chore: fix a bunch of warnings (#26)

noir-lang · Nov 1, 2024 · 4b81831 · 4b81831
1 parent 8784b19
commit 4b81831
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diff --git a/.github/workflows/nightly-canary.yml b/.github/workflows/nightly-canary.yml
@@ -28,10 +28,6 @@ jobs:
         working-directory: ./lib
         run: nargo test
 
-      - name: Run formatter
-        working-directory: ./lib
-        run: nargo fmt --check
-
       - name: Alert on dead canary
         uses: JasonEtco/create-an-issue@v2
         if: ${{ failure() }}

diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
@@ -44,3 +44,26 @@ jobs:
       - name: Run formatter
         working-directory: ./lib
         run: nargo fmt --check
+
+  # This is a job which depends on all test jobs and reports the overall status.
+  # This allows us to add/remove test jobs without having to update the required workflows.
+  tests-end:
+    name: Noir End
+    runs-on: ubuntu-latest
+    # We want this job to always run (even if the dependant jobs fail) as we want this job to fail rather than skipping.
+    if: ${{ always() }}
+    needs: 
+      - test
+      - format
+
+    steps:
+      - name: Report overall success
+        run: |
+          if [[ $FAIL == true ]]; then
+              exit 1
+          else
+              exit 0
+          fi
+        env:
+          # We treat any cancelled, skipped or failing jobs as a failure for the workflow as a whole.
+          FAIL: ${{ contains(needs.*.result, 'failure') || contains(needs.*.result, 'cancelled') || contains(needs.*.result, 'skipped') }}
diff --git a/lib/src/rsa.nr b/lib/src/rsa.nr
@@ -1,9 +1,7 @@
 use dep::bignum::BigNum;
-use dep::bignum::runtime_bignum::BigNumInstance;
-use dep::bignum::runtime_bignum::BigNumTrait;
-use dep::bignum::runtime_bignum::BigNumInstanceTrait;
+use dep::bignum::runtime_bignum::{BigNumInstance, BigNumInstanceTrait, BigNumTrait};
 
-use crate::types::{RSA, BN1024, BN2048, BNInst1024, BNInst2048, RSA1024, RSA2048};
+use crate::types::{BN1024, BN2048, BNInst1024, BNInst2048, RSA, RSA1024, RSA2048};
 
 /**
  * @brief Compare a recovered byte hash from an RSA signature to the original message hash
@@ -12,7 +10,6 @@ use crate::types::{RSA, BN1024, BN2048, BNInst1024, BNInst2048, RSA1024, RSA2048
 fn compare_signature_sha256<let N: u32>(padded_sha256_hash: [u8; N], msg_hash: [u8; 32]) -> bool {
     // Get length of sig (e.g. 1048 = 128 bytes, 2048 = 256 bytes)
     // NOTE: Assume MAX_BYTES < 2^32 bit number. MAX_BYTES of 259 > 2^8 bits so need to cast it to u32
-
     for i in 0..32 {
         // Padded hash is reversed
         assert(padded_sha256_hash[31 - i] == msg_hash[i]);
@@ -29,13 +26,13 @@ fn compare_signature_sha256<let N: u32>(padded_sha256_hash: [u8; N], msg_hash: [
     // Sub 32 bytes for hash, 19 bytes for prefix, 1 byte for 0, 1 byte for 1, 1 byte for 0
     let ps_len = N - 54;
     for i in 52..N {
-        if i as u32 < 52 + ps_len as u32 {
+        if i < 52 + ps_len {
             // PS padding which depends on RSA modulus / sig length. 1024 bits = 128 bytes = 128 - 54 = 74 bytes of 0xFF padding
             assert(padded_sha256_hash[i] == 255);
-        } else if i as u32 == 52 + ps_len as u32 {
+        } else if i == 52 + ps_len {
             // Pad 0x01
             assert(padded_sha256_hash[i] == 1);
-        } else if i as u32 == 53 + ps_len as u32 {
+        } else if i == 53 + ps_len {
             // 0x00
             assert(padded_sha256_hash[i] == 0);
         } else {
@@ -46,22 +43,24 @@ fn compare_signature_sha256<let N: u32>(padded_sha256_hash: [u8; N], msg_hash: [
 
