diff --git a/README.md b/README.md
index 74a8f77..e93536e 100644
--- a/README.md
+++ b/README.md
@@ -154,7 +154,7 @@ These are the required packages for each built-in cose.Algorithm:
 
 - cose.AlgorithmPS256, cose.AlgorithmES256: `crypto/sha256`
 - cose.AlgorithmPS384, cose.AlgorithmPS512, cose.AlgorithmES384, cose.AlgorithmES512: `crypto/sha512`
-- cose.AlgorithmEd25519: none
+- cose.AlgorithmEdDSA: none
 
 ## Features
 
diff --git a/algorithm.go b/algorithm.go
index 9e2f7d9..0a22090 100644
--- a/algorithm.go
+++ b/algorithm.go
@@ -35,8 +35,14 @@ const (
 	AlgorithmES512 Algorithm = -36
 
 	// PureEdDSA by RFC 8152.
+	//
+	// Deprecated: use AlgorithmEdDSA instead, which has
+	// the same value but with a more accurate name.
 	AlgorithmEd25519 Algorithm = -8
 
+	// PureEdDSA by RFC 8152.
+	AlgorithmEdDSA Algorithm = -8
+
 	// An invalid/unrecognised algorithm.
 	AlgorithmInvalid Algorithm = 0
 )
@@ -65,7 +71,7 @@ func (a Algorithm) String() string {
 		return "ES384"
 	case AlgorithmES512:
 		return "ES512"
-	case AlgorithmEd25519:
+	case AlgorithmEdDSA:
 		// As stated in RFC 8152 8.2, only the pure EdDSA version is used for
 		// COSE.
 		return "EdDSA"
diff --git a/algorithm_test.go b/algorithm_test.go
index b839f2e..1bf1aa0 100644
--- a/algorithm_test.go
+++ b/algorithm_test.go
@@ -96,7 +96,7 @@ func TestAlgorithm_computeHash(t *testing.T) {
 		},
 		{
 			name:    "Ed25519",
-			alg:     AlgorithmEd25519,
+			alg:     AlgorithmEdDSA,
 			wantErr: ErrUnavailableHashFunc,
 		},
 		{
diff --git a/ed25519.go b/ed25519.go
index ae88740..ebbf638 100644
--- a/ed25519.go
+++ b/ed25519.go
@@ -13,7 +13,7 @@ type ed25519Signer struct {
 
 // Algorithm returns the signing algorithm associated with the private key.
 func (es *ed25519Signer) Algorithm() Algorithm {
-	return AlgorithmEd25519
+	return AlgorithmEdDSA
 }
 
 // Sign signs message content with the private key, possibly using entropy from
@@ -34,7 +34,7 @@ type ed25519Verifier struct {
 
 // Algorithm returns the signing algorithm associated with the public key.
 func (ev *ed25519Verifier) Algorithm() Algorithm {
-	return AlgorithmEd25519
+	return AlgorithmEdDSA
 }
 
 // Verify verifies message content with the public key, returning nil for
diff --git a/ed25519_test.go b/ed25519_test.go
index d23e65b..b0d9f29 100644
--- a/ed25519_test.go
+++ b/ed25519_test.go
@@ -17,7 +17,7 @@ func generateTestEd25519Key(t *testing.T) (ed25519.PublicKey, ed25519.PrivateKey
 
 func Test_ed25519Signer(t *testing.T) {
 	// generate key
-	alg := AlgorithmEd25519
+	alg := AlgorithmEdDSA
 	_, key := generateTestEd25519Key(t)
 
 	// set up signer
@@ -51,7 +51,7 @@ func Test_ed25519Signer(t *testing.T) {
 
 func Test_ed25519Verifier_Verify_Success(t *testing.T) {
 	// generate key
-	alg := AlgorithmEd25519
+	alg := AlgorithmEdDSA
 	_, key := generateTestEd25519Key(t)
 
 	// generate a valid signature
@@ -77,7 +77,7 @@ func Test_ed25519Verifier_Verify_Success(t *testing.T) {
 
 func Test_ed25519Verifier_Verify_KeyMismatch(t *testing.T) {
 	// generate key
-	alg := AlgorithmEd25519
+	alg := AlgorithmEdDSA
 	_, key := generateTestEd25519Key(t)
 
