diff --git a/crypto/evp/evp.c b/crypto/evp/evp.c
index 4feadb7..ed7cc85 100644
--- a/crypto/evp/evp.c
+++ b/crypto/evp/evp.c
@@ -176,7 +176,7 @@
   return 0;
 }
 
-int EVP_PKEY_bits(EVP_PKEY *pkey) {
+int EVP_PKEY_bits(const EVP_PKEY *pkey) {
   if (pkey && pkey->ameth && pkey->ameth->pkey_bits) {
     return pkey->ameth->pkey_bits(pkey);
   }
@@ -225,7 +225,7 @@
   return EVP_PKEY_assign(pkey, EVP_PKEY_RSA, key);
 }
 
-RSA *EVP_PKEY_get0_RSA(EVP_PKEY *pkey) {
+RSA *EVP_PKEY_get0_RSA(const EVP_PKEY *pkey) {
   if (pkey->type != EVP_PKEY_RSA) {
     OPENSSL_PUT_ERROR(EVP, EVP_R_EXPECTING_AN_RSA_KEY);
     return NULL;
@@ -233,7 +233,7 @@
   return pkey->pkey.rsa;
 }
 
-RSA *EVP_PKEY_get1_RSA(EVP_PKEY *pkey) {
+RSA *EVP_PKEY_get1_RSA(const EVP_PKEY *pkey) {
   RSA *rsa = EVP_PKEY_get0_RSA(pkey);
   if (rsa != NULL) {
     RSA_up_ref(rsa);
@@ -253,7 +253,7 @@
   return EVP_PKEY_assign(pkey, EVP_PKEY_DSA, key);
 }
 
-DSA *EVP_PKEY_get0_DSA(EVP_PKEY *pkey) {
+DSA *EVP_PKEY_get0_DSA(const EVP_PKEY *pkey) {
   if (pkey->type != EVP_PKEY_DSA) {
     OPENSSL_PUT_ERROR(EVP, EVP_R_EXPECTING_A_DSA_KEY);
     return NULL;
@@ -261,7 +261,7 @@
   return pkey->pkey.dsa;
 }
 
-DSA *EVP_PKEY_get1_DSA(EVP_PKEY *pkey) {
+DSA *EVP_PKEY_get1_DSA(const EVP_PKEY *pkey) {
   DSA *dsa = EVP_PKEY_get0_DSA(pkey);
   if (dsa != NULL) {
     DSA_up_ref(dsa);
@@ -281,7 +281,7 @@
   return EVP_PKEY_assign(pkey, EVP_PKEY_EC, key);
 }
 
-EC_KEY *EVP_PKEY_get0_EC_KEY(EVP_PKEY *pkey) {
+EC_KEY *EVP_PKEY_get0_EC_KEY(const EVP_PKEY *pkey) {
   if (pkey->type != EVP_PKEY_EC) {
     OPENSSL_PUT_ERROR(EVP, EVP_R_EXPECTING_AN_EC_KEY_KEY);
     return NULL;
@@ -289,7 +289,7 @@
   return pkey->pkey.ec;
 }
 
-EC_KEY *EVP_PKEY_get1_EC_KEY(EVP_PKEY *pkey) {
+EC_KEY *EVP_PKEY_get1_EC_KEY(const EVP_PKEY *pkey) {
   EC_KEY *ec_key = EVP_PKEY_get0_EC_KEY(pkey);
   if (ec_key != NULL) {
     EC_KEY_up_ref(ec_key);
@@ -297,8 +297,8 @@
   return ec_key;
 }
 
-DH *EVP_PKEY_get0_DH(EVP_PKEY *pkey) { return NULL; }
-DH *EVP_PKEY_get1_DH(EVP_PKEY *pkey) { return NULL; }
+DH *EVP_PKEY_get0_DH(const EVP_PKEY *pkey) { return NULL; }
+DH *EVP_PKEY_get1_DH(const EVP_PKEY *pkey) { return NULL; }
 
 int EVP_PKEY_assign(EVP_PKEY *pkey, int type, void *key) {
   if (!EVP_PKEY_set_type(pkey, type)) {
diff --git a/crypto/evp/evp_asn1.c b/crypto/evp/evp_asn1.c
index 81c7a71..383e2f9 100644
--- a/crypto/evp/evp_asn1.c
+++ b/crypto/evp/evp_asn1.c
@@ -331,7 +331,7 @@
   }
 }
 
