diff --git a/ecdsa.go b/ecdsa.go
index 46b16abf..d35277bd 100644
--- a/ecdsa.go
+++ b/ecdsa.go
@@ -7,6 +7,7 @@ import "C"
 import (
 	"crypto"
 	"errors"
+	"io"
 	"runtime"
 )
 
@@ -109,7 +110,7 @@ func SignMarshalECDSA(priv *PrivateKeyECDSA, hash []byte) ([]byte, error) {
 	return evpSign(priv.withKey, 0, 0, 0, hash)
 }
 
-func HashSignECDSA(priv *PrivateKeyECDSA, h crypto.Hash, msg []byte) ([]byte, error) {
+func HashSignECDSA(priv *PrivateKeyECDSA, h crypto.Hash, msg io.Reader) ([]byte, error) {
 	return evpHashSign(priv.withKey, h, msg)
 }
 
@@ -117,7 +118,7 @@ func VerifyECDSA(pub *PublicKeyECDSA, hash []byte, sig []byte) bool {
 	return evpVerify(pub.withKey, 0, 0, 0, sig, hash) == nil
 }
 
-func HashVerifyECDSA(pub *PublicKeyECDSA, h crypto.Hash, msg, sig []byte) bool {
+func HashVerifyECDSA(pub *PublicKeyECDSA, h crypto.Hash, msg io.Reader, sig []byte) bool {
 	return evpHashVerify(pub.withKey, h, msg, sig) == nil
 }
 
diff --git a/ecdsa_test.go b/ecdsa_test.go
index d67b8d01..ed9f308b 100644
--- a/ecdsa_test.go
+++ b/ecdsa_test.go
@@ -1,6 +1,7 @@
 package openssl_test
 
 import (
+	"bytes"
 	"crypto"
 	"crypto/ecdsa"
 	"crypto/elliptic"
@@ -74,15 +75,15 @@ func testECDSASignAndVerify(t *testing.T, c elliptic.Curve) {
 	if openssl.VerifyECDSA(pub, hashed[:], signed) {
 		t.Errorf("Verify succeeded despite intentionally invalid hash!")
 	}
-	signed, err = openssl.HashSignECDSA(priv, crypto.SHA256, msg)
+	signed, err = openssl.HashSignECDSA(priv, crypto.SHA256, bytes.NewReader(msg))
 	if err != nil {
 		t.Fatal(err)
 	}
-	if !openssl.HashVerifyECDSA(pub, crypto.SHA256, msg, signed) {
+	if !openssl.HashVerifyECDSA(pub, crypto.SHA256, bytes.NewReader(msg), signed) {
 		t.Errorf("Verify failed")
 	}
 	signed[0] ^= 0xff
-	if openssl.HashVerifyECDSA(pub, crypto.SHA256, msg, signed) {
+	if openssl.HashVerifyECDSA(pub, crypto.SHA256, bytes.NewReader(msg), signed) {
 		t.Errorf("Verify failed")
 	}
 }
diff --git a/evp.go b/evp.go
index c7f53e3e..95c7f169 100644
--- a/evp.go
+++ b/evp.go
@@ -8,6 +8,7 @@ import (
 	"crypto"
 	"errors"
 	"hash"
+	"io"
 	"strconv"
 	"sync"
 	"unsafe"
@@ -371,7 +372,7 @@ func evpVerify(withKey withKeyFunc, padding C.int, saltLen C.int, h crypto.Hash,
 	return verifyEVP(withKey, padding, nil, nil, saltLen, h, verifyInit, verify, sig, hashed)
 }
 
-func evpHashSign(withKey withKeyFunc, h crypto.Hash, msg []byte) ([]byte, error) {
+func evpHashSign(withKey withKeyFunc, h crypto.Hash, msg io.Reader) ([]byte, error) {
 	md := cryptoHashToMD(h)
 	if md == nil {
 		return nil, errors.New("unsupported hash function: " + strconv.Itoa(int(h)))
@@ -388,8 +389,19 @@ func evpHashSign(withKey withKeyFunc, h crypto.Hash, msg []byte) ([]byte, error)
 	}) != 1 {
 		return nil, newOpenSSLError("EVP_DigestSignInit failed")
 	}
-	if C.go_openssl_EVP_DigestUpdate(ctx, unsafe.Pointer(base(msg)), C.size_t(len(msg))) != 1 {
-		return nil, newOpenSSLError("EVP_DigestUpdate failed")
+	var blockLen = C.go_openssl_EVP_MD_get_block_size(md)
+	var block = make([]byte, blockLen)
+	for {
+		n, err := msg.Read(block)
+		if err == io.EOF {
+			break
+		}
+		if err != nil {
+			return nil, err
+		}
+		if C.go_openssl_EVP_DigestUpdate(ctx, unsafe.Pointer(base(block)), C.size_t(n)) != 1 {
+			return nil, newOpenSSLError("EVP_DigestUpdate failed")
+		}
 	}
 	// Obtain the signature length
 	if C.go_openssl_EVP_DigestSignFinal(ctx, nil, &outLen) != 1 {
@@ -403,7 +415,7 @@ func evpHashSign(withKey withKeyFunc, h crypto.Hash, msg []byte) ([]byte, error)
 	return out[:outLen], nil
 }
 