 	// generate a valid signature
@@ -97,7 +97,7 @@ func Test_ed25519Verifier_Verify_KeyMismatch(t *testing.T) {
 
 func Test_ed25519Verifier_Verify_InvalidSignature(t *testing.T) {
 	// generate key
-	alg := AlgorithmEd25519
+	alg := AlgorithmEdDSA
 	vk, sk := generateTestEd25519Key(t)
 
 	// generate a valid signature with a tampered one
diff --git a/fuzz_test.go b/fuzz_test.go
index 90db8aa..4e697a1 100644
--- a/fuzz_test.go
+++ b/fuzz_test.go
@@ -24,7 +24,7 @@ import (
 var supportedAlgorithms = [...]cose.Algorithm{
 	cose.AlgorithmPS256, cose.AlgorithmPS384, cose.AlgorithmPS512,
 	cose.AlgorithmES256, cose.AlgorithmES384, cose.AlgorithmES512,
-	cose.AlgorithmEd25519,
+	cose.AlgorithmEdDSA,
 }
 
 func FuzzSign1Message_UnmarshalCBOR(f *testing.F) {
@@ -181,7 +181,7 @@ func newSignerWithEphemeralKey(alg cose.Algorithm) (sv signVerifier, err error)
 		key, err = ecdsa.GenerateKey(elliptic.P384(), rand.Reader)
 	case cose.AlgorithmES512:
 		key, err = ecdsa.GenerateKey(elliptic.P521(), rand.Reader)
-	case cose.AlgorithmEd25519:
+	case cose.AlgorithmEdDSA:
 		_, key, err = ed25519.GenerateKey(rand.Reader)
 	default:
 		err = cose.ErrAlgorithmNotSupported
diff --git a/key.go b/key.go
index 890f64c..7e21ac6 100644
--- a/key.go
+++ b/key.go
@@ -240,7 +240,7 @@ type Key struct {
 
 // NewOKPKey returns a Key created using the provided Octet Key Pair data.
 func NewOKPKey(alg Algorithm, x, d []byte) (*Key, error) {
-	if alg != AlgorithmEd25519 {
+	if alg != AlgorithmEdDSA {
 		return nil, fmt.Errorf("unsupported algorithm %q", alg)
 	}
 
@@ -389,7 +389,7 @@ func NewKeyFromPublic(pub crypto.PublicKey) (*Key, error) {
 
 		return NewEC2Key(alg, vk.X.Bytes(), vk.Y.Bytes(), nil)
 	case ed25519.PublicKey:
-		return NewOKPKey(AlgorithmEd25519, []byte(vk), nil)
+		return NewOKPKey(AlgorithmEdDSA, []byte(vk), nil)
 	default:
 		return nil, ErrInvalidPubKey
 	}
@@ -408,7 +408,7 @@ func NewKeyFromPrivate(priv crypto.PrivateKey) (*Key, error) {
 
 		return NewEC2Key(alg, sk.X.Bytes(), sk.Y.Bytes(), sk.D.Bytes())
 	case ed25519.PrivateKey:
-		return NewOKPKey(AlgorithmEd25519, []byte(sk[32:]), []byte(sk[:32]))
+		return NewOKPKey(AlgorithmEdDSA, []byte(sk[32:]), []byte(sk[:32]))
 	default:
 		return nil, ErrInvalidPrivKey
 	}
@@ -685,7 +685,7 @@ func (k *Key) PublicKey() (crypto.PublicKey, error) {
 		pub.Y.SetBytes(y)
 
