diff --git a/tpm2/constants.go b/tpm2/constants.go
index 4276a176..716ea471 100644
--- a/tpm2/constants.go
+++ b/tpm2/constants.go
@@ -28,11 +28,17 @@ import (
 	"github.com/google/go-tpm/tpmutil"
 )
 
-var hashMapping = map[Algorithm]crypto.Hash{
-	AlgSHA1:   crypto.SHA1,
-	AlgSHA256: crypto.SHA256,
-	AlgSHA384: crypto.SHA384,
-	AlgSHA512: crypto.SHA512,
+var hashInfo = []struct {
+	alg  Algorithm
+	hash crypto.Hash
+}{
+	{AlgSHA1, crypto.SHA1},
+	{AlgSHA256, crypto.SHA256},
+	{AlgSHA384, crypto.SHA384},
+	{AlgSHA512, crypto.SHA512},
+	{AlgSHA3_256, crypto.SHA3_256},
+	{AlgSHA3_384, crypto.SHA3_384},
+	{AlgSHA3_512, crypto.SHA3_512},
 }
 
 // MAX_DIGEST_BUFFER is the maximum size of []byte request or response fields.
@@ -43,6 +49,16 @@ const maxDigestBuffer = 1024
 // Algorithm represents a TPM_ALG_ID value.
 type Algorithm uint16
 
+// HashToAlgorithm looks up the TPM2 algorithm corresponding to the provided crypto.Hash
+func HashToAlgorithm(hash crypto.Hash) (Algorithm, error) {
+	for _, info := range hashInfo {
+		if info.hash == hash {
+			return info.alg, nil
+		}
+	}
+	return AlgUnknown, fmt.Errorf("go hash algorithm #%d has no TPM2 algorithm", hash)
+}
+
 // IsNull returns true if a is AlgNull or zero (unset).
 func (a Algorithm) IsNull() bool {
 	return a == AlgNull || a == AlgUnknown
@@ -61,14 +77,15 @@ func (a Algorithm) UsesHash() bool {
 // Hash returns a crypto.Hash based on the given TPM_ALG_ID.
 // An error is returned if the given algorithm is not a hash algorithm or is not available.
 func (a Algorithm) Hash() (crypto.Hash, error) {
-	hash, ok := hashMapping[a]
-	if !ok {
-		return crypto.Hash(0), fmt.Errorf("hash algorithm not supported: 0x%x", a)
-	}
-	if !hash.Available() {
-		return crypto.Hash(0), fmt.Errorf("go hash algorithm #%d not available", hash)
+	for _, info := range hashInfo {
+		if info.alg == a {
+			if !info.hash.Available() {
+				return crypto.Hash(0), fmt.Errorf("go hash algorithm #%d not available", info.hash)
+			}
+			return info.hash, nil
+		}
 	}
-	return hash, nil
+	return crypto.Hash(0), fmt.Errorf("hash algorithm not supported: 0x%x", a)
 }
 
 // Supported Algorithms.
@@ -94,6 +111,9 @@ const (
 	AlgKDF2      Algorithm = 0x0021
 	AlgECC       Algorithm = 0x0023
 	AlgSymCipher Algorithm = 0x0025
+	AlgSHA3_256  Algorithm = 0x0027
+	AlgSHA3_384  Algorithm = 0x0028
+	AlgSHA3_512  Algorithm = 0x0029
 	AlgCTR       Algorithm = 0x0040
 	AlgOFB       Algorithm = 0x0041
 	AlgCBC       Algorithm = 0x0042
diff --git a/tpm2/structures.go b/tpm2/structures.go
index c90b6837..4040a23a 100644
--- a/tpm2/structures.go
+++ b/tpm2/structures.go
@@ -961,9 +961,9 @@ func decodeHashValue(in *bytes.Buffer) (*HashValue, error) {
 	if err := tpmutil.UnpackBuf(in, &hv.Alg); err != nil {
 		return nil, fmt.Errorf("decoding Alg: %v", err)
 	}
-	hfn, ok := hashMapping[hv.Alg]
-	if !ok {
-		return nil, fmt.Errorf("hash algorithm not supported: 0x%x", hv.Alg)
+	hfn, err := hv.Alg.Hash()
+	if err != nil {
+		return nil, err
 	}
 	hv.Value = make(tpmutil.U16Bytes, hfn.Size())
 	if _, err := in.Read(hv.Value); err != nil {
diff --git a/tpm2/tpm2.go b/tpm2/tpm2.go
index edc970b5..00926001 100644
--- a/tpm2/tpm2.go
+++ b/tpm2/tpm2.go
@@ -74,7 +74,7 @@ func encodeTPMLPCRSelection(sel ...PCRSelection) ([]byte, error) {
 		// s[i].PCRs parameter is indexes of PCRs, convert that to set bits.
 		for _, n := range s.PCRs {
 			if n >= 8*sizeOfPCRSelect {
-				return nil,  fmt.Errorf("PCR index %d is out of range (exceeds maximum value %d)", n, 8*sizeOfPCRSelect-1)
+				return nil, fmt.Errorf("PCR index %d is out of range (exceeds maximum value %d)", n, 8*sizeOfPCRSelect-1)
 			}
 			byteNum := n / 8
 			bytePos := byte(1 << byte(n%8))