Export Schnorr signature API (#32)

Implement Schnorr signatures (BIP 340)

jni/c/headers/java/fr_acinq_secp256k1_Secp256k1CFunctions.h

@@ -151,6 +151,22 @@ JNIEXPORT jbyteArray JNICALL Java_fr_acinq_secp256k1_Secp256k1CFunctions_secp256
 JNIEXPORT jbyteArray JNICALL Java_fr_acinq_secp256k1_Secp256k1CFunctions_secp256k1_1compact_1to_1der
   (JNIEnv *, jclass, jlong, jbyteArray);
 
+/*
+ * Class:     fr_acinq_secp256k1_Secp256k1CFunctions
+ * Method:    secp256k1_schnorrsig_sign
+ * Signature: (J[B[B[B)[B
+ */
+JNIEXPORT jbyteArray JNICALL Java_fr_acinq_secp256k1_Secp256k1CFunctions_secp256k1_1schnorrsig_1sign
+  (JNIEnv *, jclass, jlong, jbyteArray, jbyteArray, jbyteArray);
+
+/*
+ * Class:     fr_acinq_secp256k1_Secp256k1CFunctions
+ * Method:    secp256k1_schnorrsig_verify
+ * Signature: (J[B[B[B)I
+ */
+JNIEXPORT jint JNICALL Java_fr_acinq_secp256k1_Secp256k1CFunctions_secp256k1_1schnorrsig_1verify
+  (JNIEnv *, jclass, jlong, jbyteArray, jbyteArray, jbyteArray);
+
 #ifdef __cplusplus
 }
 #endif

jni/c/src/fr_acinq_secp256k1_Secp256k1CFunctions.c

@@ -4,6 +4,7 @@
 #include "include/secp256k1.h"
 #include "include/secp256k1_ecdh.h"
 #include "include/secp256k1_recovery.h"
+#include "include/secp256k1_schnorrsig.h"
 #include "fr_acinq_secp256k1_Secp256k1CFunctions.h"
 