     true
 }
-impl<BN, BNInstance, let NumBytes: u32> RSA<BN, BNInstance, NumBytes>  where BN: BigNumTrait, BNInstance: BigNumInstanceTrait<BN> {
-    /**
- * @brief Verify an RSA signature generated via the pkcs1v15 signature scheme.
- * @details The fourth function parameter is required to define the value of `NBytes`
- *          when converting a BigNum into a byte array, the number of bytes is required and currently cannot be inferred.
- *          Once numeric generics can be derived by applying operations to other numeric generics the need for this will go away.
- *
- * @note The exponent `e` can be either 65537 or 3 (i.e. the most common values in use for RSA)
- * Rough cost: 2,048 bit RSA: 26,888 gates per verification
- *             1,024 bit RSA: 11,983 gates per verification
- * A circuit that verifies 1 signature (and does nothing else) will cost ~32k due to initialization costs of lookup tables
- **/
+impl<BN, BNInstance, let NumBytes: u32> RSA<BN, BNInstance, NumBytes>
+where
+    BN: BigNumTrait,
+    BNInstance: BigNumInstanceTrait<BN>, {
+    /// Verify an RSA signature generated via the pkcs1v15 signature scheme.
+    ///
+    /// The fourth function parameter is required to define the value of `NBytes`
+    /// when converting a BigNum into a byte array, the number of bytes is required and currently cannot be inferred.
+    /// Once numeric generics can be derived by applying operations to other numeric generics the need for this will go away.
+    ///
+    /// The exponent `e` can be either 65537 or 3 (i.e. the most common values in use for RSA)
+    ///
+    /// Rough cost: 2,048 bit RSA: 26,888 gates per verification
+    ///             1,024 bit RSA: 11,983 gates per verification
+    /// A circuit that verifies 1 signature (and does nothing else) will cost ~32k due to initialization costs of lookup tables
     pub fn verify_sha256_pkcs1v15(_: Self, instance: BNInstance, msg_hash: [u8; 32], sig: BN, exponent: u32) -> bool {
         assert((exponent == 3) | (exponent == 65537), "Exponent must be 65537 or 3");
         let mut exponentiated = instance.mul(sig, sig); // sig^2
-
         if exponent == 65537 {
             // e = 65537 = 1 0000 0000 0000 0001
             exponentiated = instance.mul(exponentiated, exponentiated); // sig^2 * sig^2 = sig^4
@@ -81,9 +80,7 @@ impl<BN, BNInstance, let NumBytes: u32> RSA<BN, BNInstance, NumBytes>  where BN:
             exponentiated = instance.mul(exponentiated, exponentiated); // sig^65536
         }
         // otherwise, e = 3 = 11
-
         exponentiated = instance.mul(exponentiated, sig); // either sig^2 * sig = sig^3 or sig^65536 * sig = sig^65537
-
         let mut padded_sha256_hash_bytes: [u8; NumBytes] = exponentiated.to_le_bytes();
         compare_signature_sha256(padded_sha256_hash_bytes, msg_hash)
     }
@@ -94,16 +91,40 @@ fn test_verify_sha256_pkcs1v15_1024() {
     let sha256_hash: [u8; 32] = dep::std::hash::sha256("hello world! test#123".as_bytes());
     let BNInstance: BNInst1024 = BigNumInstance::new(
         [
-        0x483fd4238ca29c3a06f8161ee16faf, 0xf366b16a37c2db80d2977eab0ebbdc, 0x92ba4d77ff2425727ad38eea1cc2fe, 0x3fc50862a0e6afbcae13d5f85c220a, 0xe634dcea239a6a896597d4f75af455, 0x32e1448d1489bca56d983562715680, 0x1a81ef873140c0cfc191a44bfe6e88, 0x96066f4df0e14de07329df952aba45, 0xc2e161b4944381bb
+        0x483fd4238ca29c3a06f8161ee16faf,
+        0xf366b16a37c2db80d2977eab0ebbdc,
+        0x92ba4d77ff2425727ad38eea1cc2fe,
+        0x3fc50862a0e6afbcae13d5f85c220a,
+        0xe634dcea239a6a896597d4f75af455,
+        0x32e1448d1489bca56d983562715680,
+        0x1a81ef873140c0cfc191a44bfe6e88,
+        0x96066f4df0e14de07329df952aba45,
+        0xc2e161b4944381bb
     ],
         [
-        0x9c0b9f33d5b6960db5d70095a87724, 0xfb5245423548a808b8aee833d783b8, 0x790c0d7558b38dc24122455bf48f92, 0x39227725aaea9c83a99acf4b847682, 0xbd468a00b83cb026568150030eff3a, 0xcbb4f5cef905ca04f92f266e0493e8, 0xe19ad572a7bc2bb8168c81b0867c04, 0xbe2075bf10bc8a16725befb36d7f49, 0x15049cee2f37078121
+        0x9c0b9f33d5b6960db5d70095a87724,
+        0xfb5245423548a808b8aee833d783b8,
+        0x790c0d7558b38dc24122455bf48f92,
+        0x39227725aaea9c83a99acf4b847682,
+        0xbd468a00b83cb026568150030eff3a,
+        0xcbb4f5cef905ca04f92f266e0493e8,
+        0xe19ad572a7bc2bb8168c81b0867c04,
+        0xbe2075bf10bc8a16725befb36d7f49,
+        0x15049cee2f37078121
     ]
     );
 
