diff --git a/core-test/src/test/scala/org/bitcoins/core/util/CryptoUtilTest.scala b/core-test/src/test/scala/org/bitcoins/core/util/CryptoUtilTest.scala
index 3a1c4d7260..ca756230da 100644
--- a/core-test/src/test/scala/org/bitcoins/core/util/CryptoUtilTest.scala
+++ b/core-test/src/test/scala/org/bitcoins/core/util/CryptoUtilTest.scala
@@ -1,7 +1,7 @@
 package org.bitcoins.core.util
 
 import org.bitcoins.crypto.CryptoUtil
-import org.bitcoins.testkit.core.gen.CryptoGenerators
+import org.bitcoins.testkit.core.gen.{CryptoGenerators, NumberGenerator}
 import org.bitcoins.testkit.util.BitcoinSUnitTest
 import scodec.bits._
 
@@ -93,4 +93,18 @@ class CryptoUtilTest extends BitcoinSUnitTest {
     }
   }
 
+  it must "compute tagged hashes correctly" in {
+    forAll(NumberGenerator.bytevector) { bytes =>
+      assert(
+        CryptoUtil.sha256SchnorrChallenge(bytes) == CryptoUtil
+          .taggedSha256(bytes, "BIP340/challenge"))
+      assert(
+        CryptoUtil.sha256SchnorrNonce(bytes) == CryptoUtil
+          .taggedSha256(bytes, "BIP340/nonce"))
+      assert(
+        CryptoUtil.sha256SchnorrAuxRand(bytes) == CryptoUtil
+          .taggedSha256(bytes, "BIP340/aux"))
+    }
+  }
+
 }
diff --git a/core/src/main/scala/org/bitcoins/core/crypto/ExtKey.scala b/core/src/main/scala/org/bitcoins/core/crypto/ExtKey.scala
index abef4344b4..bffe3d20e2 100644
--- a/core/src/main/scala/org/bitcoins/core/crypto/ExtKey.scala
+++ b/core/src/main/scala/org/bitcoins/core/crypto/ExtKey.scala
@@ -6,13 +6,13 @@ import org.bitcoins.core.number.{UInt32, UInt8}
 import org.bitcoins.core.util._
 import org.bitcoins.crypto.{
   BaseECKey,
-  BouncyCastleUtil,
   CryptoContext,
   CryptoUtil,
   ECDigitalSignature,
   ECPrivateKey,
   ECPublicKey,
   Factory,
+  FieldElement,
   MaskedToString,
   NetworkElement
 }
@@ -213,12 +213,14 @@ sealed abstract class ExtPrivateKey
     //parse256(IL) + kpar (mod n)
     val tweak = CryptoContext.default match {
       case CryptoContext.LibSecp256k1 =>
-        NativeSecp256k1.privKeyTweakAdd(il.toArray, key.bytes.toArray)
+        val tweakByteArr =
+          NativeSecp256k1.privKeyTweakAdd(il.toArray, key.bytes.toArray)
+        ByteVector(tweakByteArr)
       case CryptoContext.BouncyCastle =>
-        val sum = BouncyCastleUtil.addNumbers(key.bytes, il)
-        sum.toByteArray
+        val sum = key.fieldElement.add(FieldElement(il))
+        sum.bytes
     }
-    val childKey = ECPrivateKey(ByteVector(tweak))
+    val childKey = ECPrivateKey(tweak)
     val fp = CryptoUtil.sha256Hash160(key.publicKey.bytes).bytes.take(4)
     ExtPrivateKey(version, depth + UInt8.one, fp, idx, ChainCode(ir), childKey)
   }
@@ -271,6 +273,20 @@ object ExtPrivateKey extends Factory[ExtPrivateKey] {
             "Fingerprint must be 4 bytes in size, got: " + fingerprint)
   }
 
+  def freshRootKey(version: ExtKeyPrivVersion): ExtPrivateKey = {
+    val privKey = ECPrivateKey.freshPrivateKey
+    val chainCode = ChainCode.fromBytes(ECPrivateKey.freshPrivateKey.bytes)
+
+    ExtPrivateKey(
+      version,
+      UInt8.zero,
+      UInt32.zero.bytes,
+      UInt32.zero,
+      chainCode,
+      privKey
+    )
+  }
+
   /** Takes in a base58 string and tries to convert it to an extended private key */
   def fromString(base58: String): Try[ExtPrivateKey] =
     ExtKey.fromString(base58) match {
diff --git a/core/src/main/scala/org/bitcoins/core/util/NumberUtil.scala b/core/src/main/scala/org/bitcoins/core/util/NumberUtil.scala
index d1ac8d9d04..0247287d04 100644
--- a/core/src/main/scala/org/bitcoins/core/util/NumberUtil.scala
+++ b/core/src/main/scala/org/bitcoins/core/util/NumberUtil.scala
@@ -5,6 +5,7 @@ import java.math.BigInteger
 import org.bitcoins.core.number._
 import org.bitcoins.core.protocol.blockchain.BlockHeader
 import org.bitcoins.core.protocol.blockchain.BlockHeader.TargetDifficultyHelper
+import org.bitcoins.crypto.FieldElement
 import scodec.bits.{BitVector, ByteVector}
 
 import scala.math.BigInt
@@ -28,6 +29,10 @@ sealed abstract class NumberUtil extends BitcoinSLogger {
     toUnsignedInt(bytes.toArray)
   }
 
+  def uintToFieldElement(bytes: ByteVector): FieldElement = {
+    FieldElement(toUnsignedInt(bytes))
+  }
+
   /** Converts a sequence of bytes to a **big endian** unsigned integer */
   def toUnsignedInt(bytes: Array[Byte]): BigInt = {
     BigInt(new BigInteger(1, bytes))
diff --git a/crypto-test/src/test/scala/org/bitcoins/crypto/BIP340Test.scala b/crypto-test/src/test/scala/org/bitcoins/crypto/BIP340Test.scala
new file mode 100644
index 0000000000..307e20ce8b
--- /dev/null
+++ b/crypto-test/src/test/scala/org/bitcoins/crypto/BIP340Test.scala
@@ -0,0 +1,119 @@
+package org.bitcoins.crypto
+
+import org.bitcoins.testkit.util.BitcoinSUnitTest
+import org.scalatest.Assertion
+import scodec.bits.ByteVector
+
+import scala.util.{Failure, Success, Try}
+
+/** Tests from https://github.com/sipa/bips/blob/bip-taproot/bip-0340/test-vectors.csv */
+class BIP340Test extends BitcoinSUnitTest {
+  behavior of "Schnorr Signing"
+
+  def testSign(
+      index: Int,
+      secKey: ECPrivateKey,
+      auxRand: ByteVector,
+      msg: ByteVector,
+      expectedSig: SchnorrDigitalSignature): Assertion = {
+    val secpSig = secKey.schnorrSign(msg, auxRand)
+    val bouncyCastleSig = BouncyCastleUtil.schnorrSign(msg, secKey, auxRand)
+    assert(secpSig == expectedSig,
+           s"Test $index failed signing for libsecp256k1")
+    assert(bouncyCastleSig == expectedSig,
+           s"Test $index failed signing for Bouncy Castle")
+    assert(bouncyCastleSig == secpSig)
+  }
+
+  def testVerify(
+      index: Int,
+      pubKey: SchnorrPublicKey,
+      msg: ByteVector,
+      sig: SchnorrDigitalSignature,
+      expectedResult: Boolean,
+      comment: String): Assertion = {
+    val secpResult = pubKey.verify(msg, sig)
+    val bouncyCastleResult = BouncyCastleUtil.schnorrVerify(msg, pubKey, sig)
+    assert(secpResult == expectedResult,
+           s"Test $index failed verification for libsecp256k1: $comment")
+    assert(bouncyCastleResult == expectedResult,
+           s"Test $index failed verification for Bouncy Castle: $comment")
+    assert(bouncyCastleResult == secpResult)
+  }
+
+  def test(
+      index: Int,
+      secKeyOpt: Option[String],
+      pubKey: String,
+      auxRandOpt: Option[String],
+      msg: String,
+      sig: String,
+      result: Boolean,
+      comment: String): Assertion = {
+    val pkT = Try(SchnorrPublicKey(pubKey))
+    val msgBytes = ByteVector.fromHex(msg).get
+    val schnorrSigT = Try(SchnorrDigitalSignature(sig))
+
+    (pkT, schnorrSigT) match {
+      case (Success(pk), Success(schnorrSig)) =>
+        (secKeyOpt, auxRandOpt) match {
+          case (Some(secKeyStr), Some(auxRandStr)) =>
+            val secKey = ECPrivateKey(secKeyStr)
+            assert(secKey.schnorrPublicKey == pk)
+            val auxRand = ByteVector.fromHex(auxRandStr).get
+            testSign(index, secKey, auxRand, msgBytes, schnorrSig)
+          case _ => ()
+        }
+
+        testVerify(index, pk, msgBytes, schnorrSig, result, comment)
+      case (Failure(_), _) |
+          (_, Failure(_)) => // Must be verify only test resulting in false
+        assert(secKeyOpt.isEmpty)
+        assert(auxRandOpt.isEmpty)
+        assert(!result, s"Test $index failed to parse signature: $comment")
+    }
+  }
+
+  private def toOpt(str: String): Option[String] = {
+    if (str.isEmpty) {
+      None
+    } else {
+      Some(str)
+    }
+  }
+
+  it must "pass the BIP 340 test-vectors with both secp256k1 bindings and bouncy castle" in {
+    val bufferedSource =
+      io.Source.fromURL(getClass.getResource("/bip340-test-vectors.csv"))
+    try {
+      val lines = bufferedSource.getLines
+      val _ = lines.next()
+      for (line <- bufferedSource.getLines) {
+        val testVec = line.split(",").map(_.trim)
+        val index = testVec.head.toInt
+        val secKeyOpt = toOpt(testVec(1))
+        val pubKey = testVec(2)
+        val auxRandOpt = toOpt(testVec(3))
+        val msg = testVec(4)
+        val sig = testVec(5)
+        val result = testVec(6).toBoolean
+        val comment = if (testVec.length > 7) {
+          testVec(7)
+        } else {
+          ""
+        }
+
+        test(index = index,
+             secKeyOpt = secKeyOpt,
+             pubKey = pubKey,
+             auxRandOpt = auxRandOpt,
+             msg = msg,
+             sig = sig,
+             result = result,
+             comment = comment)
+      }
+    } finally {
+      bufferedSource.close()
+    }
+  }
+}
diff --git a/crypto-test/src/test/scala/org/bitcoins/crypto/BouncyCastleSecp256k1Test.scala b/crypto-test/src/test/scala/org/bitcoins/crypto/BouncyCastleSecp256k1Test.scala
index d7127d3844..d4824bdaf1 100644
--- a/crypto-test/src/test/scala/org/bitcoins/crypto/BouncyCastleSecp256k1Test.scala
+++ b/crypto-test/src/test/scala/org/bitcoins/crypto/BouncyCastleSecp256k1Test.scala
@@ -10,6 +10,9 @@ import scodec.bits.ByteVector
 