 		return pub, nil
-	case AlgorithmEd25519:
+	case AlgorithmEdDSA:
 		_, x, _ := k.OKP()
 		return ed25519.PublicKey(x), nil
 	default:
@@ -730,7 +730,7 @@ func (k *Key) PrivateKey() (crypto.PrivateKey, error) {
 			PublicKey: ecdsa.PublicKey{Curve: curve, X: bx, Y: by},
 			D:         bd,
 		}, nil
-	case AlgorithmEd25519:
+	case AlgorithmEdDSA:
 		_, x, d := k.OKP()
 		if len(x) == 0 {
 			return ed25519.NewKeyFromSeed(d), nil
@@ -823,7 +823,7 @@ func (k *Key) deriveAlgorithm() (Algorithm, error) {
 		crv, _, _ := k.OKP()
 		switch crv {
 		case CurveEd25519:
-			return AlgorithmEd25519, nil
+			return AlgorithmEdDSA, nil
 		default:
 			return AlgorithmInvalid, fmt.Errorf(
 				"unsupported curve %q for key type OKP", crv.String())
diff --git a/key_test.go b/key_test.go
index 3363be5..7162631 100644
--- a/key_test.go
+++ b/key_test.go
@@ -457,7 +457,7 @@ func TestKey_UnmarshalCBOR(t *testing.T) {
 			},
 			want: &Key{
 				KeyType:   KeyTypeOKP,
-				Algorithm: AlgorithmEd25519,
+				Algorithm: AlgorithmEdDSA,
 				KeyOps:    []KeyOp{KeyOpVerify, KeyOpSign},
 				BaseIV:    []byte{0x03, 0x02, 0x01},
 				Params: map[interface{}]interface{}{
@@ -644,7 +644,7 @@ func TestKey_MarshalCBOR(t *testing.T) {
 			name: "OKP with kty and alg",
 			key: &Key{
 				KeyType:   KeyTypeOKP,
-				Algorithm: AlgorithmEd25519,
+				Algorithm: AlgorithmEdDSA,
 			},
 			want: []byte{
 				0xa2,       // map (2)
@@ -730,7 +730,7 @@ func TestKey_MarshalCBOR(t *testing.T) {
 			name: "OKP",
 			key: &Key{
 				KeyType:   KeyTypeOKP,
-				Algorithm: AlgorithmEd25519,
+				Algorithm: AlgorithmEdDSA,
 				KeyOps:    []KeyOp{KeyOpVerify, KeyOpEncrypt},
 				Params: map[interface{}]interface{}{
 					KeyLabelOKPCurve: CurveEd25519,
@@ -846,10 +846,10 @@ func TestNewOKPKey(t *testing.T) {
 		wantErr string
 	}{
 		{
-			name: "valid", args: args{AlgorithmEd25519, x, d},
+			name: "valid", args: args{AlgorithmEdDSA, x, d},
 			want: &Key{
 				KeyType:   KeyTypeOKP,
-				Algorithm: AlgorithmEd25519,
+				Algorithm: AlgorithmEdDSA,
 				Params: map[interface{}]interface{}{
 					KeyLabelOKPCurve: CurveEd25519,
 					KeyLabelOKPX:     x,
@@ -862,7 +862,7 @@ func TestNewOKPKey(t *testing.T) {
 			want:    nil,
 			wantErr: `unsupported algorithm "unknown algorithm value -100"`,
 		}, {
-			name: "x and d missing", args: args{AlgorithmEd25519, nil, nil},
+			name: "x and d missing", args: args{AlgorithmEdDSA, nil, nil},
 			want:    nil,
 			wantErr: ErrInvalidKey.Error(),
 		},
@@ -1061,7 +1061,7 @@ func TestKey_AlgorithmOrDefault(t *testing.T) {
 					KeyLabelOKPCurve: CurveEd25519,
 				},
 			},
-			AlgorithmEd25519,
+			AlgorithmEdDSA,
 			"",
 		},
 		{
@@ -1170,7 +1170,7 @@ func TestNewKeyFromPrivate(t *testing.T) {
 		{
 			"ed25519", ed25519.PrivateKey(append(okpd, okpx...)),
 			&Key{
-				Algorithm: AlgorithmEd25519, KeyType: KeyTypeOKP,
+				Algorithm: AlgorithmEdDSA, KeyType: KeyTypeOKP,
 				Params: map[interface{}]interface{}{
 					KeyLabelOKPCurve: CurveEd25519,
 					KeyLabelOKPX:     okpx,
@@ -1228,7 +1228,7 @@ func TestNewKeyFromPublic(t *testing.T) {
 		{
