diff --git a/signature/json.go b/signature/json.go
index 1cb3c44727..9e592863da 100644
--- a/signature/json.go
+++ b/signature/json.go
@@ -14,64 +14,6 @@ func (err jsonFormatError) Error() string {
 	return string(err)
 }
 
-// validateExactMapKeys returns an error if the keys of m are not exactly expectedKeys, which must be pairwise distinct
-func validateExactMapKeys(m map[string]interface{}, expectedKeys ...string) error {
-	if len(m) != len(expectedKeys) {
-		return jsonFormatError("Unexpected keys in a JSON object")
-	}
-
-	for _, k := range expectedKeys {
-		if _, ok := m[k]; !ok {
-			return jsonFormatError(fmt.Sprintf("Key %s missing in a JSON object", k))
-		}
-	}
-	// Assuming expectedKeys are pairwise distinct, we know m contains len(expectedKeys) different values in expectedKeys.
-	return nil
-}
-
-// int64Field returns a member fieldName of m, if it is an int64, or an error.
-func int64Field(m map[string]interface{}, fieldName string) (int64, error) {
-	untyped, ok := m[fieldName]
-	if !ok {
-		return -1, jsonFormatError(fmt.Sprintf("Field %s missing", fieldName))
-	}
-	f, ok := untyped.(float64)
-	if !ok {
-		return -1, jsonFormatError(fmt.Sprintf("Field %s is not a number", fieldName))
-	}
-	v := int64(f)
-	if float64(v) != f {
-		return -1, jsonFormatError(fmt.Sprintf("Field %s is not an integer", fieldName))
-	}
-	return v, nil
-}
-
-// mapField returns a member fieldName of m, if it is a JSON map, or an error.
-func mapField(m map[string]interface{}, fieldName string) (map[string]interface{}, error) {
-	untyped, ok := m[fieldName]
-	if !ok {
-		return nil, jsonFormatError(fmt.Sprintf("Field %s missing", fieldName))
-	}
-	v, ok := untyped.(map[string]interface{})
-	if !ok {
-		return nil, jsonFormatError(fmt.Sprintf("Field %s is not a JSON object", fieldName))
-	}
-	return v, nil
-}
-
-// stringField returns a member fieldName of m, if it is a string, or an error.
-func stringField(m map[string]interface{}, fieldName string) (string, error) {
-	untyped, ok := m[fieldName]
-	if !ok {
-		return "", jsonFormatError(fmt.Sprintf("Field %s missing", fieldName))
-	}
-	v, ok := untyped.(string)
-	if !ok {
-		return "", jsonFormatError(fmt.Sprintf("Field %s is not a string", fieldName))
-	}
-	return v, nil
-}
-
 // paranoidUnmarshalJSONObject unmarshals data as a JSON object, but failing on the slightest unexpected aspect
 // (including duplicated keys, unrecognized keys, and non-matching types). Uses fieldResolver to
 // determine the destination for a field value, which should return a pointer to the destination if valid, or nil if the key is rejected.
@@ -122,3 +64,25 @@ func paranoidUnmarshalJSONObject(data []byte, fieldResolver func(string) interfa
 	}
 	return nil
 }
+
+// paranoidUnmarshalJSONObject unmarshals data as a JSON object, but failing on the slightest unexpected aspect
+// (including duplicated keys, unrecognized keys, and non-matching types). Each of the fields in exactFields
+// must be present exactly once, and none other fields are accepted.
+func paranoidUnmarshalJSONObjectExactFields(data []byte, exactFields map[string]interface{}) error {
+	seenKeys := map[string]struct{}{}
+	if err := paranoidUnmarshalJSONObject(data, func(key string) interface{} {
+		if valuePtr, ok := exactFields[key]; ok {
+			seenKeys[key] = struct{}{}
+			return valuePtr
+		}
+		return nil
+	}); err != nil {
+		return err
+	}
+	for key := range exactFields {
+		if _, ok := seenKeys[key]; !ok {
+			return jsonFormatError(fmt.Sprintf(`Key "%s" missing in a JSON object`, key))
+		}
+	}
+	return nil
+}
diff --git a/signature/json_test.go b/signature/json_test.go
index fe63a1cd1e..83fe292989 100644
--- a/signature/json_test.go
+++ b/signature/json_test.go
@@ -2,8 +2,6 @@ package signature
 
 import (
 	"encoding/json"
-	"fmt"
-	"math"
 	"testing"
 