 #define SIG_FORMAT_UNKNOWN 0
@@ -666,3 +667,86 @@ JNIEXPORT jbyteArray JNICALL Java_fr_acinq_secp256k1_Secp256k1CFunctions_secp256
     (*penv)->ReleaseByteArrayElements(penv, jsig, sig, 0);
     return jsig;
 }
+
+/*
+ * Class:     fr_acinq_secp256k1_Secp256k1CFunctions
+ * Method:    secp256k1_schnorrsig_sign
+ * Signature: (J[B[B[B)[B
+ */
+JNIEXPORT jbyteArray JNICALL Java_fr_acinq_secp256k1_Secp256k1CFunctions_secp256k1_1schnorrsig_1sign
+  (JNIEnv *penv, jclass clazz, jlong jctx, jbyteArray jmsg, jbyteArray jseckey, jbyteArray jauxrand32)
+{
+    secp256k1_context* ctx = (secp256k1_context *)jctx;
+    jbyte *seckey, *msg, *sig, *auxrand32 = NULL;
+    secp256k1_keypair keypair;
+    unsigned char signature[64];
+    int result = 0;
+    jbyteArray jsig;
+
+    if (jctx == 0) return NULL;
+    if (jmsg == NULL) return NULL;
+    if (jseckey == NULL) return NULL;
+
+    CHECKRESULT((*penv)->GetArrayLength(penv, jseckey) != 32, "secret key must be 32 bytes");
+    CHECKRESULT((*penv)->GetArrayLength(penv, jmsg) != 32, "message must be 32 bytes");
+    if (jauxrand32 != 0) {
+        CHECKRESULT((*penv)->GetArrayLength(penv, jauxrand32) != 32, "auxiliary random data must be 32 bytes");
+    }
+    seckey = (*penv)->GetByteArrayElements(penv, jseckey, 0);
+    result = secp256k1_keypair_create(ctx, &keypair, seckey);
+    (*penv)->ReleaseByteArrayElements(penv, jseckey, seckey, 0);
+    CHECKRESULT(!result, "secp256k1_keypair_create failed");
+
+    msg = (*penv)->GetByteArrayElements(penv, jmsg, 0);
+    if (jauxrand32 != 0) {
+        auxrand32 = (*penv)->GetByteArrayElements(penv, jauxrand32, 0);
+    }
+
+    result = secp256k1_schnorrsig_sign(ctx, signature, (unsigned char*)msg, &keypair, auxrand32);
+    (*penv)->ReleaseByteArrayElements(penv, jmsg, msg, 0);
+    if (auxrand32 != 0) {
+        (*penv)->ReleaseByteArrayElements(penv, jauxrand32, auxrand32, 0);
+    }
+    CHECKRESULT(!result, "secp256k1_schnorrsig_sign failed");
+
+    jsig = (*penv)->NewByteArray(penv, 64);
+    sig = (*penv)->GetByteArrayElements(penv, jsig, 0);
+    memcpy(sig, signature, 64);
+    (*penv)->ReleaseByteArrayElements(penv, jsig, sig, 0);
+    return jsig;
+}
+
+/*
+ * Class:     fr_acinq_secp256k1_Secp256k1CFunctions
+ * Method:    secp256k1_schnorrsig_verify
+ * Signature: (J[B[B[B)I
+ */
+JNIEXPORT jint JNICALL Java_fr_acinq_secp256k1_Secp256k1CFunctions_secp256k1_1schnorrsig_1verify
+  (JNIEnv *penv, jclass clazz, jlong jctx, jbyteArray jsig, jbyteArray jmsg, jbyteArray jpubkey)
+{
+    secp256k1_context* ctx = (secp256k1_context *)jctx;
+    jbyte *pub, *msg, *sig;
+    secp256k1_xonly_pubkey pubkey;
+    int result = 0;
+
+    if (jctx == 0) return 0;
+    if (jsig == NULL) return 0;
+    if (jmsg == NULL) return 0;
+    if (jpubkey == NULL) return 0;
+
+    CHECKRESULT((*penv)->GetArrayLength(penv, jsig) != 64, "signature must be 64 bytes");
+    CHECKRESULT((*penv)->GetArrayLength(penv, jpubkey) != 32, "public key must be 32 bytes");
+    CHECKRESULT((*penv)->GetArrayLength(penv, jmsg) != 32, "message must be 32 bytes");
+
+    pub = (*penv)->GetByteArrayElements(penv, jpubkey, 0);
+    result = secp256k1_xonly_pubkey_parse(ctx, &pubkey, (unsigned char*)pub);
+    (*penv)->ReleaseByteArrayElements(penv, jpubkey, pub, 0);
+    CHECKRESULT(!result, "secp256k1_ec_pubkey_parse failed");
+
+    sig = (*penv)->GetByteArrayElements(penv, jsig, 0);
+    msg = (*penv)->GetByteArrayElements(penv, jmsg, 0);
+    result = secp256k1_schnorrsig_verify(ctx, (unsigned char*)sig, (unsigned char*)msg, 32, &pubkey);
+    (*penv)->ReleaseByteArrayElements(penv, jsig, sig, 0);
+    (*penv)->ReleaseByteArrayElements(penv, jmsg, msg, 0);
+    return result;
+}

jni/src/main/java/fr/acinq/secp256k1/Secp256k1CFunctions.java

@@ -64,4 +64,8 @@ public class Secp256k1CFunctions {
     public static native byte[] secp256k1_ecdsa_recover(long ctx, byte[] sig, byte[] msg32, int recid);
 
     public static native byte[] secp256k1_compact_to_der(long ctx, byte[] sig);
+
+    public static native byte[] secp256k1_schnorrsig_sign(long ctx, byte[] msg, byte[] seckey, byte[] aux_rand32);
+
+    public static native int secp256k1_schnorrsig_verify(long ctx, byte[] sig, byte[] msg, byte[] pubkey);
 }

jni/src/main/kotlin/fr/acinq/secp256k1/NativeSecp256k1.kt

@@ -84,6 +84,14 @@ public object NativeSecp256k1 : Secp256k1 {
         return Secp256k1CFunctions.secp256k1_compact_to_der(Secp256k1Context.getContext(), sig)
     }
 
+    override fun verifySchnorr(signature: ByteArray, data: ByteArray, pub: ByteArray): Boolean {
+        return Secp256k1CFunctions.secp256k1_schnorrsig_verify(Secp256k1Context.getContext(), signature, data, pub) == 1
+    }
+
+    override fun signSchnorr(data: ByteArray, sec: ByteArray, auxrand32: ByteArray?): ByteArray {
+        return Secp256k1CFunctions.secp256k1_schnorrsig_sign(Secp256k1Context.getContext(), data, sec, auxrand32)
+    }
+
     override fun cleanup() {
         return Secp256k1CFunctions.secp256k1_context_destroy(Secp256k1Context.getContext())
     }

native/build-android.sh

@@ -35,7 +35,7 @@ export STRIP=$ANDROID_NDK/toolchains/llvm/prebuilt/$TOOLCHAIN/bin/$TOOLTARGET-st
 cd secp256k1
 