-int i2d_PublicKey(EVP_PKEY *key, uint8_t **outp) {
+int i2d_PublicKey(const EVP_PKEY *key, uint8_t **outp) {
   switch (key->type) {
     case EVP_PKEY_RSA:
       return i2d_RSAPublicKey(key->pkey.rsa, outp);
diff --git a/crypto/fipsmodule/rsa/padding.c b/crypto/fipsmodule/rsa/padding.c
index ce3df7a..b7998fe 100644
--- a/crypto/fipsmodule/rsa/padding.c
+++ b/crypto/fipsmodule/rsa/padding.c
@@ -480,7 +480,7 @@
 
 static const uint8_t kPSSZeroes[] = {0, 0, 0, 0, 0, 0, 0, 0};
 
-int RSA_verify_PKCS1_PSS_mgf1(RSA *rsa, const uint8_t *mHash,
+int RSA_verify_PKCS1_PSS_mgf1(const RSA *rsa, const uint8_t *mHash,
                               const EVP_MD *Hash, const EVP_MD *mgf1Hash,
                               const uint8_t *EM, int sLen) {
   int i;
@@ -579,7 +579,7 @@
   return ret;
 }
 
-int RSA_padding_add_PKCS1_PSS_mgf1(RSA *rsa, unsigned char *EM,
+int RSA_padding_add_PKCS1_PSS_mgf1(const RSA *rsa, unsigned char *EM,
                                    const unsigned char *mHash,
                                    const EVP_MD *Hash, const EVP_MD *mgf1Hash,
                                    int sLenRequested) {
diff --git a/decrepit/rsa/rsa_decrepit.c b/decrepit/rsa/rsa_decrepit.c
index c4ef5b6..54be9b2 100644
--- a/decrepit/rsa/rsa_decrepit.c
+++ b/decrepit/rsa/rsa_decrepit.c
@@ -85,13 +85,13 @@
   return NULL;
 }
 
-int RSA_padding_add_PKCS1_PSS(RSA *rsa, uint8_t *EM, const uint8_t *mHash,
+int RSA_padding_add_PKCS1_PSS(const RSA *rsa, uint8_t *EM, const uint8_t *mHash,
                               const EVP_MD *Hash, int sLen) {
   return RSA_padding_add_PKCS1_PSS_mgf1(rsa, EM, mHash, Hash, NULL, sLen);
 }
 
-int RSA_verify_PKCS1_PSS(RSA *rsa, const uint8_t *mHash, const EVP_MD *Hash,
-                         const uint8_t *EM, int sLen) {
+int RSA_verify_PKCS1_PSS(const RSA *rsa, const uint8_t *mHash,
+                         const EVP_MD *Hash, const uint8_t *EM, int sLen) {
   return RSA_verify_PKCS1_PSS_mgf1(rsa, mHash, Hash, NULL, EM, sLen);
 }
 
diff --git a/include/openssl/ec_key.h b/include/openssl/ec_key.h
index a94116c..6944049 100644
--- a/include/openssl/ec_key.h
+++ b/include/openssl/ec_key.h
@@ -84,6 +84,12 @@
 
 
 // EC key objects.
+//
+// An |EC_KEY| object represents a public or private EC key. A given object may
+// be used concurrently on multiple threads by non-mutating functions, provided
+// no other thread is concurrently calling a mutating function. Unless otherwise
+// documented, functions which take a |const| pointer are non-mutating and
+// functions which take a non-|const| pointer are mutating.
 
 // EC_KEY_new returns a fresh |EC_KEY| object or NULL on error.
 OPENSSL_EXPORT EC_KEY *EC_KEY_new(void);
@@ -102,7 +108,8 @@
 // EC_KEY_dup returns a fresh copy of |src| or NULL on error.
 OPENSSL_EXPORT EC_KEY *EC_KEY_dup(const EC_KEY *src);
 
-// EC_KEY_up_ref increases the reference count of |key| and returns one.
+// EC_KEY_up_ref increases the reference count of |key| and returns one. It does
+// not mutate |key| for thread-safety purposes and may be used concurrently.
 OPENSSL_EXPORT int EC_KEY_up_ref(EC_KEY *key);
 
 // EC_KEY_is_opaque returns one if |key| is opaque and doesn't expose its key
diff --git a/include/openssl/evp.h b/include/openssl/evp.h
index 3719d7f..9b00a07 100644
--- a/include/openssl/evp.h
+++ b/include/openssl/evp.h
@@ -80,6 +80,12 @@
 
 
 // Public key objects.
+//
+// An |EVP_PKEY| object represents a public or private key. A given object may
+// be used concurrently on multiple threads by non-mutating functions, provided
+// no other thread is concurrently calling a mutating function. Unless otherwise
+// documented, functions which take a |const| pointer are non-mutating and
+// functions which take a non-|const| pointer are mutating.
 