 class BouncyCastleSecp256k1Test extends BitcoinSUnitTest {
 
+  implicit override val generatorDrivenConfig: PropertyCheckConfiguration =
+    generatorDrivenConfigNewCode
+
   behavior of "CryptoLibraries"
 
   override def withFixture(test: NoArgTest): Outcome = {
@@ -24,16 +27,7 @@ class BouncyCastleSecp256k1Test extends BitcoinSUnitTest {
   it must "add private keys the same" in {
     forAll(CryptoGenerators.privateKey, CryptoGenerators.privateKey) {
       case (priv1, priv2) =>
-        val sumWithBouncyCastle =
-          BouncyCastleUtil.addNumbers(priv1.bytes, priv2.bytes)
-        val sumWithSecp = NativeSecp256k1.privKeyTweakAdd(priv1.bytes.toArray,
-                                                          priv2.bytes.toArray)
-
-        val sumKeyWithBouncyCastle =
-          ECPrivateKey(ByteVector(sumWithBouncyCastle.toByteArray))
-        val sumKeyWithSecp = ECPrivateKey(ByteVector(sumWithSecp))
-
-        assert(sumKeyWithBouncyCastle == sumKeyWithSecp)
+        assert(priv1.addWithBouncyCastle(priv2) == priv1.addWithSecp(priv2))
     }
   }
 
@@ -51,6 +45,15 @@ class BouncyCastleSecp256k1Test extends BitcoinSUnitTest {
     }
   }
 
+  it must "multiply keys the same" in {
+    forAll(CryptoGenerators.publicKey, CryptoGenerators.fieldElement) {
+      case (pubKey, tweak) =>
+        assert(
+          pubKey.tweakMultiplyWithSecp(tweak) == pubKey
+            .tweakMultiplyWithBouncyCastle(tweak))
+    }
+  }
+
   it must "validate keys the same" in {
     val keyOrGarbageGen = Gen.oneOf(CryptoGenerators.publicKey.map(_.bytes),
                                     NumberGenerator.bytevector(33))
@@ -102,4 +105,66 @@ class BouncyCastleSecp256k1Test extends BitcoinSUnitTest {
             .verify(bytes, badSig, context = LibSecp256k1))
     }
   }
+
+  /*
+  it must "compute schnorr signatures the same" in {
+    forAll(CryptoGenerators.privateKey,
+           NumberGenerator.bytevector(32),
+           NumberGenerator.bytevector(32)) {
+      case (privKey, bytes, auxRand) =>
+        assert(
+          privKey.schnorrSign(bytes, auxRand, context = BouncyCastle) == privKey
+            .schnorrSign(bytes, auxRand, context = LibSecp256k1))
+    }
+  }
+
+  it must "compute schnorr signature for fixed nonce the same" in {
+    forAll(CryptoGenerators.privateKey,
+           CryptoGenerators.privateKey,
+           NumberGenerator.bytevector(32)) {
+      case (privKey, nonceKey, bytes) =>
+        val sigBC = privKey
+          .schnorrSignWithNonce(bytes, nonceKey, context = BouncyCastle)
+        val sigSecP = privKey
+          .schnorrSignWithNonce(bytes, nonceKey, context = LibSecp256k1)
+        assert(sigBC.bytes == sigSecP.bytes)
+    }
+  }
+
+  it must "validate schnorr signatures the same" in {
+    forAll(CryptoGenerators.privateKey,
+           NumberGenerator.bytevector(32),
+           CryptoGenerators.schnorrDigitalSignature) {
+      case (privKey, bytes, badSig) =>
+        val sig = privKey.schnorrSign(bytes)
+        val pubKey = privKey.schnorrPublicKey
+        assert(
+          pubKey.verify(bytes, sig, context = BouncyCastle) == pubKey
+            .verify(bytes, sig, context = LibSecp256k1))
+        assert(
+          pubKey.verify(bytes, badSig, context = BouncyCastle) == pubKey
+            .verify(bytes, badSig, context = LibSecp256k1))
+    }
+  }
+
+  it must "compute schnorr signature points the same" in {
+    forAll(CryptoGenerators.schnorrPublicKey,
+           CryptoGenerators.schnorrNonce,
+           NumberGenerator.bytevector(32)) {
+      case (pubKey, nonce, bytes) =>
+        val bouncyCastleSigPoint =
+          pubKey.computeSigPoint(bytes,
+                                 nonce,
+                                 compressed = true,
+                                 context = BouncyCastle)
+
+        val secpSigPoint = pubKey.computeSigPoint(bytes,
+                                                  nonce,
+                                                  compressed = true,
+                                                  context = LibSecp256k1)
+
+        assert(bouncyCastleSigPoint == secpSigPoint)
+    }
+  }
+ */
 }
diff --git a/crypto-test/src/test/scala/org/bitcoins/crypto/ECPrivateKeyTest.scala b/crypto-test/src/test/scala/org/bitcoins/crypto/ECPrivateKeyTest.scala
index 2131e7c095..52bd1e52ce 100644
--- a/crypto-test/src/test/scala/org/bitcoins/crypto/ECPrivateKeyTest.scala
+++ b/crypto-test/src/test/scala/org/bitcoins/crypto/ECPrivateKeyTest.scala
@@ -80,6 +80,7 @@ class ECPrivateKeyTest extends BitcoinSUnitTest {
   it must "have serialization symmetry" in {
     forAll(CryptoGenerators.privateKey) { privKey =>
       assert(ECPrivateKey(privKey.hex) == privKey)
+      assert(ECPrivateKey.fromFieldElement(privKey.fieldElement) == privKey)
     }
   }
 