 	"github.com/stretchr/testify/assert"
@@ -24,91 +22,6 @@ func x(m mSI, fields ...string) mSI {
 	return m
 }
 
-func TestValidateExactMapKeys(t *testing.T) {
-	// Empty map and keys
-	err := validateExactMapKeys(mSI{})
-	assert.NoError(t, err)
-
-	// Success
-	err = validateExactMapKeys(mSI{"a": nil, "b": 1}, "b", "a")
-	assert.NoError(t, err)
-
-	// Extra map keys
-	err = validateExactMapKeys(mSI{"a": nil, "b": 1}, "a")
-	assert.Error(t, err)
-
-	// Extra expected keys
-	err = validateExactMapKeys(mSI{"a": 1}, "b", "a")
-	assert.Error(t, err)
-
-	// Unexpected key values
-	err = validateExactMapKeys(mSI{"a": 1}, "b")
-	assert.Error(t, err)
-}
-
-func TestInt64Field(t *testing.T) {
-	// Field not found
-	_, err := int64Field(mSI{"a": "x"}, "b")
-	assert.Error(t, err)
-
-	// Field has a wrong type
-	_, err = int64Field(mSI{"a": "string"}, "a")
-	assert.Error(t, err)
-
-	for _, value := range []float64{
-		0.5,         // Fractional input
-		math.Inf(1), // Infinity
-		math.NaN(),  // NaN
-	} {
-		_, err = int64Field(mSI{"a": value}, "a")
-		assert.Error(t, err, fmt.Sprintf("%f", value))
-	}
-
-	// Success
-	// The float64 type has 53 bits of effective precision, so ±1FFFFFFFFFFFFF is the
-	// range of integer values which can all be represented exactly (beyond that,
-	// some are representable if they are divisible by a high enough power of 2,
-	// but most are not).
-	for _, value := range []int64{0, 1, -1, 0x1FFFFFFFFFFFFF, -0x1FFFFFFFFFFFFF} {
-		testName := fmt.Sprintf("%d", value)
-		v, err := int64Field(mSI{"a": float64(value), "b": nil}, "a")
-		require.NoError(t, err, testName)
-		assert.Equal(t, value, v, testName)
-	}
-}
-
-func TestMapField(t *testing.T) {
-	// Field not found
-	_, err := mapField(mSI{"a": mSI{}}, "b")
-	assert.Error(t, err)
-
-	// Field has a wrong type
-	_, err = mapField(mSI{"a": 1}, "a")
-	assert.Error(t, err)
-
-	// Success
-	// FIXME? We can't use mSI as the type of child, that type apparently can't be converted to the raw map type.
-	child := map[string]interface{}{"b": mSI{}}
-	m, err := mapField(mSI{"a": child, "b": nil}, "a")
-	require.NoError(t, err)
-	assert.Equal(t, child, m)
-}
-
-func TestStringField(t *testing.T) {
-	// Field not found
-	_, err := stringField(mSI{"a": "x"}, "b")
-	assert.Error(t, err)
-
-	// Field has a wrong type
-	_, err = stringField(mSI{"a": 1}, "a")
-	assert.Error(t, err)
-
-	// Success
-	s, err := stringField(mSI{"a": "x", "b": nil}, "a")
-	require.NoError(t, err)
-	assert.Equal(t, "x", s)
-}
-
 // implementsUnmarshalJSON is a minimalistic type used to detect that
 // paranoidUnmarshalJSONObject uses the json.Unmarshaler interface of resolved
 // pointers.
@@ -180,3 +93,45 @@ func TestParanoidUnmarshalJSONObject(t *testing.T) {
 		assert.Error(t, err, input)
 	}
 }
+
+func TestParanoidUnmarshalJSONObjectExactFields(t *testing.T) {
+	var stringValue string
+	var float64Value float64
+	var rawValue json.RawMessage
+	var unmarshallCalled implementsUnmarshalJSON
+	exactFields := map[string]interface{}{
+		"string":       &stringValue,
+		"float64":      &float64Value,
+		"raw":          &rawValue,
+		"unmarshaller": &unmarshallCalled,
+	}
+
+	// Empty object
+	err := paranoidUnmarshalJSONObjectExactFields([]byte(`{}`), map[string]interface{}{})
+	require.NoError(t, err)
+
+	// Success
+	err = paranoidUnmarshalJSONObjectExactFields([]byte(`{"string": "a", "float64": 3.5, "raw": {"a":"b"}, "unmarshaller": true}`), exactFields)
+	require.NoError(t, err)
+	assert.Equal(t, "a", stringValue)
+	assert.Equal(t, 3.5, float64Value)
+	assert.Equal(t, json.RawMessage(`{"a":"b"}`), rawValue)
+	assert.Equal(t, implementsUnmarshalJSON(true), unmarshallCalled)
+
+	// Various kinds of invalid input
+	for _, input := range []string{
+		``,      // Empty input
+		`&`,     // Entirely invalid JSON
+		`1`,     // Not an object
+		`{&}`,   // Invalid key JSON
+		`{1:1}`, // Key not a string
+		`{"string": "a", "string": "a", "float64": 3.5, "raw": {"a":"b"}, "unmarshaller": true}`,      // Duplicate key
+		`{"string": "a", "float64": 3.5, "raw": {"a":"b"}, "unmarshaller": true, "thisisunknown", 1}`, // Unknown key
+		`{"string": &, "float64": 3.5, "raw": {"a":"b"}, "unmarshaller": true}`,                       // Invalid value JSON
+		`{"string": 1, "float64": 3.5, "raw": {"a":"b"}, "unmarshaller": true}`,                       // Type mismatch
+		`{"string": "a", "float64": 3.5, "raw": {"a":"b"}, "unmarshaller": true}{}`,                   // Extra data after object
+	} {
+		err := paranoidUnmarshalJSONObjectExactFields([]byte(input), exactFields)
+		assert.Error(t, err, input)
+	}
+}
diff --git a/signature/policy_config.go b/signature/policy_config.go
index e4c93ed528..bc6c5e9a7d 100644
--- a/signature/policy_config.go
+++ b/signature/policy_config.go
@@ -255,13 +255,8 @@ var _ json.Unmarshaler = (*prInsecureAcceptAnything)(nil)
 func (pr *prInsecureAcceptAnything) UnmarshalJSON(data []byte) error {