 // EVP_PKEY_new creates a new, empty public-key object and returns it or NULL
 // on allocation failure.
@@ -89,7 +95,9 @@
 // itself.
 OPENSSL_EXPORT void EVP_PKEY_free(EVP_PKEY *pkey);
 
-// EVP_PKEY_up_ref increments the reference count of |pkey| and returns one.
+// EVP_PKEY_up_ref increments the reference count of |pkey| and returns one. It
+// does not mutate |pkey| for thread-safety purposes and may be used
+// concurrently.
 OPENSSL_EXPORT int EVP_PKEY_up_ref(EVP_PKEY *pkey);
 
 // EVP_PKEY_is_opaque returns one if |pkey| is opaque. Opaque keys are backed by
@@ -121,7 +129,7 @@
 // EVP_PKEY_bits returns the "size", in bits, of |pkey|. For an RSA key, this
 // returns the bit length of the modulus. For an EC key, this returns the bit
 // length of the group order.
-OPENSSL_EXPORT int EVP_PKEY_bits(EVP_PKEY *pkey);
+OPENSSL_EXPORT int EVP_PKEY_bits(const EVP_PKEY *pkey);
 
 // EVP_PKEY_id returns the type of |pkey|, which is one of the |EVP_PKEY_*|
 // values.
@@ -141,21 +149,26 @@
 // zero if |key| is NULL. The |get1| functions return a fresh reference to the
 // underlying object or NULL if |pkey| is not of the correct type. The |get0|
 // functions behave the same but return a non-owning pointer.
+//
+// The |get0| and |get1| functions take |const| pointers and are thus
+// non-mutating for thread-safety purposes, but mutating functions on the
+// returned lower-level objects are considered to also mutate the |EVP_PKEY| and
+// may not be called concurrently with other operations on the |EVP_PKEY|.
 
 OPENSSL_EXPORT int EVP_PKEY_set1_RSA(EVP_PKEY *pkey, RSA *key);
 OPENSSL_EXPORT int EVP_PKEY_assign_RSA(EVP_PKEY *pkey, RSA *key);
-OPENSSL_EXPORT RSA *EVP_PKEY_get0_RSA(EVP_PKEY *pkey);
-OPENSSL_EXPORT RSA *EVP_PKEY_get1_RSA(EVP_PKEY *pkey);
+OPENSSL_EXPORT RSA *EVP_PKEY_get0_RSA(const EVP_PKEY *pkey);
+OPENSSL_EXPORT RSA *EVP_PKEY_get1_RSA(const EVP_PKEY *pkey);
 
 OPENSSL_EXPORT int EVP_PKEY_set1_DSA(EVP_PKEY *pkey, DSA *key);
 OPENSSL_EXPORT int EVP_PKEY_assign_DSA(EVP_PKEY *pkey, DSA *key);
-OPENSSL_EXPORT DSA *EVP_PKEY_get0_DSA(EVP_PKEY *pkey);
-OPENSSL_EXPORT DSA *EVP_PKEY_get1_DSA(EVP_PKEY *pkey);
+OPENSSL_EXPORT DSA *EVP_PKEY_get0_DSA(const EVP_PKEY *pkey);
+OPENSSL_EXPORT DSA *EVP_PKEY_get1_DSA(const EVP_PKEY *pkey);
 
 OPENSSL_EXPORT int EVP_PKEY_set1_EC_KEY(EVP_PKEY *pkey, EC_KEY *key);
 OPENSSL_EXPORT int EVP_PKEY_assign_EC_KEY(EVP_PKEY *pkey, EC_KEY *key);
-OPENSSL_EXPORT EC_KEY *EVP_PKEY_get0_EC_KEY(EVP_PKEY *pkey);
-OPENSSL_EXPORT EC_KEY *EVP_PKEY_get1_EC_KEY(EVP_PKEY *pkey);
+OPENSSL_EXPORT EC_KEY *EVP_PKEY_get0_EC_KEY(const EVP_PKEY *pkey);
+OPENSSL_EXPORT EC_KEY *EVP_PKEY_get1_EC_KEY(const EVP_PKEY *pkey);
 