     let signature: BN1024 = BigNum::from_array(
         [
-        0xe6fe1016893fed66550af77d706698, 0x9dd3b648afbbdb748ab97b4d609f0d, 0x83098d3b45c588c69c0e36ff9b210a, 0x5a793d529a382b34a491f68e4d959d, 0xa8c43b964794a4c11da2e57ef226df, 0x68654e3681728df9daff17a3b0bc66, 0x8aa4c9accfffae4fd5cd453c8c5335, 0x8b243f7074dacdcd869b94f3eef7fe, 0x3a8c12564704f5ad
+        0xe6fe1016893fed66550af77d706698,
+        0x9dd3b648afbbdb748ab97b4d609f0d,
+        0x83098d3b45c588c69c0e36ff9b210a,
+        0x5a793d529a382b34a491f68e4d959d,
+        0xa8c43b964794a4c11da2e57ef226df,
+        0x68654e3681728df9daff17a3b0bc66,
+        0x8aa4c9accfffae4fd5cd453c8c5335,
+        0x8b243f7074dacdcd869b94f3eef7fe,
+        0x3a8c12564704f5ad
     ]
     );
 
@@ -117,15 +138,66 @@ fn test_verify_sha256_pkcs1v15_2048() {
 
     let signature: BN2048 = BigNum::from_array(
         [
-        0xad8c7c5ec9162b4769e0cfe5ebf840, 0x0d57cdde315319930d4e9eda1a7c1e, 0xafc455e0e01ef5a57160f0df8a786c, 0xbf1c1e64e91e316ec3ec02e68c23d6, 0x8df9a02bb6a52c932ad0d2832e33a6, 0xa3eacb4ebcb99a4a48be662698a9b8, 0x4fef3847f3e94050802ab50f29a01d, 0xa493fa7d68bd2b0d9e1a1d768053c0, 0x707d984f377f71262954eabd10e268, 0xfec30d40733948f36919b3ffa07366, 0xc9bf002b29ce6a860ba284a4426e34, 0xbc839ec24aad3c05a9aaccefca9e63, 0x07fe1918a7d98dd52e49e9d775461c, 0x098fdfe7d87d48732502814ee90808, 0x64de99868676d8b02d7b43b0474636, 0x27910e77bdc54ba42a4322a5ce8200, 0xc3b7b95e779c9a11895c88fe24bced, 0x96
+        0xad8c7c5ec9162b4769e0cfe5ebf840,
+        0x0d57cdde315319930d4e9eda1a7c1e,
+        0xafc455e0e01ef5a57160f0df8a786c,
+        0xbf1c1e64e91e316ec3ec02e68c23d6,
+        0x8df9a02bb6a52c932ad0d2832e33a6,
+        0xa3eacb4ebcb99a4a48be662698a9b8,
+        0x4fef3847f3e94050802ab50f29a01d,
+        0xa493fa7d68bd2b0d9e1a1d768053c0,
+        0x707d984f377f71262954eabd10e268,
+        0xfec30d40733948f36919b3ffa07366,
+        0xc9bf002b29ce6a860ba284a4426e34,
+        0xbc839ec24aad3c05a9aaccefca9e63,
+        0x07fe1918a7d98dd52e49e9d775461c,
+        0x098fdfe7d87d48732502814ee90808,
+        0x64de99868676d8b02d7b43b0474636,
+        0x27910e77bdc54ba42a4322a5ce8200,
+        0xc3b7b95e779c9a11895c88fe24bced,
+        0x96
     ]
     );
     let BNInstance: BNInst2048 = BigNumInstance::new(
         [