 			"ed25519", ed25519.PublicKey(okpx),
 			&Key{
-				Algorithm: AlgorithmEd25519,
+				Algorithm: AlgorithmEdDSA,
 				KeyType:   KeyTypeOKP,
 				Params: map[interface{}]interface{}{
 					KeyLabelOKPCurve: CurveEd25519,
@@ -1275,20 +1275,20 @@ func TestKey_Signer(t *testing.T) {
 					KeyLabelOKPD:     d,
 				},
 			},
-			AlgorithmEd25519,
+			AlgorithmEdDSA,
 			"",
 		},
 		{
 			"without key_ops", &Key{
 				KeyType:   KeyTypeOKP,
-				Algorithm: AlgorithmEd25519,
+				Algorithm: AlgorithmEdDSA,
 				Params: map[interface{}]interface{}{
 					KeyLabelOKPCurve: CurveEd25519,
 					KeyLabelOKPX:     x,
 					KeyLabelOKPD:     d,
 				},
 			},
-			AlgorithmEd25519,
+			AlgorithmEdDSA,
 			"",
 		},
 		{
@@ -1361,19 +1361,19 @@ func TestKey_Verifier(t *testing.T) {
 					KeyLabelOKPX:     x,
 				},
 			},
-			AlgorithmEd25519,
+			AlgorithmEdDSA,
 			"",
 		},
 		{
 			"without key_ops", &Key{
 				KeyType:   KeyTypeOKP,
-				Algorithm: AlgorithmEd25519,
+				Algorithm: AlgorithmEdDSA,
 				Params: map[interface{}]interface{}{
 					KeyLabelOKPCurve: CurveEd25519,
 					KeyLabelOKPX:     x,
 				},
 			},
-			AlgorithmEd25519,
+			AlgorithmEdDSA,
 			"",
 		},
 		{
diff --git a/signer.go b/signer.go
index 6747546..18985dd 100644
--- a/signer.go
+++ b/signer.go
@@ -68,7 +68,7 @@ func NewSigner(alg Algorithm, key crypto.Signer) (Signer, error) {
 			key:    vk,
 			signer: key,
 		}, nil
-	case AlgorithmEd25519:
+	case AlgorithmEdDSA:
 		if _, ok := key.Public().(ed25519.PublicKey); !ok {
 			return nil, fmt.Errorf("%v: %w", alg, ErrInvalidPubKey)
 		}
diff --git a/signer_test.go b/signer_test.go
index e9475b9..62a17a7 100644
--- a/signer_test.go
+++ b/signer_test.go
@@ -77,7 +77,7 @@ func TestNewSigner(t *testing.T) {
 		},
 		{
 			name: "ed25519 signer",
-			alg:  AlgorithmEd25519,
+			alg:  AlgorithmEdDSA,
 			key:  ed25519Key,
 			want: &ed25519Signer{
 				key: ed25519Key,
@@ -85,7 +85,7 @@ func TestNewSigner(t *testing.T) {
 		},
 		{
 			name:    "ed25519 key mismatch",
-			alg:     AlgorithmEd25519,
+			alg:     AlgorithmEdDSA,
 			key:     rsaKey,
 			wantErr: "EdDSA: invalid public key",
 		},
diff --git a/verifier.go b/verifier.go
index 1c6e83b..b9db1f0 100644
--- a/verifier.go
+++ b/verifier.go
@@ -53,7 +53,7 @@ func NewVerifier(alg Algorithm, key crypto.PublicKey) (Verifier, error) {
 			alg: alg,
 			key: vk,
 		}, nil
-	case AlgorithmEd25519:
+	case AlgorithmEdDSA:
 		vk, ok := key.(ed25519.PublicKey)
 		if !ok {
 			return nil, fmt.Errorf("%v: %w", alg, ErrInvalidPubKey)
diff --git a/verifier_test.go b/verifier_test.go
index b662cd0..03e1e37 100644
--- a/verifier_test.go
+++ b/verifier_test.go
@@ -73,7 +73,7 @@ func TestNewVerifier(t *testing.T) {
 		},
 		{
 			name: "ed25519 verifier",
-			alg:  AlgorithmEd25519,
+			alg:  AlgorithmEdDSA,
 			key:  ed25519Key,
 			want: &ed25519Verifier{
 				key: ed25519Key,
@@ -81,7 +81,7 @@ func TestNewVerifier(t *testing.T) {
 		},
 		{
 			name:    "ed25519 invalid public key",
-			alg:     AlgorithmEd25519,
+			alg:     AlgorithmEdDSA,
 			key:     rsaKey,
 			wantErr: "EdDSA: invalid public key",
 		},