diff --git a/FIXED_POINT_ANALYSIS.md b/FIXED_POINT_ANALYSIS.md
index 3558a29..0d2bbb9 100644
--- a/FIXED_POINT_ANALYSIS.md
+++ b/FIXED_POINT_ANALYSIS.md
@@ -11,7 +11,7 @@ Fixed-point multiplication uses precomputed multiples of the secp256k1 generator
 
 These precomputed values are stored in `test/ecdsa_constants.h` as `G1_1_G1SECP256K1.SIG_AFF[]` and loaded into device constant memory `ECDSACONST.d_mul_table[]` during `initialize()`.
 
-**The problem**: The batch kernel `arith::fixedPMulByCombinedDAA` expects R1 to contain these precomputed multiples, but the current test calls `ec_pmul_random_init()` which overwrites R1 with input points instead.
+**The problem**: The batch kernel `arith::fixedPMulByCombinedDAA` expects R1 to contain these precomputed multiples, but the current test calls `ec_pmul_init()` which overwrites R1 with input points instead.
 
 ## Two Fixed-Point Implementations
 
@@ -50,9 +50,9 @@ __global__ void fixedPMulByCombinedDAA(typename EC::Base *R0,
 
 ```cpp
 // test/ecdsa_ec_fixed_pmul.cu
-solver.ec_pmul_random_init(RANDOM_S, RANDOM_KEY_X, RANDOM_KEY_Y, count);
+solver.ec_pmul_init(RANDOM_S, RANDOM_KEY_X, RANDOM_KEY_Y, count);
                            ↓
-// include/gecc/ecdsa/gsv.h:ec_pmul_random_init()
+// include/gecc/ecdsa/gsv.h:ec_pmul_init()
 processScalarPoint<<<>>>(..., R1, ...);  // ← Fills R1 with input points (WRONG!)
                            ↓
 solver.ecdsa_ec_pmul(MAX_SM_NUMS, 256, false);  // false = fixed-point
diff --git a/FIXED_POINT_SOLUTION.md b/FIXED_POINT_SOLUTION.md
index 8c42444..4931cf9 100644
--- a/FIXED_POINT_SOLUTION.md
+++ b/FIXED_POINT_SOLUTION.md
@@ -4,7 +4,7 @@
 The fixed-point multiplication test in `test/ecdsa_ec_fixed_pmul.cu` was producing incorrect results.
 
 ## Root Cause
-The test was calling `ec_pmul_random_init()` which populated R1 with arbitrary input points, but the batch kernel `fixedPMulByCombinedDAA` expected R1 to contain precomputed multiples of the generator G.
+The test was calling `ec_pmul_init()` which populated R1 with arbitrary input points, but the batch kernel `fixedPMulByCombinedDAA` expected R1 to contain precomputed multiples of the generator G.
 
 ## Solution
 Created a new test kernel that directly uses the `fixed_point_mult()` device function, which correctly accesses the precomputed table from device constant memory (`ECDSACONST.d_mul_table[]`).
@@ -21,7 +21,7 @@ Created a new test kernel that directly uses the `fixed_point_mult()` device fun
    - Stores results properly
 
 3. **Rewrote correctness test** `test_ecdsa_ec_fixed_pmul_correctness()`:
-   - Allocates memory directly (no `ec_pmul_random_init()`)
+   - Allocates memory directly (no `ec_pmul_init()`)
    - Calls the new test kernel
    - Reads results and prints them
 
diff --git a/include/gecc/ecdsa/gsv.h b/include/gecc/ecdsa/gsv.h
index b5e582a..e8401ef 100644
--- a/include/gecc/ecdsa/gsv.h
+++ b/include/gecc/ecdsa/gsv.h