-        0x6d235ca5aab99a4c05ff2a03574427, 0xec267a6bbe7ffe4b6e8da9cf24897c, 0xcdaa2e64a6116d5bdf82460a108af3, 0xf6c184c2d2f4cc7ed3b7eaf28e257e, 0x7511d2771cdf315a07ba2e0058cb8b, 0x641d6eb5119b1b8e643eda5ade2dc3, 0xffc28bdb9f8f0ddc596675feae14fc, 0xcbc67f77f37393c3419a2340f859ad, 0x5cd500e0341275ce468e62db47107d, 0x3049eba2be3f9408f2c9ed2ae27d90, 0xc2f431dd169858ac5269d2512f4189, 0x36ace99a589959ea0425444cfb440d, 0x825fbf23e4e49a3b8f1fa714681f77, 0x8125cd82c2776832cf839ee1a9332c, 0xacbefb6a860c88ecbef30d52472137, 0x24166d0e0b434e207d4e8ecfd66cc9, 0x180955377f255f7bc29506fb45a8cb, 0xf7
+        0x6d235ca5aab99a4c05ff2a03574427,
+        0xec267a6bbe7ffe4b6e8da9cf24897c,
+        0xcdaa2e64a6116d5bdf82460a108af3,
+        0xf6c184c2d2f4cc7ed3b7eaf28e257e,
+        0x7511d2771cdf315a07ba2e0058cb8b,
+        0x641d6eb5119b1b8e643eda5ade2dc3,
+        0xffc28bdb9f8f0ddc596675feae14fc,
+        0xcbc67f77f37393c3419a2340f859ad,
+        0x5cd500e0341275ce468e62db47107d,
+        0x3049eba2be3f9408f2c9ed2ae27d90,
+        0xc2f431dd169858ac5269d2512f4189,
+        0x36ace99a589959ea0425444cfb440d,
+        0x825fbf23e4e49a3b8f1fa714681f77,
+        0x8125cd82c2776832cf839ee1a9332c,
+        0xacbefb6a860c88ecbef30d52472137,
+        0x24166d0e0b434e207d4e8ecfd66cc9,
+        0x180955377f255f7bc29506fb45a8cb,
+        0xf7
     ],
         [
-        0xd08ee8d0e8ac5ce306aa570cfe1c05, 0xed045b877e042b6c144e6aa9cce044, 0x845096769616e1351bd198cb0938ae, 0xe4512a74991f500c166befa3c2f524, 0x81a05d9646ce1212d658399b5b566d, 0x1211121678c29a52c6d66eeca965b9, 0x93dfb350c2b86c8a2a2464cd84e03c, 0x9747aff06e0b9527bc5ad313c8173e, 0x1ca0a8eb7986c264406bf2a8752034, 0xe6abe17cf0f33ec2f655a85c027269, 0xd157b2f2739eec33b38908711b45df, 0xecc0246c32b828f0f603c9feea2daf, 0x76cb733ba6093e7fc2cfc29e07d7c4, 0x7c6f3519480fc9490894acf0c7087f, 0xb92c0644fa19196c5be9d142611269, 0x4db094df57cae1fa0bf4e8faec435b, 0xa2426a309776b8e5d0be5257586c59, 0x1093
+        0xd08ee8d0e8ac5ce306aa570cfe1c05,
+        0xed045b877e042b6c144e6aa9cce044,
+        0x845096769616e1351bd198cb0938ae,
+        0xe4512a74991f500c166befa3c2f524,
+        0x81a05d9646ce1212d658399b5b566d,
+        0x1211121678c29a52c6d66eeca965b9,
+        0x93dfb350c2b86c8a2a2464cd84e03c,
+        0x9747aff06e0b9527bc5ad313c8173e,
+        0x1ca0a8eb7986c264406bf2a8752034,
+        0xe6abe17cf0f33ec2f655a85c027269,
+        0xd157b2f2739eec33b38908711b45df,
+        0xecc0246c32b828f0f603c9feea2daf,
+        0x76cb733ba6093e7fc2cfc29e07d7c4,
+        0x7c6f3519480fc9490894acf0c7087f,
+        0xb92c0644fa19196c5be9d142611269,
+        0x4db094df57cae1fa0bf4e8faec435b,
+        0xa2426a309776b8e5d0be5257586c59,
+        0x1093
     ]
     );
 