 ./autogen.sh
-./configure CFLAGS=-fpic --host=$TARGET --enable-experimental --enable-module_ecdh --enable-module-recovery --enable-benchmark=no --enable-shared=no --enable-exhaustive-tests=no --enable-tests=no
+./configure CFLAGS=-fpic --host=$TARGET --enable-experimental --enable-module_ecdh --enable-module-recovery --enable-module-schnorrsig --enable-benchmark=no --enable-shared=no --enable-exhaustive-tests=no --enable-tests=no
 make clean
 make
 

native/build-ios.sh

@@ -6,7 +6,7 @@ cp xconfigure.sh secp256k1
 cd secp256k1
 
 ./autogen.sh
-sh xconfigure.sh --enable-experimental --enable-module_ecdh --enable-module-recovery --enable-benchmark=no --enable-shared=no --enable-exhaustive-tests=no --enable-tests=no
+sh xconfigure.sh --enable-experimental --enable-module_ecdh --enable-module-recovery --enable-module-schnorrsig --enable-benchmark=no --enable-shared=no --enable-exhaustive-tests=no --enable-tests=no
 
 mkdir -p ../build/ios
 cp -v _build/universal/* ../build/ios/

native/build.sh

@@ -23,7 +23,7 @@ else
 fi
 
 ./autogen.sh
-./configure $CONF_OPTS --enable-experimental --enable-module_ecdh --enable-module-recovery --enable-benchmark=no --enable-shared=no --enable-exhaustive-tests=no --enable-tests=no
+./configure $CONF_OPTS --enable-experimental --enable-module_ecdh --enable-module-recovery --enable-module-schnorrsig --enable-benchmark=no --enable-shared=no --enable-exhaustive-tests=no --enable-tests=no
 make clean
 make
 

src/commonMain/kotlin/fr/acinq/secp256k1/Secp256k1.kt

@@ -37,6 +37,24 @@ public interface Secp256k1 {
      */
     public fun sign(message: ByteArray, privkey: ByteArray): ByteArray
 
+    /**
+     * Verify a Schnorr signature.
+     *
+     * @param signature 64 bytes signature.
+     * @param message message signed.
+     * @param pubkey signer's x-only public key (32 bytes).
+     */
+    public fun verifySchnorr(signature: ByteArray, data: ByteArray, pub: ByteArray): Boolean
+
+    /**
+     * Create a Schnorr signature.
+     *
+     * @param message message to sign.
+     * @param privkey signer's private key.
+     * @param auxrand32 32 bytes of fresh randomness (optional).
+     */
+    public fun signSchnorr(data: ByteArray, sec: ByteArray, auxrand32: ByteArray?): ByteArray
+
    /**
      * Convert an ECDSA signature to a normalized lower-S form (bitcoin standardness rule).
      * Returns the normalized signature and a boolean set to true if the input signature was not normalized.

src/nativeInterop/cinterop/libsecp256k1.def

@@ -1,7 +1,7 @@
 package = secp256k1
 
-headers = secp256k1.h secp256k1_ecdh.h secp256k1_recovery.h
+headers = secp256k1.h secp256k1_ecdh.h secp256k1_recovery.h secp256k1_extrakeys.h secp256k1_schnorrsig.h
-headerFilter = secp256k1/** secp256k1_ecdh.h secp256k1_recovery.h secp256k1.h
+headerFilter = secp256k1/** secp256k1_ecdh.h secp256k1_recovery.h secp256k1_extrakeys.h secp256k1_schnorrsig.h secp256k1.h
 
 libraryPaths.linux = c/secp256k1/build/linux/
 linkerOpts.linux = -L/usr/lib64 -L/usr/lib/x86_64-linux-gnu -L/usr/local/lib

src/nativeMain/kotlin/fr/acinq/secp256k1/Secp256k1Native.kt

@@ -222,9 +222,41 @@ public object Secp256k1Native : Secp256k1 {
         }
     }
 
-    public override fun cleanup() {
+    override fun verifySchnorr(signature: ByteArray, data: ByteArray, pub: ByteArray): Boolean {
-        secp256k1_context_destroy(ctx)
+        require(signature.size == 64)
+        require(data.size == 32)
+        require(pub.size == 32)
+        memScoped {
+            val nPub = toNat(pub)
+            val pubkey = alloc<secp256k1_xonly_pubkey>()
+            secp256k1_xonly_pubkey_parse(ctx, pubkey.ptr, nPub).requireSuccess("secp256k1_xonly_pubkey_parse() failed")
+            val nData = toNat(data)
+            val nSig = toNat(signature)
+            return secp256k1_schnorrsig_verify(ctx, nSig, nData, 32, pubkey.ptr) == 1
         }
     }
 