 	*pr = prInsecureAcceptAnything{}
 	var tmp prInsecureAcceptAnything
-	if err := paranoidUnmarshalJSONObject(data, func(key string) interface{} {
-		switch key {
-		case "type":
-			return &tmp.Type
-		default:
-			return nil
-		}
+	if err := paranoidUnmarshalJSONObjectExactFields(data, map[string]interface{}{
+		"type": &tmp.Type,
 	}); err != nil {
 		return err
 	}
@@ -290,13 +285,8 @@ var _ json.Unmarshaler = (*prReject)(nil)
 func (pr *prReject) UnmarshalJSON(data []byte) error {
 	*pr = prReject{}
 	var tmp prReject
-	if err := paranoidUnmarshalJSONObject(data, func(key string) interface{} {
-		switch key {
-		case "type":
-			return &tmp.Type
-		default:
-			return nil
-		}
+	if err := paranoidUnmarshalJSONObjectExactFields(data, map[string]interface{}{
+		"type": &tmp.Type,
 	}); err != nil {
 		return err
 	}
@@ -465,15 +455,9 @@ func (pr *prSignedBaseLayer) UnmarshalJSON(data []byte) error {
 	*pr = prSignedBaseLayer{}
 	var tmp prSignedBaseLayer
 	var baseLayerIdentity json.RawMessage
-	if err := paranoidUnmarshalJSONObject(data, func(key string) interface{} {
-		switch key {
-		case "type":
-			return &tmp.Type
-		case "baseLayerIdentity":
-			return &baseLayerIdentity
-		default:
-			return nil
-		}
+	if err := paranoidUnmarshalJSONObjectExactFields(data, map[string]interface{}{
+		"type":              &tmp.Type,
+		"baseLayerIdentity": &baseLayerIdentity,
 	}); err != nil {
 		return err
 	}
@@ -481,9 +465,6 @@ func (pr *prSignedBaseLayer) UnmarshalJSON(data []byte) error {
 	if tmp.Type != prTypeSignedBaseLayer {
 		return InvalidPolicyFormatError(fmt.Sprintf("Unexpected policy requirement type \"%s\"", tmp.Type))
 	}
-	if baseLayerIdentity == nil {
-		return InvalidPolicyFormatError(fmt.Sprintf("baseLayerIdentity not specified"))
-	}
 	bli, err := newPolicyReferenceMatchFromJSON(baseLayerIdentity)
 	if err != nil {
 		return err
@@ -541,13 +522,8 @@ var _ json.Unmarshaler = (*prmMatchExact)(nil)
 func (prm *prmMatchExact) UnmarshalJSON(data []byte) error {
 	*prm = prmMatchExact{}
 	var tmp prmMatchExact
-	if err := paranoidUnmarshalJSONObject(data, func(key string) interface{} {
-		switch key {
-		case "type":
-			return &tmp.Type
-		default:
-			return nil
-		}
+	if err := paranoidUnmarshalJSONObjectExactFields(data, map[string]interface{}{
+		"type": &tmp.Type,
 	}); err != nil {
 		return err
 	}
@@ -576,13 +552,8 @@ var _ json.Unmarshaler = (*prmMatchRepoDigestOrExact)(nil)
 func (prm *prmMatchRepoDigestOrExact) UnmarshalJSON(data []byte) error {
 	*prm = prmMatchRepoDigestOrExact{}
 	var tmp prmMatchRepoDigestOrExact
-	if err := paranoidUnmarshalJSONObject(data, func(key string) interface{} {
-		switch key {
-		case "type":
-			return &tmp.Type
-		default:
-			return nil
-		}
+	if err := paranoidUnmarshalJSONObjectExactFields(data, map[string]interface{}{
+		"type": &tmp.Type,
 	}); err != nil {
 		return err
 	}
@@ -611,13 +582,8 @@ var _ json.Unmarshaler = (*prmMatchRepository)(nil)
 func (prm *prmMatchRepository) UnmarshalJSON(data []byte) error {
 	*prm = prmMatchRepository{}
 	var tmp prmMatchRepository
-	if err := paranoidUnmarshalJSONObject(data, func(key string) interface{} {
-		switch key {
-		case "type":
-			return &tmp.Type
-		default:
-			return nil
-		}
+	if err := paranoidUnmarshalJSONObjectExactFields(data, map[string]interface{}{
+		"type": &tmp.Type,
 	}); err != nil {
 		return err
 	}
@@ -656,15 +622,9 @@ var _ json.Unmarshaler = (*prmExactReference)(nil)
 func (prm *prmExactReference) UnmarshalJSON(data []byte) error {
 	*prm = prmExactReference{}
 	var tmp prmExactReference
-	if err := paranoidUnmarshalJSONObject(data, func(key string) interface{} {
-		switch key {
-		case "type":
-			return &tmp.Type
-		case "dockerReference":
-			return &tmp.DockerReference
-		default:
-			return nil
-		}
+	if err := paranoidUnmarshalJSONObjectExactFields(data, map[string]interface{}{
+		"type":            &tmp.Type,
+		"dockerReference": &tmp.DockerReference,
 	}); err != nil {
 		return err
 	}
@@ -704,15 +664,9 @@ var _ json.Unmarshaler = (*prmExactRepository)(nil)
 func (prm *prmExactRepository) UnmarshalJSON(data []byte) error {
 	*prm = prmExactRepository{}
 	var tmp prmExactRepository
-	if err := paranoidUnmarshalJSONObject(data, func(key string) interface{} {
-		switch key {
-		case "type":
-			return &tmp.Type
-		case "dockerRepository":
-			return &tmp.DockerRepository
-		default:
-			return nil
-		}
+	if err := paranoidUnmarshalJSONObjectExactFields(data, map[string]interface{}{
+		"type":             &tmp.Type,
+		"dockerRepository": &tmp.DockerRepository,
 	}); err != nil {
 		return err
 	}
diff --git a/signature/policy_config_test.go b/signature/policy_config_test.go
index 12cb832ab7..c1d930ba22 100644
--- a/signature/policy_config_test.go
+++ b/signature/policy_config_test.go
@@ -297,8 +297,8 @@ func TestPolicyUnmarshalJSON(t *testing.T) {
 