@@ -104,4 +105,16 @@ class ECPrivateKeyTest extends BitcoinSUnitTest {
     ECPrivateKey().toString must be("Masked(ECPrivateKeyImpl)")
   }
 
+  it must "successfully negate itself" in {
+    forAll(CryptoGenerators.nonZeroPrivKey) { privKey =>
+      val negPrivKey = privKey.negate
+      val pubKey = privKey.publicKey
+      val negPubKey = negPrivKey.publicKey
+      assert(pubKey.bytes.tail == negPubKey.bytes.tail)
+      assert(pubKey.bytes.head != negPubKey.bytes.head)
+      assert(
+        privKey.fieldElement.add(negPrivKey.fieldElement) == FieldElement.zero)
+    }
+  }
+
 }
diff --git a/crypto-test/src/test/scala/org/bitcoins/crypto/FieldElementTest.scala b/crypto-test/src/test/scala/org/bitcoins/crypto/FieldElementTest.scala
new file mode 100644
index 0000000000..2e7bba55f4
--- /dev/null
+++ b/crypto-test/src/test/scala/org/bitcoins/crypto/FieldElementTest.scala
@@ -0,0 +1,97 @@
+package org.bitcoins.crypto
+
+import org.bitcoins.testkit.core.gen.CryptoGenerators
+import org.bitcoins.testkit.util.BitcoinSUnitTest
+
+class FieldElementTest extends BitcoinSUnitTest {
+
+  implicit override val generatorDrivenConfig: PropertyCheckConfiguration =
+    generatorDrivenConfigNewCode
+
+  behavior of "FieldElement"
+
+  private val N = CryptoParams.curve.getN
+
+  it must "have serialization symmetry" in {
+    forAll(CryptoGenerators.fieldElement) { fe =>
+      assert(FieldElement(fe.bytes) == fe)
+    }
+  }
+
+  it must "add zero correctly" in {
+    forAll(CryptoGenerators.fieldElement) { fe =>
+      assert(fe.add(FieldElement.zero) == fe)
+      assert(FieldElement.zero.add(fe) == fe)
+    }
+  }
+
+  it must "add small numbers correctly" in {
+    forAll(CryptoGenerators.smallFieldElement,
+           CryptoGenerators.smallFieldElement) {
+      case (fe1, fe2) =>
+        val feSum = fe1.add(fe2).toBigInteger
+        val bigIntSum = fe1.toBigInteger.add(fe2.toBigInteger)
+
+        assert(feSum == bigIntSum)
+    }
+  }
+
+  it must "add large numbers correctly" in {
+    forAll(CryptoGenerators.largeFieldElement,
+           CryptoGenerators.largeFieldElement) {
+      case (fe1, fe2) =>
+        val feSum = fe1.add(fe2).toBigInteger
+        val bigIntSum = fe1.toBigInteger.add(fe2.toBigInteger).subtract(N)
+
+        assert(feSum == bigIntSum)
+    }
+  }
+
+  it must "subtract numbers correctly" in {
+    forAll(CryptoGenerators.fieldElement, CryptoGenerators.fieldElement) {
+      case (fe1, fe2) =>
+        if (fe1.toBigInteger.compareTo(fe2.toBigInteger) > 0) {
+          val feDiff = fe1.subtract(fe2).toBigInteger
+          val bigIntDiff = fe1.toBigInteger.subtract(fe2.toBigInteger)
+
+          assert(feDiff == bigIntDiff)
+        } else {
+          val feDiff = fe2.subtract(fe1).toBigInteger
+          val bigIntDiff = fe2.toBigInteger.subtract(fe1.toBigInteger)
+
+          assert(feDiff == bigIntDiff)
+        }
+    }
+  }
+
+  it must "wrap around correctly" in {
+    assert(FieldElement.nMinusOne.add(FieldElement.one) == FieldElement.zero)
+    assert(
+      FieldElement.zero.subtract(FieldElement.one) == FieldElement.nMinusOne)
+  }
+
+  it must "multiply small numbers correctly" in {
+    forAll(CryptoGenerators.reallySmallFieldElement,
+           CryptoGenerators.reallySmallFieldElement) {
+      case (fe1, fe2) =>
+        val feProduct = fe1.multiply(fe2).toBigInteger
+        val bigIntProduct = fe1.toBigInteger.multiply(fe2.toBigInteger)
+
+        assert(feProduct == bigIntProduct)
+    }
+  }
+
+  it must "negate correctly" in {
+    forAll(CryptoGenerators.fieldElement) { fe =>
+      val negFe = fe.negate
+      assert(fe.add(negFe) == FieldElement.zero)
+    }
+  }
+
+  it must "invert correctly" in {
+    forAll(CryptoGenerators.fieldElement) { fe =>
+      val feInv = fe.inverse
+      assert(fe.multiply(feInv) == FieldElement.one)
+    }
+  }
+}
diff --git a/crypto-test/src/test/scala/org/bitcoins/crypto/SchnorrDigitalSignatureTest.scala b/crypto-test/src/test/scala/org/bitcoins/crypto/SchnorrDigitalSignatureTest.scala
new file mode 100644
index 0000000000..77d5b8cd57
--- /dev/null
+++ b/crypto-test/src/test/scala/org/bitcoins/crypto/SchnorrDigitalSignatureTest.scala
@@ -0,0 +1,132 @@
+package org.bitcoins.crypto
+
+import org.bitcoins.core.util.NumberUtil
+import org.bitcoins.testkit.core.gen.{CryptoGenerators, NumberGenerator}
+import org.bitcoins.testkit.util.BitcoinSUnitTest
+
+class SchnorrDigitalSignatureTest extends BitcoinSUnitTest {
+
+  implicit override val generatorDrivenConfig: PropertyCheckConfiguration =
+    generatorDrivenConfigNewCode
+
+  behavior of "SchnorrDigitalSignature"
+
+  it must "have serialization symmetry" in {
+    forAll(CryptoGenerators.schnorrDigitalSignature) { sig =>
+      assert(SchnorrDigitalSignature(sig.bytes) == sig)
+    }
+  }
+
+  it must "must create and verify a digital signature" in {
+    forAll(NumberGenerator.bytevector(32), CryptoGenerators.privateKey) {
+      case (bytes, privKey) =>
+        val sig = privKey.schnorrSign(bytes)
+        assert(privKey.publicKey.schnorrVerify(bytes, sig))
+    }
+  }
+
+  it must "must not reuse R values" in {
+    forAll(CryptoGenerators.privateKey,
+           NumberGenerator.bytevector(32),
+           NumberGenerator.bytevector(32)) {
+      case (privKey, bytes1, bytes2) =>
+        val sig1 = privKey.schnorrSign(bytes1)
+        val sig2 = privKey.schnorrSign(bytes2)
+        assert(sig1.bytes != sig2.bytes)
+        assert(sig1.rx != sig2.rx)
+    }
+  }
+
+  it must "generate R values correctly" in {
+    forAll(CryptoGenerators.privateKey,
+           NumberGenerator.bytevector(32),
+           NumberGenerator.bytevector(32)) {
+      case (privKey, auxRand, bytes) =>
+        val nonce = SchnorrNonce.kFromBipSchnorr(privKey, bytes, auxRand)
+
+        val sig1 = privKey.schnorrSign(bytes, auxRand)
+        val sig2 = privKey.schnorrSignWithNonce(bytes, nonce)
+
+        assert(sig1 == sig2)
+    }
+  }
+
+  it must "correctly compute signature points" in {
+    forAll(CryptoGenerators.privateKey, NumberGenerator.bytevector(32)) {
+      case (privKey, data) =>
+        val pubKey = privKey.publicKey
+        val sig = privKey.schnorrSign(data)
+
+        val sigPoint = pubKey.schnorrComputePoint(data, sig.rx)
+        assert(sigPoint == sig.sig.toPrivateKey.publicKey)
+    }
+  }
+
+  it must "correctly compute signature points for sigs with fixed nonces" in {
+    forAll(CryptoGenerators.privateKey,
+           NumberGenerator.bytevector(32),
+           CryptoGenerators.privateKey) {
+      case (privKey, data, nonce) =>
+        val pubKey = privKey.publicKey
+        val sig = privKey.schnorrSignWithNonce(data, nonce)
+        assert(sig.rx == nonce.schnorrNonce)
+
+        val sigPoint = pubKey.schnorrComputePoint(data, sig.rx)
+        assert(sigPoint == sig.sig.toPrivateKey.publicKey)
+    }
+  }
+
+  /** Schnorr signatures have the property that if two messages are signed with the same key
+    * and nonce, then they are leaked:
+    *
+    * sig1 = nonce + message1*privKey
+    * sig2 = nonce + message2*privKey
+    *
+    * => sig1 - sig2 = (message1 - message2)*privKey
+    * => privKey = (sig1 - sig2) * inverse(message1 - message2)
+    */
+  it must "leak keys if two messages are signed" in {
+    forAll(CryptoGenerators.nonZeroPrivKey,
+           CryptoGenerators.nonZeroPrivKey,
+           NumberGenerator.bytevector(32),
+           NumberGenerator.bytevector(32)) {
+      case (privKey, nonce, message1, message2) =>
+        // This will only work if we sign two different messages
+        assert(message1 != message2)
+
+        // Sign both messages using the same privKey and nonce
+        val sig1 = privKey.schnorrSignWithNonce(message1, nonce)
+        val sig2 = privKey.schnorrSignWithNonce(message2, nonce)
+
+        // s1 = nonce + e1*privKey
+        val s1 = sig1.sig
+        // s2 = nonce + e2*privKey
+        val s2 = sig2.sig
+
+        // When signing a message you actually sign SHA256_challenge(Rx || pubKey || message)
+        val bytesToHash1 = sig1.rx.bytes ++ privKey.schnorrPublicKey.bytes ++ message1
+        val e1Bytes = CryptoUtil.sha256SchnorrChallenge(bytesToHash1).bytes
+
+        val bytesToHash2 = sig2.rx.bytes ++ privKey.schnorrPublicKey.bytes ++ message2
+        val e2Bytes = CryptoUtil.sha256SchnorrChallenge(bytesToHash2).bytes
+
+        val e1 = NumberUtil.uintToFieldElement(e1Bytes)
+        val e2 = NumberUtil.uintToFieldElement(e2Bytes)
+
+        val k = nonce.nonceKey.fieldElement
+        val x = privKey.schnorrKey.fieldElement
+
+        // Test that we have correctly computed the components
+        assert(k.add(e1.multiply(x)) == s1)
+        assert(k.add(e2.multiply(x)) == s2)
+
+        // Note that all of s1, s2, e1, and e2 are public information:
+        // s1 - s2 = nonce + e1*privKey - (nonce + e2*privKey) = privKey*(e1-e2)
+        // => privKey = (s1 - s2) * modInverse(e1 - e2)
+        val privNum = s1.subtract(s2).multInv(e1.subtract(e2))
+
+        // Assert that we've correctly recovered the private key form public info
+        assert(privNum == x)
+    }
+  }
+}
diff --git a/crypto-test/src/test/scala/org/bitcoins/crypto/SchnorrNonceTest.scala b/crypto-test/src/test/scala/org/bitcoins/crypto/SchnorrNonceTest.scala
new file mode 100644
index 0000000000..8e8c89e7fa
--- /dev/null
+++ b/crypto-test/src/test/scala/org/bitcoins/crypto/SchnorrNonceTest.scala
@@ -0,0 +1,39 @@
+package org.bitcoins.crypto
+
+import org.bitcoins.testkit.core.gen.CryptoGenerators
+import org.bitcoins.testkit.util.BitcoinSUnitTest
+
+class SchnorrNonceTest extends BitcoinSUnitTest {
+
+  implicit override val generatorDrivenConfig: PropertyCheckConfiguration =
+    generatorDrivenConfigNewCode
+
+  behavior of "SchnorrNonce"
+
+  it must "fail for incorrect lengths" in {
+    assertThrows[IllegalArgumentException](
+      SchnorrNonce(
+        "676f8c22de526e0c0904719847e63bda47b4eceb6986bdbaf8695db362811a"))
+
+    assertThrows[IllegalArgumentException](
+      SchnorrNonce(
+        "676f8c22de526e0c0904719847e63bda47b4eceb6986bdbaf8695db362811a010203"))
+  }
+
+  it must "fail for invalid x coordinate" in {
+    assertThrows[IllegalArgumentException](
+      SchnorrNonce(
+        "EEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34"))
+
+    assertThrows[IllegalArgumentException](
+      SchnorrNonce(
+        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC30"))
+  }
+
+  it must "have serialization symmetry" in {
+    forAll(CryptoGenerators.schnorrNonce) { pubKey =>
+      assert(SchnorrNonce(pubKey.bytes) == pubKey)
+      assert(SchnorrNonce(pubKey.xCoord) == pubKey)
+    }
+  }
+}
diff --git a/crypto-test/src/test/scala/org/bitcoins/crypto/SchnorrPublicKeyTest.scala b/crypto-test/src/test/scala/org/bitcoins/crypto/SchnorrPublicKeyTest.scala
new file mode 100644
index 0000000000..9b507296a5
--- /dev/null
+++ b/crypto-test/src/test/scala/org/bitcoins/crypto/SchnorrPublicKeyTest.scala
@@ -0,0 +1,39 @@
+package org.bitcoins.crypto
+
+import org.bitcoins.testkit.core.gen.CryptoGenerators
+import org.bitcoins.testkit.util.BitcoinSUnitTest
+
+class SchnorrPublicKeyTest extends BitcoinSUnitTest {
+
+  implicit override val generatorDrivenConfig: PropertyCheckConfiguration =
+    generatorDrivenConfigNewCode
+
+  behavior of "SchnorrPublicKey"
+
+  it must "fail for incorrect lengths" in {
+    assertThrows[IllegalArgumentException](
+      SchnorrPublicKey(
+        "676f8c22de526e0c0904719847e63bda47b4eceb6986bdbaf8695db362811a"))
+
+    assertThrows[IllegalArgumentException](
+      SchnorrPublicKey(
+        "676f8c22de526e0c0904719847e63bda47b4eceb6986bdbaf8695db362811a010203"))
+  }
+
+  it must "fail for invalid x coordinate" in {
+    assertThrows[IllegalArgumentException](
+      SchnorrPublicKey(
+        "EEFDEA4CDB677750A420FEE807EACF21EB9898AE79B9768766E4FAA04A2D4A34"))
+
+    assertThrows[IllegalArgumentException](
+      SchnorrPublicKey(
+        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC30"))
+  }
+
+  it must "have serialization symmetry" in {
+    forAll(CryptoGenerators.schnorrPublicKey) { pubKey =>
+      assert(SchnorrPublicKey(pubKey.bytes) == pubKey)
+      assert(SchnorrPublicKey(pubKey.xCoord) == pubKey)
+    }
+  }
+}
diff --git a/crypto/src/main/scala/org/bitcoins/crypto/BouncyCastleUtil.scala b/crypto/src/main/scala/org/bitcoins/crypto/BouncyCastleUtil.scala
index 5d41133151..c34875a567 100644
--- a/crypto/src/main/scala/org/bitcoins/crypto/BouncyCastleUtil.scala
+++ b/crypto/src/main/scala/org/bitcoins/crypto/BouncyCastleUtil.scala
@@ -11,23 +11,20 @@ import org.bouncycastle.crypto.signers.{ECDSASigner, HMacDSAKCalculator}
 import org.bouncycastle.math.ec.{ECCurve, ECPoint}
 import scodec.bits.ByteVector
 
