)  
+]
+)
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic1/mulperiodic1.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic1/mulperiodic1.uplc.expected
new file mode 100644
index 00000000000..3760fc7a698
--- /dev/null
+++ b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic1/mulperiodic1.uplc.expected
@@ -0,0 +1 @@
+(program 1.0.0 (con bool True))
\ No newline at end of file
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic2/mulperiodic2.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic2/mulperiodic2.uplc
new file mode 100644
index 00000000000..8b0277589cc
--- /dev/null
+++ b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic2/mulperiodic2.uplc
@@ -0,0 +1,23 @@
+-- Scalar multiplication should be periodic modulo the group size
+(program 1.0.0
+ [
+  [
+   (builtin bls12_381_G1_equal)
+   [
+    [
+     (builtin bls12_381_G1_scalarMul)
+     [
+      [ (builtin addInteger) (con integer 123) ]
+      (con integer 52435875175126190479447740508185965837690552500527637822603658699938581184513)
+     ]
+    ]
+   (con bls12_381_G1_element 0xabd61864f519748032551e42e0ac417fd828f079454e3e3c9891c5c29ed7f10bdecc046854e3931cb7002779bd76d71f)
+   ]
+  ]
+  [
+   [ (builtin bls12_381_G1_scalarMul) (con integer 123) ]
+   (con bls12_381_G1_element 0xabd61864f519748032551e42e0ac417fd828f079454e3e3c9891c5c29ed7f10bdecc046854e3931cb7002779bd76d71f)
+  ]
+ ]
+)
+
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic2/mulperiodic2.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic2/mulperiodic2.uplc.expected
new file mode 100644
index 00000000000..3760fc7a698
--- /dev/null
+++ b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic2/mulperiodic2.uplc.expected
@@ -0,0 +1 @@
+(program 1.0.0 (con bool True))
\ No newline at end of file
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic3/mulperiodic3.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic3/mulperiodic3.uplc
new file mode 100644
index 00000000000..8aeb4591ce8
--- /dev/null
+++ b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic3/mulperiodic3.uplc
@@ -0,0 +1,27 @@
+-- Scalar multiplication should be periodic modulo the group size
+(program
+ 1.0.0
+ [
+  [
+   (builtin bls12_381_G1_equal)
+   [
+    [
+     (builtin bls12_381_G1_scalarMul)
+     [
+      [ (builtin addInteger) (con integer 123) ]
+      [
+       [ (builtin multiplyInteger) (con integer 987654321) ]
+       (con integer 52435875175126190479447740508185965837690552500527637822603658699938581184513)
+      ]
+     ]
+    ]
+   (con bls12_381_G1_element 0xabd61864f519748032551e42e0ac417fd828f079454e3e3c9891c5c29ed7f10bdecc046854e3931cb7002779bd76d71f)
+   ]
+  ]
+  [
+   [ (builtin bls12_381_G1_scalarMul) (con integer 123) ]
+   (con bls12_381_G1_element 0xabd61864f519748032551e42e0ac417fd828f079454e3e3c9891c5c29ed7f10bdecc046854e3931cb7002779bd76d71f)
+  ]
+ ]
+)
+
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic3/mulperiodic3.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic3/mulperiodic3.uplc.expected
new file mode 100644
index 00000000000..3760fc7a698
--- /dev/null
+++ b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic3/mulperiodic3.uplc.expected
@@ -0,0 +1 @@
+(program 1.0.0 (con bool True))
\ No newline at end of file
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic4/mulperiodic4.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic4/mulperiodic4.uplc
new file mode 100644
index 00000000000..250e6fa3711
--- /dev/null
+++ b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic4/mulperiodic4.uplc
@@ -0,0 +1,27 @@
+-- Scalar multiplication should be periodic modulo the group size
+(program
+ 1.0.0
+ [
+  [
+   (builtin bls12_381_G1_equal)
+   [
+    [
+     (builtin bls12_381_G1_scalarMul)
+     [
+      [ (builtin addInteger) (con integer 123) ]
+      [
+       [ (builtin multiplyInteger) (con integer -987654321) ]
+       (con integer 52435875175126190479447740508185965837690552500527637822603658699938581184513)
+      ]
+     ]
+    ]
+   (con bls12_381_G1_element 0xabd61864f519748032551e42e0ac417fd828f079454e3e3c9891c5c29ed7f10bdecc046854e3931cb7002779bd76d71f)
+   ]
+  ]
+  [
+   [ (builtin bls12_381_G1_scalarMul) (con integer 123) ]
+   (con bls12_381_G1_element 0xabd61864f519748032551e42e0ac417fd828f079454e3e3c9891c5c29ed7f10bdecc046854e3931cb7002779bd76d71f)
+  ]
+ ]
+)
+
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic4/mulperiodic4.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic4/mulperiodic4.uplc.expected
new file mode 100644
index 00000000000..3760fc7a698
--- /dev/null
+++ b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G1_scalarMul/mulperiodic4/mulperiodic4.uplc.expected
@@ -0,0 +1 @@
+(program 1.0.0 (con bool True))
\ No newline at end of file
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/addmul/addmul.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/addmul/addmul.uplc
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/addmul/addmul.uplc
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/addmul/addmul.uplc
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/addmul/addmul.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/addmul/addmul.uplc.expected
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/addmul/addmul.uplc.expected
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/addmul/addmul.uplc.expected
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mul0/mul0.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mul0/mul0.uplc