@@ -1529,8 +1529,8 @@ template <typename BaseField, typename BaseOrder, typename EC, const ECDSAConsta
   }
 
 
-  // batch EC PMUL Breakdown Test
-  void ec_pmul_random_init(const u64 s[][MAX_LIMBS], const u64 key_x[][MAX_LIMBS], const u64 key_y[][MAX_LIMBS], u32 count) {
+  // batch EC PMUL initialization
+  void ec_pmul_init(const u64 s[][MAX_LIMBS], const u64 key_x[][MAX_LIMBS], const u64 key_y[][MAX_LIMBS], u32 count) {
     verify_count = count;
     cudaMallocManaged(&verify_s, Order::SIZE * count); //25MB
     cudaMallocManaged(&verify_t, Order::SIZE * count);
diff --git a/test/ecdsa_ec_fixed_pmul.cu b/test/ecdsa_ec_fixed_pmul.cu
index fe2a078..09c3afa 100644
--- a/test/ecdsa_ec_fixed_pmul.cu
+++ b/test/ecdsa_ec_fixed_pmul.cu
@@ -30,7 +30,7 @@ void test_ecdsa_ec_fixed_pmul() {
     printf("--------------------------- %u (%d << %d) --------------------------\n", count, MAX_SM_NUMS, i);
 
     // solver.verify_init(R, S, E, KEY_X, KEY_Y, count);
-    solver.ec_pmul_random_init(RANDOM_S, RANDOM_KEY_X, RANDOM_KEY_Y, count);
+    solver.ec_pmul_init(RANDOM_S, RANDOM_KEY_X, RANDOM_KEY_Y, count);
     // warm up
     solver.ecdsa_ec_pmul(MAX_SM_NUMS<<2, 256, false);
     cudaDeviceSynchronize();
diff --git a/test/ecdsa_ec_unknown_pmul.cu b/test/ecdsa_ec_unknown_pmul.cu
index 53fe0dc..401f7d6 100644
--- a/test/ecdsa_ec_unknown_pmul.cu
+++ b/test/ecdsa_ec_unknown_pmul.cu
@@ -23,7 +23,7 @@ void test_ecdsa_ec_unknown_pmul() {
     count = MAX_SM_NUMS * (1<<i); //1<<18 ~ 1<<23
     printf("--------------------------- %u (%d << %d) --------------------------\n", count, MAX_SM_NUMS, i);
 
-    solver.ec_pmul_random_init(RANDOM_S, RANDOM_KEY_X, RANDOM_KEY_Y, count);
+    solver.ec_pmul_init(RANDOM_S, RANDOM_KEY_X, RANDOM_KEY_Y, count);
     // warm up
     solver.ecdsa_ec_pmul(MAX_SM_NUMS<<2, 256, true);
     cudaDeviceSynchronize();
@@ -68,7 +68,7 @@ void test_ecdsa_ec_unknown_pmul_correctness() {
   printf("Testing %u point multiplications\n\n", count);
 
   // Initialize with test data
-  solver.ec_pmul_random_init(RANDOM_S, RANDOM_KEY_X, RANDOM_KEY_Y, count);
+  solver.ec_pmul_init(RANDOM_S, RANDOM_KEY_X, RANDOM_KEY_Y, count);
 
   // Print inputs (first 3 samples)
   printf("Input scalars (s):\n");
diff --git a/test/modinv_data_parallel_profiling.cu b/test/modinv_data_parallel_profiling.cu
index 1666174..6b87d98 100644
--- a/test/modinv_data_parallel_profiling.cu
+++ b/test/modinv_data_parallel_profiling.cu
@@ -24,7 +24,7 @@ void test_modinv_in_data_parallel() {
     printf("--------------------------- %u (~1<< %d) --------------------------\n", count, ((int)log2(MAX_SM_NUMS)) + i);
 
     // solver.verify_init(R, S, E, KEY_X, KEY_Y, count);
-    solver.ec_pmul_random_init(RANDOM_S, RANDOM_KEY_X, RANDOM_KEY_Y, count);
+    solver.ec_pmul_init(RANDOM_S, RANDOM_KEY_X, RANDOM_KEY_Y, count);
     // warm up
     solver.batch_modinv_MTA(MAX_SM_NUMS<<2, 256);
     cudaDeviceSynchronize();