diff --git a/test/utils/cryptography/P256.test.js b/test/utils/cryptography/P256.test.js
index b9655cad3f..f8735420d1 100644
--- a/test/utils/cryptography/P256.test.js
+++ b/test/utils/cryptography/P256.test.js
@@ -120,6 +120,27 @@ describe('P256', function () {
     });
   });
 
+  describe('edge cases', function () {
+    // In theory, all private keys between 1 and P256.N-1 should be supported. However, the `_jAdd` limitation,
+    // that indirectly affects `_preComputeJacobianPoints` causes issues for some private/public key pairs
+    //
+    // In particular, the following key pairs are not supported:
+    // * private = 1 (P = G)
+    // * private = 2 (P = 2G)
+    // * private = 3 (P = 3G)
+    // * private = N - 3 (P = -3G)
+    // * private = N - 2 (P = -2G)
+    // * private = N - 1 (P = -G)
+    for (const privateKey of [1n, 2n, 3n, -3n, -2n, -1n]) {
+      it(`unsuported case: P = ${privateKey} * G`, async function () {
+        const { messageHash, signature, publicKey } = prepareSignature(
+          privateKey < 0 ? privateKey + secp256r1.CURVE.n : privateKey,
+        );
+        expect(await this.mock.$verifySolidity(messageHash, ...signature, ...publicKey)).to.be.false;
+      });
+    }
+  });
+
   // test cases for https://github.com/C2SP/wycheproof/blob/4672ff74d68766e7785c2cac4c597effccef2c5c/testvectors/ecdsa_secp256r1_sha256_p1363_test.json
   describe('wycheproof tests', function () {
     for (const { key, tests } of require('./ecdsa_secp256r1_sha256_p1363_test.json').testGroups) {