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mul0/mul0.uplc
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mul0/mul0.uplc
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mul0/mul0.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mul0/mul0.uplc.expected
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mul0/mul0.uplc.expected
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mul0/mul0.uplc.expected
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mul1/mul1.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mul1/mul1.uplc
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mul1/mul1.uplc
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mul1/mul1.uplc
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mul1/mul1.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mul1/mul1.uplc.expected
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mul1/mul1.uplc.expected
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mul1/mul1.uplc.expected
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mul19+25/mul19+25.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mul19+25/mul19+25.uplc
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mul19+25/mul19+25.uplc
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mul19+25/mul19+25.uplc
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mul19+25/mul19+25.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mul19+25/mul19+25.uplc.expected
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mul19+25/mul19+25.uplc.expected
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mul19+25/mul19+25.uplc.expected
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mul44/mul44.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mul44/mul44.uplc
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mul44/mul44.uplc
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mul44/mul44.uplc
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mul44/mul44.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mul44/mul44.uplc.expected
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mul44/mul44.uplc.expected
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mul44/mul44.uplc.expected
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mul4x11/mul4x11.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mul4x11/mul4x11.uplc
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mul4x11/mul4x11.uplc
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mul4x11/mul4x11.uplc
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mul4x11/mul4x11.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mul4x11/mul4x11.uplc.expected
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mul4x11/mul4x11.uplc.expected
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mul4x11/mul4x11.uplc.expected
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/muladd/muladd.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/muladd/muladd.uplc
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/muladd/muladd.uplc
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/muladd/muladd.uplc
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/muladd/muladd.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/muladd/muladd.uplc.expected
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/muladd/muladd.uplc.expected
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/muladd/muladd.uplc.expected
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mulneg1/mulneg1.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulneg1/mulneg1.uplc
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mulneg1/mulneg1.uplc
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulneg1/mulneg1.uplc
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mulneg1/mulneg1.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulneg1/mulneg1.uplc.expected
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mulneg1/mulneg1.uplc.expected
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulneg1/mulneg1.uplc.expected
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mulneg44/mulneg44.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulneg44/mulneg44.uplc
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mulneg44/mulneg44.uplc
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulneg44/mulneg44.uplc
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mulneg44/mulneg44.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulneg44/mulneg44.uplc.expected
similarity index 100%
rename from plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_mul/mulneg44/mulneg44.uplc.expected
rename to plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulneg44/mulneg44.uplc.expected
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic1/mulperiodic1.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic1/mulperiodic1.uplc
new file mode 100644
index 00000000000..b9c3fc157d1
--- /dev/null
+++ b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic1/mulperiodic1.uplc
@@ -0,0 +1,14 @@
+-- Scalar multiplication by the group size should give you the zero element of the group.
+(program 1.0.0
+[
+ [ (builtin bls12_381_G2_equal)
+  [
+   (builtin bls12_381_G2_scalarMul)
+   (con integer 52435875175126190479447740508185965837690552500527637822603658699938581184513 )
+   (con bls12_381_G2_element 0xb0629fa1158c2d23a10413fe91d381a84d25e31d041cd0377d25828498fd02011b35893938ced97535395e4815201e67108bcd4665e0db25d602d76fa791fab706c54abf5e1a9e44b4ac1e6badf3d2ac0328f5e30be341677c8bac5dda7682f1)
+  ]
+ ]