+    override fun signSchnorr(data: ByteArray, sec: ByteArray, auxrand32: ByteArray?): ByteArray {
+        require(sec.size == 32)
+        require(data.size == 32)
+        auxrand32?.let { require(it.size == 32) }
+        memScoped {
+            val nSec = toNat(sec)
+            val nData = toNat(data)
+            val nAuxrand32 = auxrand32?.let { toNat(it) }
+            val nSig = allocArray<UByteVar>(64)
+            val keypair = alloc<secp256k1_keypair>()
+            secp256k1_keypair_create(ctx, keypair.ptr, nSec).requireSuccess("secp256k1_keypair_create() failed")
+            secp256k1_schnorrsig_sign(ctx, nSig, nData, keypair.ptr, nAuxrand32).requireSuccess("secp256k1_ecdsa_sign() failed")
+            return nSig.readBytes(64)
+        }
+    }
+    
+    public override fun cleanup() {
+        secp256k1_context_destroy(ctx)
+    }
+
+
+}
+
 internal actual fun getSecpk256k1(): Secp256k1 = Secp256k1Native

tests/src/commonTest/kotlin/fr/acinq/secp256k1/Secp256k1Test.kt

@@ -287,6 +287,71 @@ class Secp256k1Test {
         )
     }
 
+    @Test
+    fun testSchnorrSignature() {
+        val seckey = Hex.decode("0000000000000000000000000000000000000000000000000000000000000003")
+        val msg = Hex.decode("0000000000000000000000000000000000000000000000000000000000000000")
+        val auxrand32 = Hex.decode("0000000000000000000000000000000000000000000000000000000000000000")
+        val sig = Secp256k1.signSchnorr(msg, seckey, auxrand32)
+        assertEquals(
+            "E907831F80848D1069A5371B402410364BDF1C5F8307B0084C55F1CE2DCA821525F66A4A85EA8B71E482A74F382D2CE5EBEEE8FDB2172F477DF4900D310536C0",
+            Hex.encode(sig).uppercase(),
+        )
+        val pubkey = Secp256k1.pubkeyCreate(seckey).drop(1).take(32).toByteArray()
+        assertEquals(
+            "F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9",
+            Hex.encode(pubkey).uppercase()
+        )
+        assertTrue(Secp256k1.verifySchnorr(sig, msg, pubkey))
+    }
+
+    @Test
+    fun testSchnorrTestVectors() {
+        // BIP340 test vectors copied from https://github.com/bitcoin/bips/blob/master/bip-0340/test-vectors.csv
+        val bip340TestVectors = """index,secret key,public key,aux_rand,message,signature,verification result,comment
+0,0000000000000000000000000000000000000000000000000000000000000003,F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9,0000000000000000000000000000000000000000000000000000000000000000,0000000000000000000000000000000000000000000000000000000000000000,E907831F80848D1069A5371B402410364BDF1C5F8307B0084C55F1CE2DCA821525F66A4A85EA8B71E482A74F382D2CE5EBEEE8FDB2172F477DF4900D310536C0,TRUE,
+1,B7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,0000000000000000000000000000000000000000000000000000000000000001,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,6896BD60EEAE296DB48A229FF71DFE071BDE413E6D43F917DC8DCF8C78DE33418906D11AC976ABCCB20B091292BFF4EA897EFCB639EA871CFA95F6DE339E4B0A,TRUE,
+2,C90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B14E5C9,DD308AFEC5777E13121FA72B9CC1B7CC0139715309B086C960E18FD969774EB8,C87AA53824B4D7AE2EB035A2B5BBBCCC080E76CDC6D1692C4B0B62D798E6D906,7E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C,5831AAEED7B44BB74E5EAB94BA9D4294C49BCF2A60728D8B4C200F50DD313C1BAB745879A5AD954A72C45A91C3A51D3C7ADEA98D82F8481E0E1E03674A6F3FB7,TRUE,
+3,0B432B2677937381AEF05BB02A66ECD012773062CF3FA2549E44F58ED2401710,25D1DFF95105F5253C4022F628A996AD3A0D95FBF21D468A1B33F8C160D8F517,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF,7EB0509757E246F19449885651611CB965ECC1A187DD51B64FDA1EDC9637D5EC97582B9CB13DB3933705B32BA982AF5AF25FD78881EBB32771FC5922EFC66EA3,TRUE,test fails if msg is reduced modulo p or n