-import scala.util.Try
+import scala.util.{Failure, Success, Try}
 
 object BouncyCastleUtil {
 
   private val curve: ECCurve = CryptoParams.curve.getCurve
   private val G: ECPoint = CryptoParams.curve.getG
-  private val N: BigInteger = CryptoParams.curve.getN
 
   private def getBigInteger(bytes: ByteVector): BigInteger = {
     new BigInteger(1, bytes.toArray)
   }
 
-  def addNumbers(num1: ByteVector, num2: ByteVector): BigInteger = {
-    val bigInteger1 = getBigInteger(num1)
-    val bigInteger2 = getBigInteger(num2)
-
-    bigInteger1.add(bigInteger2).mod(N)
+  def pubKeyTweakMul(publicKey: ECPublicKey, tweak: ByteVector): ECPublicKey = {
+    val point = publicKey.toPoint.multiply(getBigInteger(tweak))
+    ECPublicKey.fromPoint(point, publicKey.isCompressed)
   }
 
   def decodePoint(bytes: ByteVector): ECPoint = {
@@ -109,4 +106,79 @@ object BouncyCastleUtil {
     }
     resultTry.getOrElse(false)
   }
+
+  def schnorrSign(
+      dataToSign: ByteVector,
+      privateKey: ECPrivateKey,
+      auxRand: ByteVector): SchnorrDigitalSignature = {
+    val nonceKey =
+      SchnorrNonce.kFromBipSchnorr(privateKey, dataToSign, auxRand)
+
+    schnorrSignWithNonce(dataToSign, privateKey, nonceKey)
+  }
+
+  def schnorrSignWithNonce(
+      dataToSign: ByteVector,
+      privateKey: ECPrivateKey,
+      nonceKey: ECPrivateKey): SchnorrDigitalSignature = {
+    val rx = nonceKey.schnorrNonce
+    val k = nonceKey.nonceKey.fieldElement
+    val x = privateKey.schnorrKey.fieldElement
+    val e = CryptoUtil
+      .sha256SchnorrChallenge(
+        rx.bytes ++ privateKey.schnorrPublicKey.bytes ++ dataToSign)
+      .bytes
+
+    val challenge = x.multiply(FieldElement(e))
+    val sig = k.add(challenge)
+
+    SchnorrDigitalSignature(rx, sig)
+  }
+
+  def schnorrVerify(
+      data: ByteVector,
+      schnorrPubKey: SchnorrPublicKey,
+      signature: SchnorrDigitalSignature): Boolean = {
+    val rx = signature.rx
+    val sT = Try(signature.sig.toPrivateKey)
+
+    sT match {
+      case Success(s) =>
+        val eBytes = CryptoUtil
+          .sha256SchnorrChallenge(rx.bytes ++ schnorrPubKey.bytes ++ data)
+          .bytes
+
+        val e = FieldElement(eBytes)
+        val negE = e.negate
+
+        val sigPoint = s.publicKey
+        val challengePoint = schnorrPubKey.publicKey.tweakMultiply(negE)
+        val computedR = challengePoint.add(sigPoint)
+        val yCoord = computedR.toPoint.getRawYCoord
+
+        yCoord != null && yCoord.sqrt() != null && computedR.schnorrNonce == rx
+      case Failure(_) => false
+    }
+  }
+
+  def schnorrComputeSigPoint(
+      data: ByteVector,
+      nonce: SchnorrNonce,
+      pubKey: SchnorrPublicKey,
+      compressed: Boolean): ECPublicKey = {
+    val eBytes = CryptoUtil
+      .sha256SchnorrChallenge(nonce.bytes ++ pubKey.bytes ++ data)
+      .bytes
+
+    val e = FieldElement(eBytes)
+
+    val compressedSigPoint =
+      nonce.publicKey.add(pubKey.publicKey.tweakMultiply(e))
+
+    if (compressed) {
+      compressedSigPoint
+    } else {
+      compressedSigPoint.decompressed
+    }
+  }
 }
diff --git a/crypto/src/main/scala/org/bitcoins/crypto/CryptoBytesUtil.scala b/crypto/src/main/scala/org/bitcoins/crypto/CryptoBytesUtil.scala
index 45c1663d28..498b7aeb0b 100644
--- a/crypto/src/main/scala/org/bitcoins/crypto/CryptoBytesUtil.scala
+++ b/crypto/src/main/scala/org/bitcoins/crypto/CryptoBytesUtil.scala
@@ -67,6 +67,7 @@ trait CryptoBytesUtil {
   def flipEndianness(bytes: ByteVector): String = encodeHex(bytes.reverse)
 
   private val Z: Char = '0'
+
   /**
     * Adds the amount padding bytes needed to fix the size of the hex string
     * for instance, ints are required to be 4 bytes. If the number is just 1
@@ -78,7 +79,7 @@ trait CryptoBytesUtil {
     var counter = 0
     while (counter < paddingNeeded) {
       builder.append(Z)
-      counter+=1
+      counter += 1
     }
     builder.appendAll(hex)
     builder.result()
diff --git a/crypto/src/main/scala/org/bitcoins/crypto/CryptoUtil.scala b/crypto/src/main/scala/org/bitcoins/crypto/CryptoUtil.scala
index 6c26d1926f..51217d2fbf 100644
--- a/crypto/src/main/scala/org/bitcoins/crypto/CryptoUtil.scala
+++ b/crypto/src/main/scala/org/bitcoins/crypto/CryptoUtil.scala
@@ -37,6 +37,48 @@ trait CryptoUtil {
     sha256(bits.toByteVector)
   }
 
+  def taggedSha256(bytes: ByteVector, tag: String): Sha256Digest = {
+    val tagHash = sha256(ByteVector(tag.getBytes()))
+    val tagBytes = tagHash.bytes ++ tagHash.bytes
+    sha256(tagBytes ++ bytes)
+  }
+
+  // The tag "BIP340/challenge"
+  private val schnorrChallengeTagBytes = {
+    ByteVector
+      .fromValidHex(
+        "07e00dcd3055c1b36ee93effe4d7f266024cdef4116982ff5dfdc1a97e77062907e00dcd3055c1b36ee93effe4d7f266024cdef4116982ff5dfdc1a97e770629"
+      )
+  }
+
+  def sha256SchnorrChallenge(bytes: ByteVector): Sha256Digest = {
+    sha256(schnorrChallengeTagBytes ++ bytes)
+  }
+
+  // The tag "BIP340/nonce"
+  private val schnorrNonceTagBytes = {
+    ByteVector
+      .fromValidHex(
+        "a2ba14a6b39c1c505260bf3aceb07febde3ab34c35c9259d25bd6972f15e6564a2ba14a6b39c1c505260bf3aceb07febde3ab34c35c9259d25bd6972f15e6564"
+      )
+  }
+
+  def sha256SchnorrNonce(bytes: ByteVector): Sha256Digest = {
+    sha256(schnorrNonceTagBytes ++ bytes)
+  }
+
+  // The tag "BIP340/aux"
+  private val schnorrAuxTagBytes = {
+    ByteVector
+      .fromValidHex(
+        "4b07426ad8630dcdbadf8dee1e94f09ac2df4e7ee2629e5e6b27c8666c8cf31e4b07426ad8630dcdbadf8dee1e94f09ac2df4e7ee2629e5e6b27c8666c8cf31e"
+      )
+  }
+
+  def sha256SchnorrAuxRand(bytes: ByteVector): Sha256Digest = {
+    sha256(schnorrAuxTagBytes ++ bytes)
+  }
+
   /** Performs SHA1(bytes). */
   def sha1(bytes: ByteVector): Sha1Digest = {
     val hash = MessageDigest.getInstance("SHA-1").digest(bytes.toArray).toList
diff --git a/crypto/src/main/scala/org/bitcoins/crypto/ECDigitalSignature.scala b/crypto/src/main/scala/org/bitcoins/crypto/ECDigitalSignature.scala
index 40f36475c1..f678ebd55e 100644
--- a/crypto/src/main/scala/org/bitcoins/crypto/ECDigitalSignature.scala
+++ b/crypto/src/main/scala/org/bitcoins/crypto/ECDigitalSignature.scala
@@ -10,6 +10,9 @@ sealed abstract class ECDigitalSignature {
   require(s.signum == 1 || s.signum == 0, s"s must not be negative, got $s")
   def hex: String = CryptoBytesUtil.encodeHex(bytes)
 
+  def ==(p: ECDigitalSignature): Boolean = this.bytes == p.bytes
+  def !=(p: ECDigitalSignature): Boolean = !(this == p)
+
   def bytes: ByteVector
 
   def isEmpty: Boolean = bytes.isEmpty
diff --git a/crypto/src/main/scala/org/bitcoins/crypto/ECKey.scala b/crypto/src/main/scala/org/bitcoins/crypto/ECKey.scala
index f8e31e3d5f..03cee0b968 100644
--- a/crypto/src/main/scala/org/bitcoins/crypto/ECKey.scala
+++ b/crypto/src/main/scala/org/bitcoins/crypto/ECKey.scala
@@ -71,6 +71,104 @@ sealed abstract class ECPrivateKey
       implicit ec: ExecutionContext): Future[ECDigitalSignature] =
     Future(sign(hash))
 
