diff --git a/aead/aead_factory.go b/aead/aead_factory.go
index ad20488..785524e 100644
--- a/aead/aead_factory.go
+++ b/aead/aead_factory.go
@@ -50,11 +50,26 @@ func NewWithConfig(handle *keyset.Handle, config keyset.Config) (tink.AEAD, erro
 // wrappedAead is an AEAD implementation that uses the underlying primitive set for encryption
 // and decryption.
 type wrappedAead struct {
-	ps        *primitiveset.PrimitiveSet
+	primary    aeadAndKeyID
+	primitives map[string][]aeadAndKeyID
+
 	encLogger monitoring.Logger
 	decLogger monitoring.Logger
 }
 
+type aeadAndKeyID struct {
+	primitive tink.AEAD
+	keyID     uint32
+}
+
+func (a *aeadAndKeyID) Encrypt(plaintext, associatedData []byte) ([]byte, error) {
+	return a.primitive.Encrypt(plaintext, associatedData)
+}
+
+func (a *aeadAndKeyID) Decrypt(ciphertext, associatedData []byte) ([]byte, error) {
+	return a.primitive.Decrypt(ciphertext, associatedData)
+}
+
 // aeadPrimitiveAdapter is an adapter that turns a non-full [tink.AEAD]
 // primitive into a full [tink.AEAD] primitive.
 type fullAEADPrimitiveAdapter struct {
@@ -74,32 +89,39 @@ func (a *fullAEADPrimitiveAdapter) Decrypt(ciphertext, associatedData []byte) ([
 	return a.primitive.Decrypt(ciphertext[len(a.prefix):], associatedData)
 }
 
-// getFullPrimitive returns a full [tink.AEAD] from the given
+// extractFullAEAD returns a full aeadAndKeyID primitive from the given
 // [primitiveset.Entry].
-func getFullPrimitive(entry *primitiveset.Entry) (tink.AEAD, error) {
+func extractFullAEAD(entry *primitiveset.Entry) (*aeadAndKeyID, error) {
 	if entry.FullPrimitive != nil {
 		a, ok := (entry.FullPrimitive).(tink.AEAD)
 		if !ok {
 			return nil, fmt.Errorf("aead_factory: not an AEAD primitive")
 		}
-		return a, nil
+		return &aeadAndKeyID{primitive: a, keyID: entry.KeyID}, nil
 	}
 	a, ok := (entry.Primitive).(tink.AEAD)
 	if !ok {
 		return nil, fmt.Errorf("aead_factory: not an AEAD primitive")
 	}
-	return &fullAEADPrimitiveAdapter{primitive: a, prefix: []byte(entry.Prefix)}, nil
+	return &aeadAndKeyID{
+		primitive: &fullAEADPrimitiveAdapter{primitive: a, prefix: []byte(entry.Prefix)},
+		keyID:     entry.KeyID,
+	}, nil
 }
 
 func newWrappedAead(ps *primitiveset.PrimitiveSet) (*wrappedAead, error) {
-	if _, err := getFullPrimitive(ps.Primary); err != nil {
+	primary, err := extractFullAEAD(ps.Primary)
+	if err != nil {
 		return nil, err
 	}
+	primitives := make(map[string][]aeadAndKeyID)
 	for _, entries := range ps.Entries {
 		for _, entry := range entries {
-			if _, err := getFullPrimitive(entry); err != nil {
+			p, err := extractFullAEAD(entry)
+			if err != nil {
 				return nil, err
 			}
+			primitives[entry.Prefix] = append(primitives[entry.Prefix], *p)
 		}
 	}
 	encLogger, decLogger, err := createLoggers(ps)
@@ -107,9 +129,10 @@ func newWrappedAead(ps *primitiveset.PrimitiveSet) (*wrappedAead, error) {
 		return nil, err
 	}
 	return &wrappedAead{
-		ps:        ps,
-		encLogger: encLogger,
-		decLogger: decLogger,
+		primary:    *primary,
+		primitives: primitives,
+		encLogger:  encLogger,
+		decLogger:  decLogger,
 	}, nil
 }
 
@@ -144,17 +167,12 @@ func createLoggers(ps *primitiveset.PrimitiveSet) (monitoring.Logger, monitoring
 // Encrypt encrypts the given plaintext with the given associatedData.
 // It returns the concatenation of the primary's identifier and the ciphertext.
 func (a *wrappedAead) Encrypt(plaintext, associatedData []byte) ([]byte, error) {
-	primary := a.ps.Primary
-	p, err := getFullPrimitive(primary)
-	if err != nil {
-		return nil, err
-	}
-	ct, err := p.Encrypt(plaintext, associatedData)
+	ct, err := a.primary.Encrypt(plaintext, associatedData)
 	if err != nil {
 		a.encLogger.LogFailure()
 		return nil, err
 	}
-	a.encLogger.Log(primary.KeyID, len(plaintext))
+	a.encLogger.Log(a.primary.keyID, len(plaintext))
 	return ct, nil
 }
 
@@ -162,42 +180,34 @@ func (a *wrappedAead) Encrypt(plaintext, associatedData []byte) ([]byte, error)
 // associatedData. It returns the corresponding plaintext if the
 // ciphertext is authenticated.
 func (a *wrappedAead) Decrypt(ciphertext, associatedData []byte) ([]byte, error) {
-	// try non-raw keys
+	// Try non-raw keys.
 	prefixSize := cryptofmt.NonRawPrefixSize
 	if len(ciphertext) > prefixSize {
 		prefix := ciphertext[:prefixSize]
-		entries, err := a.ps.EntriesForPrefix(string(prefix))
-		if err == nil {
-			for _, entry := range entries {
-				p, err := getFullPrimitive(entry)
-				if err != nil {
-					return nil, err
-				}
-				pt, err := p.Decrypt(ciphertext, associatedData)
+		primitivesForPrefix, ok := a.primitives[string(prefix)]
+		if ok {
+			for _, primitive := range primitivesForPrefix {
+				pt, err := primitive.Decrypt(ciphertext, associatedData)
 				if err == nil {
 					numBytes := len(ciphertext[prefixSize:])
-					a.decLogger.Log(entry.KeyID, numBytes)
+					a.decLogger.Log(primitive.keyID, numBytes)
 					return pt, nil
 				}
 			}
 		}
 	}
-	// try raw keys
-	entries, err := a.ps.RawEntries()
-	if err == nil {
-		for _, entry := range entries {
-			p, err := getFullPrimitive(entry)
-			if err != nil {
-				return nil, err
-			}
-			pt, err := p.Decrypt(ciphertext, associatedData)
+	// Try raw keys.
+	rawPrimitives, ok := a.primitives[cryptofmt.RawPrefix]
+	if ok {
+		for _, primitive := range rawPrimitives {
+			pt, err := primitive.Decrypt(ciphertext, associatedData)
 			if err == nil {
-				a.decLogger.Log(entry.KeyID, len(ciphertext))
+				a.decLogger.Log(primitive.keyID, len(ciphertext))
 				return pt, nil
 			}
 		}
 	}
-	// nothing worked
+	// Nothing worked.
 	a.decLogger.LogFailure()
 	return nil, fmt.Errorf("aead_factory: decryption failed")
 }