@@ -139,15 +211,66 @@ fn test_verify_sha256_pkcs1v15_2048_exponent_3() {
 
     let signature: BN2048 = BigNum::from_array(
         [
-        0xcd01362e23da8aa633cb5a0fb9808d, 0xd3be03e14b0c1eea086ef6aca3d51a, 0xc7bb806d6723bb12c95ce0e3bc5588, 0x05f9843f35688f97a88273cc30b661, 0x25679e918a53da7baa6840d660305c, 0xb89d2c648f85e1372ae090aa89e19c, 0xb90686c46e3c9be1e0f4006047bf5b, 0xd2d27921c3c5b8613d4fec51eb7045, 0xf5e86133acb02bd34dbac6805c5958, 0x84fe10899677d060461b0c3619dcfc, 0x8c9a26f5a68450509aca9d347f0d51, 0xccb9f4406f2c75407b871d39a06cb1, 0xcc95879813f3f90c64f7b5c21b3b0e, 0xc519654312dce978c9f368724d8c8f, 0x5ec258287e34b65bd13cb4c05381ae, 0xd8b5e5f82508cde542538a1973f37f, 0xe035ef2e15b18975521e6ff25072c0, 0x34
+        0xcd01362e23da8aa633cb5a0fb9808d,
+        0xd3be03e14b0c1eea086ef6aca3d51a,
+        0xc7bb806d6723bb12c95ce0e3bc5588,
+        0x05f9843f35688f97a88273cc30b661,
+        0x25679e918a53da7baa6840d660305c,
+        0xb89d2c648f85e1372ae090aa89e19c,
+        0xb90686c46e3c9be1e0f4006047bf5b,
+        0xd2d27921c3c5b8613d4fec51eb7045,
+        0xf5e86133acb02bd34dbac6805c5958,
+        0x84fe10899677d060461b0c3619dcfc,
+        0x8c9a26f5a68450509aca9d347f0d51,
+        0xccb9f4406f2c75407b871d39a06cb1,
+        0xcc95879813f3f90c64f7b5c21b3b0e,
+        0xc519654312dce978c9f368724d8c8f,
+        0x5ec258287e34b65bd13cb4c05381ae,
+        0xd8b5e5f82508cde542538a1973f37f,
+        0xe035ef2e15b18975521e6ff25072c0,
+        0x34
     ]
     );
     let BNInstance: BNInst2048 = BigNumInstance::new(
         [
-        0xea12ae77c634ac18e8914b0f112919, 0x7a385b52ed45602b3166e3006cab17, 0xce91edcb26009ae4ca5ec9032ace54, 0xec45aa323af9389e814dfa59e4e106, 0x50332220bbc7184b2b54c87acb79fb, 0x1fead59aea9260a545bb9b1e098753, 0xb362f1fc50b04e6581b34f97a769b5, 0x409c9d7b3a3ecb214e9dc5524e21a3, 0x88974631f1a1eed0c9d1fa6cc3c622, 0xadacc23ed4a6e2c0e968ad1da6e5b5, 0x480a5bbcc4e18d45937957d44adff2, 0x4d54fd4d3ab7ac249866b6aeaaf37f, 0x7eb6e94460e5dab5f15c55faf1bf5b, 0xc0bca2fb49828eb02a02cb3d95f48a, 0xeeb45b7149ee2bffe342120c8ef177, 0x9108e90248dfab616da128279b0391, 0xd446716c4e0be2123afd277a2cf8a7, 0xe5
+        0xea12ae77c634ac18e8914b0f112919,
+        0x7a385b52ed45602b3166e3006cab17,
+        0xce91edcb26009ae4ca5ec9032ace54,
+        0xec45aa323af9389e814dfa59e4e106,
+        0x50332220bbc7184b2b54c87acb79fb,
+        0x1fead59aea9260a545bb9b1e098753,
+        0xb362f1fc50b04e6581b34f97a769b5,
+        0x409c9d7b3a3ecb214e9dc5524e21a3,
+        0x88974631f1a1eed0c9d1fa6cc3c622,
+        0xadacc23ed4a6e2c0e968ad1da6e5b5,
+        0x480a5bbcc4e18d45937957d44adff2,
+        0x4d54fd4d3ab7ac249866b6aeaaf37f,
+        0x7eb6e94460e5dab5f15c55faf1bf5b,
+        0xc0bca2fb49828eb02a02cb3d95f48a,
+        0xeeb45b7149ee2bffe342120c8ef177,
+        0x9108e90248dfab616da128279b0391,
+        0xd446716c4e0be2123afd277a2cf8a7,
+        0xe5
     ],
         [
-        0x8653d918663eb92721c6efedf149e4, 0x3dbb26bf3a033499240fd8ef578107, 0x69a15f7a032e80ef1496b60b3b95ae, 0xc9aff3026bae96644fc904d80d3c0a, 0x4cb0ae9774e8045235dd864f81314f, 0x65c558cd398b18126e7f3788d196c6, 0x5d7cdb26a9343a94726693b0b5a6c6, 0x4b3cd2b0ef752aa26ba6a7fba6f795, 0x6632fa88182883e987e0db1bcaaaea, 0x38098156f929b4fda6d3026667b3a0, 0x5d5bee367212e64a7d1bd3307082a4, 0xf2622828a7f6e5d906388ec2aa850c, 0xacfdba93e953a71ce0a75f3f88c96f, 0xf8a2b79dfe7264e30b058d44747277, 0x8cf6a50c2e0723546a03d684e3fda, 0xc95e8eb25fe50e2ad34e494492abf, 0x6a078f758586eb4b1e60059a1826b1, 0x11d2
+        0x8653d918663eb92721c6efedf149e4,
+        0x3dbb26bf3a033499240fd8ef578107,
+        0x69a15f7a032e80ef1496b60b3b95ae,
+        0xc9aff3026bae96644fc904d80d3c0a,
+        0x4cb0ae9774e8045235dd864f81314f,
+        0x65c558cd398b18126e7f3788d196c6,
+        0x5d7cdb26a9343a94726693b0b5a6c6,
+        0x4b3cd2b0ef752aa26ba6a7fba6f795,
+        0x6632fa88182883e987e0db1bcaaaea,
+        0x38098156f929b4fda6d3026667b3a0,
+        0x5d5bee367212e64a7d1bd3307082a4,
+        0xf2622828a7f6e5d906388ec2aa850c,
+        0xacfdba93e953a71ce0a75f3f88c96f,
+        0xf8a2b79dfe7264e30b058d44747277,
+        0x8cf6a50c2e0723546a03d684e3fda,
+        0xc95e8eb25fe50e2ad34e494492abf,
+        0x6a078f758586eb4b1e60059a1826b1,
+        0x11d2
     ]
     );
 