+4,,D69C3509BB99E412E68B0FE8544E72837DFA30746D8BE2AA65975F29D22DC7B9,,4DF3C3F68FCC83B27E9D42C90431A72499F17875C81A599B566C9889B9696703,00000000000000000000003B78CE563F89A0ED9414F5AA28AD0D96D6795F9C6376AFB1548AF603B3EB45C9F8207DEE1060CB71C04E80F593060B07D28308D7F4,TRUE,
+5,,EEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,6CFF5C3BA86C69EA4B7376F31A9BCB4F74C1976089B2D9963DA2E5543E17776969E89B4C5564D00349106B8497785DD7D1D713A8AE82B32FA79D5F7FC407D39B,FALSE,public key not on the curve
+6,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,FFF97BD5755EEEA420453A14355235D382F6472F8568A18B2F057A14602975563CC27944640AC607CD107AE10923D9EF7A73C643E166BE5EBEAFA34B1AC553E2,FALSE,has_even_y(R) is false
+7,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,1FA62E331EDBC21C394792D2AB1100A7B432B013DF3F6FF4F99FCB33E0E1515F28890B3EDB6E7189B630448B515CE4F8622A954CFE545735AAEA5134FCCDB2BD,FALSE,negated message
+8,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,6CFF5C3BA86C69EA4B7376F31A9BCB4F74C1976089B2D9963DA2E5543E177769961764B3AA9B2FFCB6EF947B6887A226E8D7C93E00C5ED0C1834FF0D0C2E6DA6,FALSE,negated s value
+9,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,0000000000000000000000000000000000000000000000000000000000000000123DDA8328AF9C23A94C1FEECFD123BA4FB73476F0D594DCB65C6425BD186051,FALSE,sG - eP is infinite. Test fails in single verification if has_even_y(inf) is defined as true and x(inf) as 0
+10,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,00000000000000000000000000000000000000000000000000000000000000017615FBAF5AE28864013C099742DEADB4DBA87F11AC6754F93780D5A1837CF197,FALSE,sG - eP is infinite. Test fails in single verification if has_even_y(inf) is defined as true and x(inf) as 1
+11,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,4A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D69E89B4C5564D00349106B8497785DD7D1D713A8AE82B32FA79D5F7FC407D39B,FALSE,sig[0:32] is not an X coordinate on the curve
+12,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F69E89B4C5564D00349106B8497785DD7D1D713A8AE82B32FA79D5F7FC407D39B,FALSE,sig[0:32] is equal to field size
+13,,DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,6CFF5C3BA86C69EA4B7376F31A9BCB4F74C1976089B2D9963DA2E5543E177769FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141,FALSE,sig[32:64] is equal to curve order
+14,,FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC30,,243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89,6CFF5C3BA86C69EA4B7376F31A9BCB4F74C1976089B2D9963DA2E5543E17776969E89B4C5564D00349106B8497785DD7D1D713A8AE82B32FA79D5F7FC407D39B,FALSE,public key is not a valid X coordinate because it exceeds the field size"""
+
+        bip340TestVectors.split('\n').drop(1).forEach {
+            val testData = it.split(',')
+            val index = testData[0]
+            val seckey = Hex.decode(testData[1])
+            val pubkey = Hex.decode(testData[2])
+            val auxrand = if (testData[3].isEmpty()) null else Hex.decode(testData[3])
+            val msg = Hex.decode(testData[4])
+            val sig = testData[5]
+            val expected = when (testData[6]) {
+                "FALSE" -> false
+                else -> true
+            }
+            val comment = testData[7]
+
+            if (seckey.isNotEmpty()) {
+                val ourSig = Secp256k1.signSchnorr(msg, seckey, auxrand)
+                assertEquals(Hex.encode(ourSig).uppercase(), sig)
+            }
+            val result = try {
+                Secp256k1.verifySchnorr(Hex.decode(sig), msg, pubkey)
+            } catch (t: Throwable) {
+                false
+            }
+            assertEquals(expected, result, "test [$index, $comment] failed")
+        }
+    }
+
     @Test
     fun fuzzEcdsaSignVerify() {
         val random = Random.Default
@@ -308,5 +373,4 @@ class Secp256k1Test {
             assertTrue(Secp256k1.verify(der, message, pub))
         }
     }
-
 }