-func evpHashVerify(withKey withKeyFunc, h crypto.Hash, msg, sig []byte) error {
+func evpHashVerify(withKey withKeyFunc, h crypto.Hash, msg io.Reader, sig []byte) error {
 	md := cryptoHashToMD(h)
 	if md == nil {
 		return errors.New("unsupported hash function: " + strconv.Itoa(int(h)))
@@ -418,8 +430,19 @@ func evpHashVerify(withKey withKeyFunc, h crypto.Hash, msg, sig []byte) error {
 	}) != 1 {
 		return newOpenSSLError("EVP_DigestVerifyInit failed")
 	}
-	if C.go_openssl_EVP_DigestUpdate(ctx, unsafe.Pointer(base(msg)), C.size_t(len(msg))) != 1 {
-		return newOpenSSLError("EVP_DigestUpdate failed")
+	var blockLen = C.go_openssl_EVP_MD_get_block_size(md)
+	var block = make([]byte, blockLen)
+	for {
+		n, err := msg.Read(block)
+		if err == io.EOF {
+			break
+		}
+		if err != nil {
+			return err
+		}
+		if C.go_openssl_EVP_DigestUpdate(ctx, unsafe.Pointer(base(block)), C.size_t(n)) != 1 {
+			return newOpenSSLError("EVP_DigestUpdate failed")
+		}
 	}
 	if C.go_openssl_EVP_DigestVerifyFinal(ctx, base(sig), C.size_t(len(sig))) != 1 {
 		return newOpenSSLError("EVP_DigestVerifyFinal failed")
diff --git a/rsa.go b/rsa.go
index 5aef65b8..7a0415b4 100644
--- a/rsa.go
+++ b/rsa.go
@@ -9,6 +9,7 @@ import (
 	"crypto/subtle"
 	"errors"
 	"hash"
+	"io"
 	"runtime"
 	"unsafe"
 )
@@ -289,7 +290,7 @@ func SignRSAPKCS1v15(priv *PrivateKeyRSA, h crypto.Hash, hashed []byte) ([]byte,
 	return evpSign(priv.withKey, C.GO_RSA_PKCS1_PADDING, 0, h, hashed)
 }
 
-func HashSignRSAPKCS1v15(priv *PrivateKeyRSA, h crypto.Hash, msg []byte) ([]byte, error) {
+func HashSignRSAPKCS1v15(priv *PrivateKeyRSA, h crypto.Hash, msg io.Reader) ([]byte, error) {
 	return evpHashSign(priv.withKey, h, msg)
 }
 
@@ -306,7 +307,7 @@ func VerifyRSAPKCS1v15(pub *PublicKeyRSA, h crypto.Hash, hashed, sig []byte) err
 	return evpVerify(pub.withKey, C.GO_RSA_PKCS1_PADDING, 0, h, sig, hashed)
 }
 
-func HashVerifyRSAPKCS1v15(pub *PublicKeyRSA, h crypto.Hash, msg, sig []byte) error {
+func HashVerifyRSAPKCS1v15(pub *PublicKeyRSA, h crypto.Hash, msg io.Reader, sig []byte) error {
 	return evpHashVerify(pub.withKey, h, msg, sig)
 }
 
diff --git a/rsa_test.go b/rsa_test.go
index c926e9cf..b5b45603 100644
--- a/rsa_test.go
+++ b/rsa_test.go
@@ -130,7 +130,7 @@ func TestSignVerifyPKCS1v15(t *testing.T) {
 	if err != nil {
 		t.Fatal(err)
 	}
-	signed2, err := openssl.HashSignRSAPKCS1v15(priv, crypto.SHA256, msg)
+	signed2, err := openssl.HashSignRSAPKCS1v15(priv, crypto.SHA256, bytes.NewReader(msg))
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -141,7 +141,7 @@ func TestSignVerifyPKCS1v15(t *testing.T) {
 	if err != nil {
 		t.Fatal(err)
 	}
-	err = openssl.HashVerifyRSAPKCS1v15(pub, crypto.SHA256, msg, signed2)
+	err = openssl.HashVerifyRSAPKCS1v15(pub, crypto.SHA256, bytes.NewReader(msg), signed2)
 	if err != nil {
 		t.Fatal(err)
 	}
diff --git a/shims.h b/shims.h
index 858c47e7..7e26d16d 100644
--- a/shims.h
+++ b/shims.h
@@ -355,4 +355,5 @@ DEFINEFUNC(int, PKCS5_PBKDF2_HMAC, (const char *pass, int passlen, const unsigne
 DEFINEFUNC_3_0(int, EVP_PKEY_CTX_set_tls1_prf_md, (GO_EVP_PKEY_CTX_PTR arg0, const GO_EVP_MD_PTR arg1), (arg0, arg1)) \
 DEFINEFUNC_3_0(int, EVP_PKEY_CTX_set1_tls1_prf_secret, (GO_EVP_PKEY_CTX_PTR arg0, const unsigned char *arg1, int arg2), (arg0, arg1, arg2)) \
 DEFINEFUNC_3_0(int, EVP_PKEY_CTX_add1_tls1_prf_seed, (GO_EVP_PKEY_CTX_PTR arg0, const unsigned char *arg1, int arg2), (arg0, arg1, arg2)) \
+DEFINEFUNC_RENAMED_3_0(int, EVP_MD_get_block_size, EVP_MD_block_size, (const GO_EVP_MD_PTR md), (md)) \