diff --git a/jwt.go b/jwt.go
index a04dfef..feae914 100644
--- a/jwt.go
+++ b/jwt.go
@@ -4,7 +4,7 @@ import (
 	"crypto"
 	"crypto/ecdsa"
 	"crypto/rsa"
-	"crypto/sha256"
+	"math/big"
 	"strings"
 
 	"crypto/x509"
@@ -157,37 +157,82 @@ func verifyIssuedAt(issuedAt float64) error {
 	return nil
 }
 
-// verifySignature verifies the token signature
+// verifySignature verifies the token signature using the provided public key and algorithm
 func verifySignature(tokenString string, publicKeyPEM []byte, alg string) error {
+	// Split the token into its three parts
 	parts := strings.Split(tokenString, ".")
+	if len(parts) != 3 {
+		return fmt.Errorf("invalid token format")
+	}
 	signedContent := parts[0] + "." + parts[1]
+
+	// Decode the signature from the token
 	signature, err := base64.RawURLEncoding.DecodeString(parts[2])
 	if err != nil {
 		return fmt.Errorf("failed to decode signature: %w", err)
 	}
 
+	// Decode the PEM-encoded public key
 	block, _ := pem.Decode(publicKeyPEM)
 	if block == nil {
 		return fmt.Errorf("failed to parse PEM block containing the public key")
 	}
 
+	// Parse the public key
 	pubKey, err := x509.ParsePKIXPublicKey(block.Bytes)
 	if err != nil {
 		return fmt.Errorf("failed to parse public key: %w", err)
 	}
 
-	h := sha256.New()
+	// Determine the hash function to use based on the algorithm
+	var hashFunc crypto.Hash
+
+	switch alg {
+	case "RS256", "PS256", "ES256":
+		hashFunc = crypto.SHA256
+	case "RS384", "PS384", "ES384":
+		hashFunc = crypto.SHA384
+	case "RS512", "PS512", "ES512":
+		hashFunc = crypto.SHA512
+	default:
+		return fmt.Errorf("unsupported algorithm: %s", alg)
+	}
+
+	// Hash the signed content
+	h := hashFunc.New()
 	h.Write([]byte(signedContent))
 	hashed := h.Sum(nil)
 
+	// Verify the signature based on the key type and algorithm
 	switch pubKey := pubKey.(type) {
 	case *rsa.PublicKey:
-		return rsa.VerifyPKCS1v15(pubKey, crypto.SHA256, hashed, signature)
-	case *ecdsa.PublicKey:
-		if !ecdsa.VerifyASN1(pubKey, hashed, signature) {
-			return fmt.Errorf("invalid ECDSA signature")
+		if strings.HasPrefix(alg, "RS") {
+			// RSA PKCS#1 v1.5 signature
+			return rsa.VerifyPKCS1v15(pubKey, hashFunc, hashed, signature)
+		} else if strings.HasPrefix(alg, "PS") {
+			// RSA PSS signature
+			return rsa.VerifyPSS(pubKey, hashFunc, hashed, signature, nil)
+		} else {
+			return fmt.Errorf("unexpected key type for algorithm %s", alg)
+		}
+	case *ecdsa.PublicKey:
+		if strings.HasPrefix(alg, "ES") {
+			// ECDSA signature
+			var r, s big.Int
+			sigLen := len(signature)
+			if sigLen%2 != 0 {
+				return fmt.Errorf("invalid ECDSA signature length")
+			}
+			r.SetBytes(signature[:sigLen/2])
+			s.SetBytes(signature[sigLen/2:])
+			if ecdsa.Verify(pubKey, hashed, &r, &s) {
+				return nil
+			} else {
+				return fmt.Errorf("invalid ECDSA signature")
+			}
+		} else {
+			return fmt.Errorf("unexpected key type for algorithm %s", alg)
 		}
-		return nil
 	default:
 		return fmt.Errorf("unsupported public key type: %T", pubKey)
 	}