 // EVP_PKEY_new_ed25519_public returns a newly allocated |EVP_PKEY| wrapping an
 // Ed25519 public key, or NULL on allocation error.
@@ -240,6 +253,9 @@
 // Ed25519, |type| should be NULL. The |EVP_MD_CTX| itself is unused but is
 // present so the API is uniform. See |EVP_DigestSign|.
 //
+// This function does not mutate |pkey| for thread-safety purposes and may be
+// used concurrently with other non-mutating functions on |pkey|.
+//
 // It returns one on success, or zero on error.
 OPENSSL_EXPORT int EVP_DigestSignInit(EVP_MD_CTX *ctx, EVP_PKEY_CTX **pctx,
                                       const EVP_MD *type, ENGINE *e,
@@ -293,6 +309,9 @@
 // Ed25519, |type| should be NULL. The |EVP_MD_CTX| itself is unused but is
 // present so the API is uniform. See |EVP_DigestVerify|.
 //
+// This function does not mutate |pkey| for thread-safety purposes and may be
+// used concurrently with other non-mutating functions on |pkey|.
+//
 // It returns one on success, or zero on error.
 OPENSSL_EXPORT int EVP_DigestVerifyInit(EVP_MD_CTX *ctx, EVP_PKEY_CTX **pctx,
                                         const EVP_MD *type, ENGINE *e,
@@ -353,7 +372,9 @@
 // It returns one on success and zero otherwise.
 //
 // It does not modify |ctx|, thus it's possible to continue to use |ctx| in
-// order to sign a longer message.
+// order to sign a longer message. It also does not mutate |pkey| for
+// thread-safety purposes and may be used concurrently with other non-mutating
+// functions on |pkey|.
 OPENSSL_EXPORT int EVP_SignFinal(const EVP_MD_CTX *ctx, uint8_t *sig,
                                  unsigned int *out_sig_len, EVP_PKEY *pkey);
 
@@ -386,7 +407,9 @@
 // It returns one on success and zero otherwise.
 //
 // It does not modify |ctx|, thus it's possible to continue to use |ctx| in
-// order to sign a longer message.
+// order to verify a longer message. It also does not mutate |pkey| for
+// thread-safety purposes and may be used concurrently with other non-mutating
+// functions on |pkey|.
 OPENSSL_EXPORT int EVP_VerifyFinal(EVP_MD_CTX *ctx, const uint8_t *sig,
                                    size_t sig_len, EVP_PKEY *pkey);
 
@@ -779,7 +802,7 @@
 // EC keys are serialized as an EC point per SEC 1.
 //
 // Use |RSA_marshal_public_key| or |EC_POINT_point2cbb| instead.
-OPENSSL_EXPORT int i2d_PublicKey(EVP_PKEY *key, uint8_t **outp);
+OPENSSL_EXPORT int i2d_PublicKey(const EVP_PKEY *key, uint8_t **outp);
 
 // d2i_PrivateKey parses an ASN.1, DER-encoded, private key from |len| bytes at
 // |*inp|. If |out| is not NULL then, on exit, a pointer to the result is in
@@ -804,10 +827,10 @@
                                             long len);
 
 // EVP_PKEY_get0_DH returns NULL.
-OPENSSL_EXPORT DH *EVP_PKEY_get0_DH(EVP_PKEY *pkey);
+OPENSSL_EXPORT DH *EVP_PKEY_get0_DH(const EVP_PKEY *pkey);
 
 // EVP_PKEY_get1_DH returns NULL.
-OPENSSL_EXPORT DH *EVP_PKEY_get1_DH(EVP_PKEY *pkey);
+OPENSSL_EXPORT DH *EVP_PKEY_get1_DH(const EVP_PKEY *pkey);
 
 
 // Preprocessor compatibility section (hidden).
diff --git a/include/openssl/rsa.h b/include/openssl/rsa.h
index 7ed5dce..98bb31c 100644
--- a/include/openssl/rsa.h
+++ b/include/openssl/rsa.h
@@ -72,8 +72,14 @@
 
 
 // Allocation and destruction.
+//
+// An |RSA| object represents a public or private RSA key. A given object may be
+// used concurrently on multiple threads by non-mutating functions, provided no
+// other thread is concurrently calling a mutating function. Unless otherwise
+// documented, functions which take a |const| pointer are non-mutating and
+// functions which take a non-|const| pointer are mutating.
 