+ (con bls12_381_G2_element
+  0xc00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)
+]
+)
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic1/mulperiodic1.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic1/mulperiodic1.uplc.expected
new file mode 100644
index 00000000000..3760fc7a698
--- /dev/null
+++ b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic1/mulperiodic1.uplc.expected
@@ -0,0 +1 @@
+(program 1.0.0 (con bool True))
\ No newline at end of file
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic2/mulperiodic2.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic2/mulperiodic2.uplc
new file mode 100644
index 00000000000..134e98d0951
--- /dev/null
+++ b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic2/mulperiodic2.uplc
@@ -0,0 +1,26 @@
+-- Scalar multiplication should be periodic modulo the group size
+(program
+ 1.0.0
+ [
+  [
+   (builtin bls12_381_G2_equal)
+   [
+    [
+     (builtin bls12_381_G2_scalarMul)
+     [
+      [ (builtin addInteger) (con integer 123) ]
+      (con integer 52435875175126190479447740508185965837690552500527637822603658699938581184513)
+     ]
+    ]
+    (con bls12_381_G2_element
+     0xb0629fa1158c2d23a10413fe91d381a84d25e31d041cd0377d25828498fd02011b35893938ced97535395e4815201e67108bcd4665e0db25d602d76fa791fab706c54abf5e1a9e44b4ac1e6badf3d2ac0328f5e30be341677c8bac5dda7682f1)
+   ]
+  ]
+  [
+   [ (builtin bls12_381_G2_scalarMul) (con integer 123) ]
+   (con bls12_381_G2_element
+    0xb0629fa1158c2d23a10413fe91d381a84d25e31d041cd0377d25828498fd02011b35893938ced97535395e4815201e67108bcd4665e0db25d602d76fa791fab706c54abf5e1a9e44b4ac1e6badf3d2ac0328f5e30be341677c8bac5dda7682f1)
+  ]
+ ]
+)
+
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic2/mulperiodic2.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic2/mulperiodic2.uplc.expected
new file mode 100644
index 00000000000..3760fc7a698
--- /dev/null
+++ b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic2/mulperiodic2.uplc.expected
@@ -0,0 +1 @@
+(program 1.0.0 (con bool True))
\ No newline at end of file
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic3/mulperiodic3.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic3/mulperiodic3.uplc
new file mode 100644
index 00000000000..0218e35941e
--- /dev/null
+++ b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic3/mulperiodic3.uplc
@@ -0,0 +1,29 @@
+-- Scalar multiplication should be periodic modulo the group size
+(program
+ 1.0.0
+ [
+  [
+   (builtin bls12_381_G2_equal)
+   [
+    [
+     (builtin bls12_381_G2_scalarMul)
+     [
+      [ (builtin addInteger) (con integer 123) ]
+      [
+       [ (builtin multiplyInteger) (con integer 987654321) ]
+       (con integer 52435875175126190479447740508185965837690552500527637822603658699938581184513)
+      ]
+     ]
+    ]
+    (con bls12_381_G2_element
+     0xb0629fa1158c2d23a10413fe91d381a84d25e31d041cd0377d25828498fd02011b35893938ced97535395e4815201e67108bcd4665e0db25d602d76fa791fab706c54abf5e1a9e44b4ac1e6badf3d2ac0328f5e30be341677c8bac5dda7682f1)
+   ]
+  ]
+  [
+   [ (builtin bls12_381_G2_scalarMul) (con integer 123) ]
+   (con bls12_381_G2_element
+    0xb0629fa1158c2d23a10413fe91d381a84d25e31d041cd0377d25828498fd02011b35893938ced97535395e4815201e67108bcd4665e0db25d602d76fa791fab706c54abf5e1a9e44b4ac1e6badf3d2ac0328f5e30be341677c8bac5dda7682f1)
+  ]
+ ]
+)
+
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic3/mulperiodic3.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic3/mulperiodic3.uplc.expected
new file mode 100644
index 00000000000..3760fc7a698
--- /dev/null
+++ b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic3/mulperiodic3.uplc.expected
@@ -0,0 +1 @@
+(program 1.0.0 (con bool True))
\ No newline at end of file
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic4/mulperiodic4.uplc b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic4/mulperiodic4.uplc
new file mode 100644
index 00000000000..5bb2845d8d9
--- /dev/null
+++ b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic4/mulperiodic4.uplc
@@ -0,0 +1,29 @@
+-- Scalar multiplication should be periodic modulo the group size
+(program
+ 1.0.0
+ [
+  [
+   (builtin bls12_381_G2_equal)
+   [
+    [
+     (builtin bls12_381_G2_scalarMul)
+     [
+      [ (builtin addInteger) (con integer 123) ]
+      [
+       [ (builtin multiplyInteger) (con integer -987654321) ]
+       (con integer 52435875175126190479447740508185965837690552500527637822603658699938581184513)
+      ]
+     ]
+    ]
+    (con bls12_381_G2_element
+     0xb0629fa1158c2d23a10413fe91d381a84d25e31d041cd0377d25828498fd02011b35893938ced97535395e4815201e67108bcd4665e0db25d602d76fa791fab706c54abf5e1a9e44b4ac1e6badf3d2ac0328f5e30be341677c8bac5dda7682f1)
+   ]
+  ]
+  [
+   [ (builtin bls12_381_G2_scalarMul) (con integer 123) ]
+   (con bls12_381_G2_element
+    0xb0629fa1158c2d23a10413fe91d381a84d25e31d041cd0377d25828498fd02011b35893938ced97535395e4815201e67108bcd4665e0db25d602d76fa791fab706c54abf5e1a9e44b4ac1e6badf3d2ac0328f5e30be341677c8bac5dda7682f1)
+  ]
+ ]
+)
+
diff --git a/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic4/mulperiodic4.uplc.expected b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic4/mulperiodic4.uplc.expected
new file mode 100644
index 00000000000..3760fc7a698
--- /dev/null
+++ b/plutus-conformance/test-cases/uplc/evaluation/builtin/semantics/bls12_381_G2_scalarMul/mulperiodic4/mulperiodic4.uplc.expected
@@ -0,0 +1 @@
+(program 1.0.0 (con bool True))
\ No newline at end of file