+  def schnorrSign(dataToSign: ByteVector): SchnorrDigitalSignature = {
+    val auxRand = ECPrivateKey.freshPrivateKey.bytes
+    schnorrSign(dataToSign, auxRand)
+  }
+
+  // TODO: match on CryptoContext once secp version is added
+  def schnorrSign(
+      dataToSign: ByteVector,
+      auxRand: ByteVector): SchnorrDigitalSignature = {
+    schnorrSignWithBouncyCastle(dataToSign, auxRand)
+  }
+
+  /*
+  def schnorrSignWithSecp(
+      dataToSign: ByteVector,
+      auxRand: ByteVector): SchnorrDigitalSignature = {
+    val sigBytes =
+      NativeSecp256k1.schnorrSign(dataToSign.toArray,
+                                  bytes.toArray,
+                                  auxRand.toArray)
+    SchnorrDigitalSignature(ByteVector(sigBytes))
+  }
+   */
+
+  def schnorrSignWithBouncyCastle(
+      dataToSign: ByteVector,
+      auxRand: ByteVector): SchnorrDigitalSignature = {
+    BouncyCastleUtil.schnorrSign(dataToSign, this, auxRand)
+  }
+
+  // TODO: match on CryptoContext once secp version is added
+  def schnorrSignWithNonce(
+      dataToSign: ByteVector,
+      nonce: ECPrivateKey): SchnorrDigitalSignature = {
+    schnorrSignWithNonceWithBouncyCastle(dataToSign, nonce)
+  }
+
+  /*
+  def schnorrSignWithNonceWithSecp(
+      dataToSign: ByteVector,
+      nonce: ECPrivateKey): SchnorrDigitalSignature = {
+    val sigBytes =
+      NativeSecp256k1.schnorrSignWithNonce(dataToSign.toArray,
+                                           bytes.toArray,
+                                           nonce.bytes.toArray)
+    SchnorrDigitalSignature(ByteVector(sigBytes))
+  }
+   */
+
+  def schnorrSignWithNonceWithBouncyCastle(
+      dataToSign: ByteVector,
+      nonce: ECPrivateKey): SchnorrDigitalSignature = {
+    BouncyCastleUtil.schnorrSignWithNonce(dataToSign, this, nonce)
+  }
+
+  def nonceKey: ECPrivateKey = {
+    if (schnorrNonce.publicKey == publicKey) {
+      this
+    } else {
+      this.negate
+    }
+  }
+
+  def schnorrKey: ECPrivateKey = {
+    if (schnorrPublicKey.publicKey == publicKey) {
+      this
+    } else {
+      this.negate
+    }
+  }
+
+  def negate: ECPrivateKey = {
+    val negPrivKeyNum = CryptoParams.curve.getN
+      .subtract(new BigInteger(1, bytes.toArray))
+    ECPrivateKey(ByteVector(negPrivKeyNum.toByteArray))
+  }
+
+  def add(other: ECPrivateKey): ECPrivateKey = {
+    add(other, CryptoContext.default)
+  }
+
+  def add(other: ECPrivateKey, context: CryptoContext): ECPrivateKey = {
+    context match {
+      case CryptoContext.LibSecp256k1 => addWithSecp(other)
+      case CryptoContext.BouncyCastle => addWithBouncyCastle(other)
+    }
+  }
+
+  def addWithSecp(other: ECPrivateKey): ECPrivateKey = {
+    val sumBytes =
+      NativeSecp256k1.privKeyTweakAdd(bytes.toArray, other.bytes.toArray)
+    ECPrivateKey(ByteVector(sumBytes))
+  }
+
+  def addWithBouncyCastle(other: ECPrivateKey): ECPrivateKey = {
+    fieldElement.add(other.fieldElement).toPrivateKey
+  }
+
   /** Signifies if the this private key corresponds to a compressed public key */
   def isCompressed: Boolean
 
@@ -99,6 +197,16 @@ sealed abstract class ECPrivateKey
     BouncyCastleUtil.computePublicKey(this)
   }
 
+  def schnorrPublicKey: SchnorrPublicKey = {
+    SchnorrPublicKey(publicKey.bytes)
+  }
+
+  def schnorrNonce: SchnorrNonce = {
+    SchnorrNonce(publicKey.bytes)
+  }
+
+  def fieldElement: FieldElement = FieldElement(bytes)
+
   override def toStringSensitive: String = s"ECPrivateKey($hex,$isCompressed)"
 }
 
@@ -148,6 +256,10 @@ object ECPrivateKey extends Factory[ECPrivateKey] {
   def fromHex(hex: String, isCompressed: Boolean): ECPrivateKey =
     fromBytes(CryptoBytesUtil.decodeHex(hex), isCompressed)
 
+  def fromFieldElement(fieldElement: FieldElement): ECPrivateKey = {
+    fieldElement.toPrivateKey
+  }
+
   /** Generates a fresh [[org.bitcoins.crypto.ECPrivateKey ECPrivateKey]] that has not been used before. */
   def apply(): ECPrivateKey = ECPrivateKey(true)
 
@@ -223,6 +335,23 @@ sealed abstract class ECPublicKey extends BaseECKey {
   def verify(hex: String, signature: ECDigitalSignature): Boolean =
     verify(CryptoBytesUtil.decodeHex(hex), signature)
 
+  def schnorrVerify(
+      data: ByteVector,
+      signature: SchnorrDigitalSignature): Boolean = {
+    schnorrPublicKey.verify(data, signature)
+  }
+
+  def schnorrComputePoint(
+      data: ByteVector,
+      nonce: SchnorrNonce,
+      compressed: Boolean = isCompressed): ECPublicKey = {
+    schnorrPublicKey.computeSigPoint(data, nonce, compressed)
+  }
+
+  def schnorrPublicKey: SchnorrPublicKey = SchnorrPublicKey(bytes)
+
+  def schnorrNonce: SchnorrNonce = SchnorrNonce(bytes)
+
   override def toString: String = "ECPublicKey(" + hex + ")"
 
   /** Checks if the [[org.bitcoins.crypto.ECPublicKey ECPublicKey]] is compressed */
@@ -275,6 +404,30 @@ sealed abstract class ECPublicKey extends BaseECKey {
 
     ECPublicKey.fromPoint(sumPoint)
   }
+
+  def tweakMultiply(tweak: FieldElement): ECPublicKey = {
+    tweakMultiply(tweak, CryptoContext.default)
+  }
+
+  def tweakMultiply(
+      tweak: FieldElement,
+      context: CryptoContext): ECPublicKey = {
+    context match {
+      case CryptoContext.LibSecp256k1 => tweakMultiplyWithSecp(tweak)
+      case CryptoContext.BouncyCastle => tweakMultiplyWithBouncyCastle(tweak)
+    }
+  }
+
+  def tweakMultiplyWithSecp(tweak: FieldElement): ECPublicKey = {
+    val mulBytes = NativeSecp256k1.pubKeyTweakMul(bytes.toArray,
+                                                  tweak.bytes.toArray,
+                                                  isCompressed)
+    ECPublicKey(ByteVector(mulBytes))
+  }
+
+  def tweakMultiplyWithBouncyCastle(tweak: FieldElement): ECPublicKey = {
+    BouncyCastleUtil.pubKeyTweakMul(this, tweak.bytes)
+  }
 }
 