 	// Various allowed modifications to the policy
 	allowedModificationFns := []func(mSI){
-		// Delete the map of specific policies
-		func(v mSI) { delete(v, "specific") },
+		// Delete the map of transport-specific scopes
+		func(v mSI) { delete(v, "transports") },
 		// Use an empty map of transport-specific scopes
 		func(v mSI) { v["transports"] = map[string]PolicyTransportScopes{} },
 	}
diff --git a/signature/signature.go b/signature/signature.go
index 30238e6115..79174c845d 100644
--- a/signature/signature.go
+++ b/signature/signature.go
@@ -120,78 +120,69 @@ func (s *untrustedSignature) UnmarshalJSON(data []byte) error {
 // strictUnmarshalJSON is UnmarshalJSON, except that it may return the internal jsonFormatError error type.
 // Splitting it into a separate function allows us to do the jsonFormatError → InvalidSignatureError in a single place, the caller.
 func (s *untrustedSignature) strictUnmarshalJSON(data []byte) error {
-	var untyped interface{}
-	if err := json.Unmarshal(data, &untyped); err != nil {
-		return err
-	}
-	o, ok := untyped.(map[string]interface{})
-	if !ok {
-		return InvalidSignatureError{msg: "Invalid signature format"}
-	}
-	if err := validateExactMapKeys(o, "critical", "optional"); err != nil {
+	var critical, optional json.RawMessage
+	if err := paranoidUnmarshalJSONObjectExactFields(data, map[string]interface{}{
+		"critical": &critical,
+		"optional": &optional,
+	}); err != nil {
 		return err
 	}
 