-// RSA_new returns a new, empty RSA object or NULL on error.
+// RSA_new returns a new, empty |RSA| object or NULL on error.
 OPENSSL_EXPORT RSA *RSA_new(void);
 
 // RSA_new_method acts the same as |RSA_new| but takes an explicit |ENGINE|.
@@ -83,7 +89,8 @@
 // reference count drops to zero.
 OPENSSL_EXPORT void RSA_free(RSA *rsa);
 
-// RSA_up_ref increments the reference count of |rsa| and returns one.
+// RSA_up_ref increments the reference count of |rsa| and returns one. It does
+// not mutate |rsa| for thread-safety purposes and may be used concurrently.
 OPENSSL_EXPORT int RSA_up_ref(RSA *rsa);
 
 
@@ -164,6 +171,9 @@
 
 
 // Encryption / Decryption
+//
+// These functions are considered non-mutating for thread-safety purposes and
+// may be used concurrently.
 
 // Padding types for encryption.
 #define RSA_PKCS1_PADDING 1
@@ -231,6 +241,9 @@
 
 
 // Signing / Verification
+//
+// These functions are considered non-mutating for thread-safety purposes and
+// may be used concurrently.
 
 // RSA_sign signs |in_len| bytes of digest from |in| with |rsa| using
 // RSASSA-PKCS1-v1_5. It writes, at most, |RSA_size(rsa)| bytes to |out|. On
@@ -372,8 +385,9 @@
 // returns zero then a more detailed error is available on the error queue.
 OPENSSL_EXPORT int RSA_check_key(const RSA *rsa);
 
-// RSA_check_fips performs public key validity tests on |key|. It returns one
-// if they pass and zero otherwise. Opaque keys always fail.
+// RSA_check_fips performs public key validity tests on |key|. It returns one if
+// they pass and zero otherwise. Opaque keys always fail. This function does not
+// mutate |rsa| for thread-safety purposes and may be used concurrently.
 OPENSSL_EXPORT int RSA_check_fips(RSA *key);
 
 // RSA_verify_PKCS1_PSS_mgf1 verifies that |EM| is a correct PSS padding of
@@ -390,7 +404,8 @@
 //
 // This function implements only the low-level padding logic. Use
 // |RSA_verify_pss_mgf1| instead.
-OPENSSL_EXPORT int RSA_verify_PKCS1_PSS_mgf1(RSA *rsa, const uint8_t *mHash,
+OPENSSL_EXPORT int RSA_verify_PKCS1_PSS_mgf1(const RSA *rsa,
+                                             const uint8_t *mHash,
                                              const EVP_MD *Hash,
                                              const EVP_MD *mgf1Hash,
                                              const uint8_t *EM, int sLen);
@@ -407,7 +422,7 @@
 //
 // This function implements only the low-level padding logic. Use
 // |RSA_sign_pss_mgf1| instead.
-OPENSSL_EXPORT int RSA_padding_add_PKCS1_PSS_mgf1(RSA *rsa, uint8_t *EM,
+OPENSSL_EXPORT int RSA_padding_add_PKCS1_PSS_mgf1(const RSA *rsa, uint8_t *EM,
                                                   const uint8_t *mHash,
                                                   const EVP_MD *Hash,
                                                   const EVP_MD *mgf1Hash,
@@ -567,7 +582,7 @@
 //
 // This function implements only the low-level padding logic. Use
 // |RSA_sign_pss_mgf1| instead.
-OPENSSL_EXPORT int RSA_padding_add_PKCS1_PSS(RSA *rsa, uint8_t *EM,
+OPENSSL_EXPORT int RSA_padding_add_PKCS1_PSS(const RSA *rsa, uint8_t *EM,
                                              const uint8_t *mHash,
                                              const EVP_MD *Hash, int sLen);
 
@@ -576,7 +591,7 @@
 //
 // This function implements only the low-level padding logic. Use
 // |RSA_verify_pss_mgf1| instead.
-OPENSSL_EXPORT int RSA_verify_PKCS1_PSS(RSA *rsa, const uint8_t *mHash,
+OPENSSL_EXPORT int RSA_verify_PKCS1_PSS(const RSA *rsa, const uint8_t *mHash,
                                         const EVP_MD *Hash, const uint8_t *EM,
                                         int sLen);