diff --git a/lib/src/types.nr b/lib/src/types.nr
@@ -1,14 +1,13 @@
 use dep::bignum::BigNum;
+use dep::bignum::fields::{Params1024, Params2048};
 use dep::bignum::runtime_bignum::BigNumInstance;
-use dep::bignum::fields::Params2048;
-use dep::bignum::fields::Params1024;
 
-struct RSA<BN, BNInstance, let NumBytes: u32>{}
+pub struct RSA<BN, BNInstance, let NumBytes: u32> {}
 
-type BN1024 = BigNum<9, Params1024>;
-type BN2048 = BigNum<18, Params2048>;
-type BNInst1024 = BigNumInstance<9, Params1024>;
-type BNInst2048 = BigNumInstance<18, Params2048>;
+pub(crate) type BN1024 = BigNum<9, Params1024>;
+pub(crate) type BN2048 = BigNum<18, Params2048>;
+pub(crate) type BNInst1024 = BigNumInstance<9, Params1024>;
+pub(crate) type BNInst2048 = BigNumInstance<18, Params2048>;
 
-type RSA1024 = RSA<BN1024, BNInst1024, 128>;
-type RSA2048 = RSA<BN2048, BNInst2048, 256>;
+pub(crate) type RSA1024 = RSA<BN1024, BNInst1024, 128>;
+pub(crate) type RSA2048 = RSA<BN2048, BNInst2048, 256>;