 object ECPublicKey extends Factory[ECPublicKey] {
diff --git a/crypto/src/main/scala/org/bitcoins/crypto/FieldElement.scala b/crypto/src/main/scala/org/bitcoins/crypto/FieldElement.scala
new file mode 100644
index 0000000000..d397c3ad47
--- /dev/null
+++ b/crypto/src/main/scala/org/bitcoins/crypto/FieldElement.scala
@@ -0,0 +1,132 @@
+package org.bitcoins.crypto
+
+import java.math.BigInteger
+
+import org.bouncycastle.math.ec.ECPoint
+import scodec.bits.ByteVector
+
+import scala.util.Try
+
+/**
+  * Represents integers modulo the secp256k1 field size: pow(2,256) - 0x1000003D1.
+  *
+  * Supports arithmetic for these elements including +, -, *, and inverses.
+  * Supports 32 byte serialization as is needed for ECPrivateKeys.
+  */
+case class FieldElement(bytes: ByteVector) extends NetworkElement {
+  require(bytes.length == 32, s"Field elements must have 32 bytes, got $bytes")
+
+  private val privKeyT: Try[ECPrivateKey] = Try(ECPrivateKey(bytes))
+
+  require(
+    privKeyT.isSuccess || isZero,
+    s"$bytes is not a valid field element: ${privKeyT.failed.get.getMessage}")
+
+  def isZero: Boolean = bytes.toArray.forall(_ == 0.toByte)
+
+  def toPrivateKey: ECPrivateKey =
+    if (!isZero) {
+      privKeyT.get
+    } else {
+      throw new RuntimeException("Cannot turn zero into a private key")
+    }
+
+  def toBigInteger: BigInteger = FieldElement.getBigInteger(bytes)
+
+  def add(other: FieldElement): FieldElement = {
+    FieldElement.add(this, other)
+  }
+
+  def subtract(other: FieldElement): FieldElement = {
+    add(other.negate)
+  }
+
+  def multiply(other: FieldElement): FieldElement = {
+    FieldElement.multiply(this, other)
+  }
+
+  def multInv(other: FieldElement): FieldElement = {
+    multiply(other.inverse)
+  }
+
+  def negate: FieldElement = {
+    FieldElement.negate(this)
+  }
+
+  def getPoint: ECPoint = FieldElement.computePoint(this)
+
+  def getPublicKey: ECPublicKey = toPrivateKey.publicKey
+
+  def inverse: FieldElement = FieldElement.computeInverse(this)
+}
+
+object FieldElement extends Factory[FieldElement] {
+  override def fromBytes(bytes: ByteVector): FieldElement = {
+    if (bytes.length < 32) {
+      new FieldElement(bytes.padLeft(32))
+    } else if (bytes.length == 32) {
+      new FieldElement(bytes)
+    } else if (bytes.length == 33 && bytes.head == 0.toByte) {
+      new FieldElement(bytes.tail)
+    } else {
+      throw new IllegalArgumentException(
+        s"Field element cannot have more than 32 bytes, got $bytes")
+    }
+  }
+
+  def apply(num: BigInt): FieldElement = {
+    FieldElement(num.underlying())
+  }
+
+  def apply(num: BigInteger): FieldElement = {
+    FieldElement.fromByteArray(num.mod(N).toByteArray)
+  }
+
+  def fromByteArray(bytes: Array[Byte]): FieldElement = {
+    FieldElement(ByteVector(bytes))
+  }
+
+  val zero: FieldElement = FieldElement(ByteVector.empty)
+  val one: FieldElement = FieldElement(ByteVector.fromByte(1))
+
+  val nMinusOne: FieldElement = FieldElement(
+    "fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364140")
+
+  private val G: ECPoint = CryptoParams.curve.getG
+  private val N: BigInteger = CryptoParams.curve.getN
+
+  private def getBigInteger(bytes: ByteVector): BigInteger = {
+    new BigInteger(1, bytes.toArray)
+  }
+
+  def add(fe1: FieldElement, fe2: FieldElement): FieldElement = {
+    val num1 = fe1.toBigInteger
+    val num2 = fe2.toBigInteger
+
+    val sum = num1.add(num2).mod(N)
+    FieldElement(sum)
+  }
+
+  def multiply(fe1: FieldElement, fe2: FieldElement): FieldElement = {
+    val num1 = fe1.toBigInteger
+    val num2 = fe2.toBigInteger
+
+    val sum = num1.multiply(num2).mod(N)
+    FieldElement(sum)
+  }
+
+  def negate(fe: FieldElement): FieldElement = {
+    val neg = N.subtract(fe.toBigInteger)
+    FieldElement(neg)
+  }
+
+  def computePoint(fe: FieldElement): ECPoint = G.multiply(fe.toBigInteger)
+
+  /** Computes the inverse (mod M) of the input using the Euclidean Algorithm (log time)
+    * Cribbed from [[https://www.geeksforgeeks.org/multiplicative-inverse-under-modulo-m/]]
+    */
+  def computeInverse(fe: FieldElement): FieldElement = {
+    val inv = fe.toBigInteger.modInverse(N)
+    FieldElement(inv)
+  }
+}
diff --git a/crypto/src/main/scala/org/bitcoins/crypto/SchnorrDigitalSignature.scala b/crypto/src/main/scala/org/bitcoins/crypto/SchnorrDigitalSignature.scala
new file mode 100644
index 0000000000..36757468bb
--- /dev/null
+++ b/crypto/src/main/scala/org/bitcoins/crypto/SchnorrDigitalSignature.scala
@@ -0,0 +1,17 @@
+package org.bitcoins.crypto
+
+import scodec.bits.ByteVector
+
+case class SchnorrDigitalSignature(rx: SchnorrNonce, sig: FieldElement)
+    extends NetworkElement {
+  override def bytes: ByteVector = rx.bytes ++ sig.bytes
+}
+
+object SchnorrDigitalSignature extends Factory[SchnorrDigitalSignature] {
+  override def fromBytes(bytes: ByteVector): SchnorrDigitalSignature = {
+    require(bytes.length == 64,
+            s"SchnorrDigitalSignature must be exactly 64 bytes, got $bytes")
+    SchnorrDigitalSignature(SchnorrNonce(bytes.take(32)),
+                            FieldElement(bytes.drop(32)))
+  }
+}
diff --git a/crypto/src/main/scala/org/bitcoins/crypto/SchnorrNonce.scala b/crypto/src/main/scala/org/bitcoins/crypto/SchnorrNonce.scala
new file mode 100644
index 0000000000..5b9bc037cd
--- /dev/null
+++ b/crypto/src/main/scala/org/bitcoins/crypto/SchnorrNonce.scala
@@ -0,0 +1,89 @@
+package org.bitcoins.crypto
+
+import scodec.bits.ByteVector
+
+import scala.annotation.tailrec
+import scala.util.Try
+
+case class SchnorrNonce(bytes: ByteVector) extends NetworkElement {
+  require(bytes.length == 32, s"Schnorr nonce must be 32 bytes, get $bytes")
+
+  private val evenKey: ECPublicKey = ECPublicKey(s"02$hex")
+  private val oddKey: ECPublicKey = ECPublicKey(s"03$hex")
+
+  private val yCoordEven: Boolean = {
+    evenKey.toPoint.getRawYCoord.sqrt() != null
+  }
+
+  /** Computes the public key associated with a SchnorrNonce as specified in bip-schnorr.
+    * They y-coordinate is chosen to be a quadratic residue.
+    */
+  val publicKey: ECPublicKey = {
+    if (yCoordEven) {
+      evenKey
+    } else {
+      oddKey
+    }
+  }
+
+  require(Try(publicKey).isSuccess,
+          s"Schnorr nonce must be a valid x coordinate, got $bytes")
+  require(
+    publicKey.toPoint.getRawYCoord.sqrt != null,
