feat(hints): Add alternative string for hint IS_ZERO_PACK (lambdaclas…

…s#1081)

* Add alternative hint code IS_ZERO_PACK_V2

* Integrate into existing tests

* Add changelog entry

* Update is_zero.cairo

---------

Co-authored-by: Pedro Fontana <fontana.pedro93@gmail.com>

CHANGELOG.md

@@ -2,6 +2,16 @@
 
 #### Upcoming Changes
 
+* feat(hints): Add alternative string for hint IS_ZERO_PACK [#1081](https://github.com/lambdaclass/cairo-rs/pull/1081)
+
+    `BuiltinHintProcessor` now supports the following hint:
+
+    ```python
+    %{
+        from starkware.cairo.common.cairo_secp.secp_utils import SECP_P, pack
+        x = pack(ids.x, PRIME) % SECP_P
+    %}
+
 * Implement hint for `starkware.cairo.common.cairo_keccak.keccak._copy_inputs` as described by whitelist `starknet/security/whitelists/cairo_keccak.json` [#1058](https://github.com/lambdaclass/cairo-rs/pull/1058)
 
 `BuiltinHintProcessor` now supports the following hint:

cairo_programs/is_zero.cairo

@@ -59,6 +59,33 @@ func is_zero_alt{range_check_ptr}(x: BigInt3) -> (res: felt) {
     return (res=0);
 }
 
+// Returns 1 if x == 0 (mod secp256k1_prime), and 0 otherwise.
+//
+// Completeness assumption: x's limbs are in the range (-BASE, 2*BASE).
+// Soundness assumption: x's limbs are in the range (-2**107.49, 2**107.49).
+func is_zero_v2_pack{range_check_ptr}(x: BigInt3) -> (res: felt) {
+    %{
+        from starkware.cairo.common.cairo_secp.secp_utils import SECP_P, pack
+        x = pack(ids.x, PRIME) % SECP_P
+    %}
+    if (nondet %{ x == 0 %} != 0) {
+        verify_zero(UnreducedBigInt3(d0=x.d0, d1=x.d1, d2=x.d2));
+        return (res=1);
+    }
+
+    %{
+        from starkware.python.math_utils import div_mod
+
+        value = x_inv = div_mod(1, x, SECP_P)
+    %}
+    let (x_inv) = nondet_bigint3();
+    let (x_x_inv) = unreduced_mul(x, x_inv);
+
+    // Check that x * x_inv = 1 to verify that x != 0.
+    verify_zero(UnreducedBigInt3(d0=x_x_inv.d0 - 1, d1=x_x_inv.d1, d2=x_x_inv.d2));
+    return (res=0);
+}
+
 func test_is_zero{range_check_ptr}() -> () {
     let zero = BigInt3(0, 0, 0);
 
@@ -101,9 +128,32 @@ func test_is_zero_alt{range_check_ptr}() -> () {
     return ();
 }
 
+func test_is_zero_v2_pack{range_check_ptr}() -> () {
+    let zero = BigInt3(0, 0, 0);
+
+    let (res: felt) = is_zero(zero);
+    assert res = 1;
+
+    let one = BigInt3(1, 0, 0);
+
+    let (res: felt) = is_zero(one);
+    assert res = 0;
+
+    let secp256k1_prime = BigInt3(
+        77371252455336262886226991, 77371252455336267181195263, 19342813113834066795298815
+    );
+
+    let (res: felt) = is_zero_v2_pack(secp256k1_prime);
+    assert res = 1;
+
+    return ();
+}
+
+
 func main{range_check_ptr}() -> () {
     test_is_zero();
     test_is_zero_alt();
+    test_is_zero_v2_pack();
 
     return ();
 }

src/hint_processor/builtin_hint_processor/builtin_hint_processor_definition.rs

@@ -401,7 +401,7 @@ impl HintProcessor for BuiltinHintProcessor {
             hint_code::BIGINT_TO_UINT256 => {
                 bigint_to_uint256(vm, &hint_data.ids_data, &hint_data.ap_tracking, constants)
             }
-            hint_code::IS_ZERO_PACK => {
+            hint_code::IS_ZERO_PACK_V1 | hint_code::IS_ZERO_PACK_V2 => {
                 is_zero_pack(vm, exec_scopes, &hint_data.ids_data, &hint_data.ap_tracking)
             }
             hint_code::IS_ZERO_NONDET | hint_code::IS_ZERO_INT => is_zero_nondet(vm, exec_scopes),

src/hint_processor/builtin_hint_processor/hint_code.rs

@@ -546,10 +546,13 @@ ids.low = int.from_bytes(hashed[16:32], 'big')"#;
 
 pub const IS_ZERO_NONDET: &str = "memory[ap] = to_felt_or_relocatable(x == 0)";
 pub const IS_ZERO_INT: &str = "memory[ap] = int(x == 0)";
-pub const IS_ZERO_PACK: &str = r#"from starkware.cairo.common.cairo_secp.secp_utils import SECP_P, pack
+pub const IS_ZERO_PACK_V1: &str = r#"from starkware.cairo.common.cairo_secp.secp_utils import SECP_P, pack
 
 x = pack(ids.x, PRIME) % SECP_P"#;
 
+pub const IS_ZERO_PACK_V2: &str = r#"from starkware.cairo.common.cairo_secp.secp_utils import SECP_P, pack
+x = pack(ids.x, PRIME) % SECP_P"#;
+
 pub const IS_ZERO_PACK_EXTERNAL_SECP: &str = r#"from starkware.cairo.common.cairo_secp.secp_utils import pack
 
 x = pack(ids.x, PRIME) % SECP_P"#;

src/hint_processor/builtin_hint_processor/secp/field_utils.rs

@@ -408,7 +408,8 @@ mod tests {
     fn run_is_zero_pack_ok() {
         let mut exec_scopes = ExecutionScopes::new();
         let hint_codes = vec![
-            hint_code::IS_ZERO_PACK,
+            hint_code::IS_ZERO_PACK_V1,
+            hint_code::IS_ZERO_PACK_V2,
             // NOTE: this one requires IS_ZERO_ASSIGN_SCOPE_VARS to execute first.
             hint_code::IS_ZERO_PACK_EXTERNAL_SECP,
         ];