-	c, err := mapField(o, "critical")
-	if err != nil {
-		return err
-	}
-	if err := validateExactMapKeys(c, "type", "image", "identity"); err != nil {
-		return err
-	}
-
-	optional, err := mapField(o, "optional")
-	if err != nil {
+	var creatorID string
+	var timestamp float64
+	var gotCreatorID, gotTimestamp = false, false
+	if err := paranoidUnmarshalJSONObject(optional, func(key string) interface{} {
+		switch key {
+		case "creator":
+			gotCreatorID = true
+			return &creatorID
+		case "timestamp":
+			gotTimestamp = true
+			return &timestamp
+		default:
+			var ignore interface{}
+			return &ignore
+		}
+	}); err != nil {
 		return err
 	}
-	if _, ok := optional["creator"]; ok {
-		creatorID, err := stringField(optional, "creator")
-		if err != nil {
-			return err
-		}
+	if gotCreatorID {
 		s.UntrustedCreatorID = &creatorID
 	}
-	if _, ok := optional["timestamp"]; ok {
-		timestamp, err := int64Field(optional, "timestamp")
-		if err != nil {
-			return err
+	if gotTimestamp {
+		intTimestamp := int64(timestamp)
+		if float64(intTimestamp) != timestamp {
+			return InvalidSignatureError{msg: "Field optional.timestamp is not is not an integer"}
 		}
-		s.UntrustedTimestamp = &timestamp
+		s.UntrustedTimestamp = &intTimestamp
 	}
 
-	t, err := stringField(c, "type")
-	if err != nil {
+	var t string
+	var image, identity json.RawMessage
+	if err := paranoidUnmarshalJSONObjectExactFields(critical, map[string]interface{}{
+		"type":     &t,
+		"image":    &image,
+		"identity": &identity,
+	}); err != nil {
 		return err
 	}
 	if t != signatureType {
 		return InvalidSignatureError{msg: fmt.Sprintf("Unrecognized signature type %s", t)}
 	}
 
-	image, err := mapField(c, "image")
-	if err != nil {
-		return err
-	}
-	if err := validateExactMapKeys(image, "docker-manifest-digest"); err != nil {
-		return err
-	}
-	digestString, err := stringField(image, "docker-manifest-digest")
-	if err != nil {
+	var digestString string
+	if err := paranoidUnmarshalJSONObjectExactFields(image, map[string]interface{}{
+		"docker-manifest-digest": &digestString,
+	}); err != nil {
 		return err
 	}
 	s.UntrustedDockerManifestDigest = digest.Digest(digestString)
 
-	identity, err := mapField(c, "identity")
-	if err != nil {
-		return err
-	}
-	if err := validateExactMapKeys(identity, "docker-reference"); err != nil {
-		return err
-	}
-	reference, err := stringField(identity, "docker-reference")
-	if err != nil {
+	if err := paranoidUnmarshalJSONObjectExactFields(identity, map[string]interface{}{
+		"docker-reference": &s.UntrustedDockerReference,
+	}); err != nil {
 		return err
 	}
-	s.UntrustedDockerReference = reference
 
 	return nil
 }
diff --git a/signature/signature_test.go b/signature/signature_test.go
index 3ddcffe574..1afbfd6de5 100644
--- a/signature/signature_test.go
+++ b/signature/signature_test.go
@@ -153,6 +153,7 @@ func TestUnmarshalJSON(t *testing.T) {
 		func(v mSI) { x(v, "optional")["creator"] = 1 },
 		// Invalid "timestamp"
 		func(v mSI) { x(v, "optional")["timestamp"] = "unexpected" },
+		func(v mSI) { x(v, "optional")["timestamp"] = 0.5 }, // Fractional input
 	}
 	for _, fn := range breakFns {
 		err = tryUnmarshalModifiedSignature(t, &s, validJSON, fn)