+    "Schnorr nonce must be an x coordinate for which a quadratic residue y coordinate exists")
+
+  def xCoord: FieldElement = {
+    FieldElement(bytes)
+  }
+}
+
+object SchnorrNonce extends Factory[SchnorrNonce] {
+
+  @tailrec
+  def fromBytes(bytes: ByteVector): SchnorrNonce = {
+    if (bytes.length == 32) {
+      new SchnorrNonce(bytes)
+    } else if (bytes.length < 32) {
+      // means we need to pad the private key with 0 bytes so we have 32 bytes
+      SchnorrNonce.fromBytes(bytes.padLeft(32))
+    } else if (bytes.length == 33) {
+      // this is for the case when java serialies a BigInteger to 33 bytes to hold the signed num representation
+      SchnorrNonce.fromBytes(bytes.tail)
+    } else {
+      throw new IllegalArgumentException(
+        "Schnorr nonce cannot be greater than 33 bytes in size, got: " +
+          CryptoBytesUtil.encodeHex(bytes) + " which is of size: " + bytes.size)
+    }
+  }
+
+  def kFromBipSchnorr(
+      privKey: ECPrivateKey,
+      message: ByteVector,
+      auxRand: ByteVector): ECPrivateKey = {
+    val privKeyForUse = privKey.schnorrKey
+
+    val randHash = CryptoUtil.sha256SchnorrAuxRand(auxRand).bytes
+    val maskedKey = randHash.xor(privKeyForUse.bytes)
+
+    val nonceHash = CryptoUtil.sha256SchnorrNonce(
+      maskedKey ++ privKey.schnorrPublicKey.bytes ++ message)
+
+    ECPrivateKey(nonceHash.bytes).nonceKey
+  }
+
+  /** Computes the bip-schnorr nonce for a given message and private key.
+    * This is intended to ensure that no two messages are signed with the
+    * same nonce.
+    */
+  def fromBipSchnorr(
+      privKey: ECPrivateKey,
+      message: ByteVector,
+      auxRand: ByteVector): SchnorrNonce = {
+    val k = kFromBipSchnorr(privKey, message, auxRand)
+    k.publicKey.schnorrNonce
+  }
+
+  def apply(xCoor: FieldElement): SchnorrNonce = {
+    SchnorrNonce(xCoor.bytes)
+  }
+}
diff --git a/crypto/src/main/scala/org/bitcoins/crypto/SchnorrPublicKey.scala b/crypto/src/main/scala/org/bitcoins/crypto/SchnorrPublicKey.scala
new file mode 100644
index 0000000000..a1d1e60075
--- /dev/null
+++ b/crypto/src/main/scala/org/bitcoins/crypto/SchnorrPublicKey.scala
@@ -0,0 +1,114 @@
+package org.bitcoins.crypto
+
+import org.bitcoin.NativeSecp256k1
+import scodec.bits.ByteVector
+
+import scala.annotation.tailrec
+import scala.util.Try
+
+case class SchnorrPublicKey(bytes: ByteVector) extends NetworkElement {
+  require(bytes.length == 32,
+          s"Schnorr public keys must be 32 bytes, got $bytes")
+  require(Try(publicKey).isSuccess,
+          s"Schnorr public key must be a valid x coordinate, got $bytes")
+
+  // TODO: match on CryptoContext once secp version is added
+  def verify(data: ByteVector, signature: SchnorrDigitalSignature): Boolean = {
+    verifyWithBouncyCastle(data, signature)
+  }
+
+  /*
+  def verifyWithSecp(
+      data: ByteVector,
+      signature: SchnorrDigitalSignature): Boolean = {
+    NativeSecp256k1.schnorrVerify(signature.bytes.toArray,
+                                  data.toArray,
+                                  bytes.toArray)
+  }
+   */
+
+  def verifyWithBouncyCastle(
+      data: ByteVector,
+      signature: SchnorrDigitalSignature): Boolean = {
+    BouncyCastleUtil.schnorrVerify(data, this, signature)
+  }
+
+  def computeSigPoint(data: ByteVector, nonce: SchnorrNonce): ECPublicKey = {
+    computeSigPoint(data, nonce, compressed = true)
+  }
+
+  // TODO: match on CryptoContext once secp version is added
+  def computeSigPoint(
+      data: ByteVector,
+      nonce: SchnorrNonce,
+      compressed: Boolean): ECPublicKey = {
+    computeSigPointWithBouncyCastle(data, nonce, compressed)
+  }
+
+  /*
+  def computeSigPointWithSecp(
+      data: ByteVector,
+      nonce: SchnorrNonce,
+      compressed: Boolean = true): ECPublicKey = {
+    val sigPointBytes = NativeSecp256k1.schnorrComputeSigPoint(
+      data.toArray,
+      nonce.bytes.toArray,
+      bytes.toArray,
+      compressed)
+    ECPublicKey(ByteVector(sigPointBytes))
+  }
+   */
+
+  def computeSigPointWithBouncyCastle(
+      data: ByteVector,
+      nonce: SchnorrNonce,
+      compressed: Boolean = true): ECPublicKey = {
+    BouncyCastleUtil.schnorrComputeSigPoint(data, nonce, this, compressed)
+  }
+
+  def publicKey: ECPublicKey = {
+    val pubKeyBytes = ByteVector.fromByte(2) ++ bytes
+
+    val validPubKey = CryptoContext.default match {
+      case CryptoContext.LibSecp256k1 =>
+        NativeSecp256k1.isValidPubKey(pubKeyBytes.toArray)
+      case CryptoContext.BouncyCastle =>
+        BouncyCastleUtil.validatePublicKey(pubKeyBytes)
+    }
+
+    require(
+      validPubKey,
+      s"Cannot construct schnorr public key from invalid x coordinate: $bytes")
+
+    ECPublicKey(pubKeyBytes)
+  }
+
+  def xCoord: FieldElement = FieldElement(bytes)
+}
+
+object SchnorrPublicKey extends Factory[SchnorrPublicKey] {
+
+  @tailrec
+  def fromBytes(bytes: ByteVector): SchnorrPublicKey = {
+    require(bytes.length <= 33,
+            s"XOnlyPublicKey must be less than 33 bytes, got $bytes")
+
+    if (bytes.length == 32)
+      new SchnorrPublicKey(bytes)
+    else if (bytes.length < 32) {
+      // means we need to pad the private key with 0 bytes so we have 32 bytes
+      SchnorrPublicKey.fromBytes(bytes.padLeft(32))
+    } else if (bytes.length == 33) {
+      // this is for the case when java serialies a BigInteger to 33 bytes to hold the signed num representation
+      SchnorrPublicKey.fromBytes(bytes.tail)
+    } else {
+      throw new IllegalArgumentException(
+        "XOnlyPublicKey cannot be greater than 33 bytes in size, got: " +
+          CryptoBytesUtil.encodeHex(bytes) + " which is of size: " + bytes.size)
+    }
+  }
+
+  def apply(xCoor: FieldElement): SchnorrPublicKey = {
+    SchnorrPublicKey(xCoor.bytes)
+  }
+}
diff --git a/testkit/src/main/scala/org/bitcoins/testkit/core/gen/CryptoGenerators.scala b/testkit/src/main/scala/org/bitcoins/testkit/core/gen/CryptoGenerators.scala
index b2e3f728da..56390192a6 100644
--- a/testkit/src/main/scala/org/bitcoins/testkit/core/gen/CryptoGenerators.scala
+++ b/testkit/src/main/scala/org/bitcoins/testkit/core/gen/CryptoGenerators.scala
@@ -15,6 +15,10 @@ import org.bitcoins.crypto.{
   ECDigitalSignature,
   ECPrivateKey,
   ECPublicKey,
+  FieldElement,
+  SchnorrDigitalSignature,
+  SchnorrNonce,
+  SchnorrPublicKey,
   Sha256Digest,
   Sha256Hash160Digest
 }
@@ -131,6 +135,36 @@ sealed abstract class CryptoGenerators {
 
   def privateKey: Gen[ECPrivateKey] = Gen.delay(ECPrivateKey())
 
+  def fieldElement: Gen[FieldElement] = privateKey.map(_.fieldElement)
+
+  def smallFieldElement: Gen[FieldElement] =
+    NumberGenerator
+      .bytevector(30)
+      .map(bytes => FieldElement(ByteVector.fill(2)(0) ++ bytes))
+
+  def reallySmallFieldElement: Gen[FieldElement] =
+    NumberGenerator
+      .bytevector(15)
+      .map(bytes => FieldElement(ByteVector.fill(17)(0) ++ bytes))
+
+  def largeFieldElement: Gen[FieldElement] =
+    NumberGenerator
+      .bytevector(30)
+      .map(bytes => FieldElement(ByteVector.fill(2)(Byte.MinValue) ++ bytes))
+
+  def nonZeroFieldElement: Gen[FieldElement] =
+    nonZeroPrivKey.map(_.fieldElement)
+
+  /** Generates a random non-zero private key */
+  def nonZeroPrivKey: Gen[ECPrivateKey] =
+    privateKey.filter(_.bytes.toArray.exists(_ != 0.toByte))
+
+  def schnorrNonce: Gen[SchnorrNonce] =
+    nonZeroPrivKey.map(_.publicKey.bytes.tail).map(SchnorrNonce.fromBytes)
+
+  def schnorrPublicKey: Gen[SchnorrPublicKey] =
+    publicKey.map(_.schnorrPublicKey)
+
   /**
     * Generate a sequence of private keys
     * @param num maximum number of keys to generate
@@ -187,6 +221,13 @@ sealed abstract class CryptoGenerators {
       hash <- CryptoGenerators.doubleSha256Digest
     } yield privKey.sign(hash)
 
+  def schnorrDigitalSignature: Gen[SchnorrDigitalSignature] = {
+    for {
+      privKey <- privateKey
+      hash <- CryptoGenerators.doubleSha256Digest
+    } yield privKey.schnorrSign(hash.bytes)
+  }
+
   def sha256Digest: Gen[Sha256Digest] =
     for {
       bytes <- NumberGenerator.bytevector