5.  Data Structures and Computations

   This section specifies the data structures and computations used by
   ECC-based key mechanisms specified in the previous three sections.
   The presentation language used here is the same as that used in TLS.
   Since this specification extends TLS, these descriptions should be
   merged with those in the TLS specification and any others that extend
   TLS.  This means that enum types may not specify all possible values,
   and structures with multiple formats chosen with a select() clause
   may not indicate all possible cases.

5.1.  Client Hello Extensions

   This section specifies two TLS extensions that can be included with
   the ClientHello message as described in [RFC4366]: the Supported
   Elliptic Curves Extension and the Supported Point Formats Extension.

   When these extensions are sent:

   The extensions SHOULD be sent along with any ClientHello message that
   proposes ECC cipher suites.

   Meaning of these extensions:

   These extensions allow a client to enumerate the elliptic curves it
   supports and/or the point formats it can parse.

   Structure of these extensions:

   The general structure of TLS extensions is described in [RFC4366],
   and this specification adds two types to ExtensionType.

      enum {
          elliptic_curves(10),
          ec_point_formats(11)
      } ExtensionType;

   o  elliptic_curves (Supported Elliptic Curves Extension): Indicates
      the set of elliptic curves supported by the client.  For this
      extension, the opaque extension_data field contains
      NamedCurveList.  See Section 5.1.1 for details.

   o  ec_point_formats (Supported Point Formats Extension): Indicates
      the set of point formats that the client can parse.  For this
      extension, the opaque extension_data field contains
      ECPointFormatList.  See Section 5.1.2 for details.

   Actions of the sender:

   A client that proposes ECC cipher suites in its ClientHello message
   appends these extensions (along with any others), enumerating the
   curves it supports and the point formats it can parse.  Clients
   SHOULD send both the Supported Elliptic Curves Extension and the
   Supported Point Formats Extension.  If the Supported Point Formats
   Extension is indeed sent, it MUST contain the value 0 (uncompressed)
   as one of the items in the list of point formats.

   Actions of the receiver:

   A server that receives a ClientHello containing one or both of these
   extensions MUST use the client's enumerated capabilities to guide its
   selection of an appropriate cipher suite.  One of the proposed ECC
   cipher suites must be negotiated only if the server can successfully
   complete the handshake while using the curves and point formats
   supported by the client (cf. Sections 5.3 and 5.4).

   NOTE: A server participating in an ECDHE_ECDSA key exchange may use
   different curves for the ECDSA or EdDSA key in its certificate and
   for the ephemeral ECDH key in the ServerKeyExchange message.  The
   server MUST consider the extensions in both cases.

   If a server does not understand the Supported Elliptic Curves
   Extension, does not understand the Supported Point Formats Extension,
   or is unable to complete the ECC handshake while restricting itself
   to the enumerated curves and point formats, it MUST NOT negotiate the
   use of an ECC cipher suite.  Depending on what other cipher suites
   are proposed by the client and supported by the server, this may
   result in a fatal handshake failure alert due to the lack of common
   cipher suites.

5.1.1.  Supported Elliptic Curves Extension

   RFC 4492 defined 25 different curves in the NamedCurve registry (now
   renamed the "TLS Supported Groups" registry, although the enumeration
   below is still named NamedCurve) for use in TLS.  Only three have
   seen much use.  This specification is deprecating the rest (with
   numbers 1-22).  This specification also deprecates the explicit

   curves with identifiers 0xFF01 and 0xFF02.  It also adds the new
   curves defined in [RFC7748].  The end result is as follows:

           enum {
               deprecated(1..22),
               secp256r1 (23), secp384r1 (24), secp521r1 (25),
               x25519(29), x448(30),
               reserved (0xFE00..0xFEFF),
               deprecated(0xFF01..0xFF02),
               (0xFFFF)
           } NamedCurve;

   Note that other specifications have since added other values to this
   enumeration.  Some of those values are not curves at all, but finite
   field groups.  See [RFC7919].

   secp256r1, etc: Indicates support of the corresponding named curve or
   groups.  The named curves secp256r1, secp384r1, and secp521r1 are
   specified in SEC 2 [SECG-SEC2].  These curves are also recommended in
   ANSI X9.62 [ANSI.X9-62.2005] and FIPS 186-4 [FIPS.186-4].  The rest
   of this document refers to these three curves as the "NIST curves"
   because they were originally standardized by the National Institute
   of Standards and Technology.  The curves x25519 and x448 are defined
   in [RFC7748].  Values 0xFE00 through 0xFEFF are reserved for private
   use.

   The predecessor of this document also supported explicitly defined
   prime and char2 curves, but these are deprecated by this
   specification.

   The NamedCurve name space (now titled "TLS Supported Groups") is
   maintained by IANA.  See Section 9 for information on how new value
   assignments are added.

           struct {
               NamedCurve named_curve_list<2..2^16-1>
           } NamedCurveList;

   Items in named_curve_list are ordered according to the client's
   preferences (favorite choice first).

   As an example, a client that only supports secp256r1 (aka NIST P-256;
   value 23 = 0x0017) and secp384r1 (aka NIST P-384; value 24 = 0x0018)
   and prefers to use secp256r1 would include a TLS extension consisting
   of the following octets.  Note that the first two octets indicate the
   extension type (Supported Elliptic Curves Extension):

           00 0A 00 06 00 04 00 17 00 18

5.1.2.  Supported Point Formats Extension

           enum {
               uncompressed (0),
               deprecated (1..2),
               reserved (248..255)
           } ECPointFormat;
           struct {
               ECPointFormat ec_point_format_list<1..2^8-1>
           } ECPointFormatList;

   Three point formats were included in the definition of ECPointFormat
   above.  This specification deprecates all but the uncompressed point
   format.  Implementations of this document MUST support the
   uncompressed format for all of their supported curves and MUST NOT
   support other formats for curves defined in this specification.  For
   backwards compatibility purposes, the point format list extension MAY
   still be included and contain exactly one value: the uncompressed
   point format (0).  RFC 4492 specified that if this extension is
   missing, it means that only the uncompressed point format is
   supported, so interoperability with implementations that support the
   uncompressed format should work with or without the extension.

   If the client sends the extension and the extension does not contain
   the uncompressed point format, and the client has used the Supported
   Groups extension to indicate support for any of the curves defined in
   this specification, then the server MUST abort the handshake and
   return an illegal_parameter alert.

   The ECPointFormat name space (now titled "TLS EC Point Formats") is
   maintained by IANA.  See Section 9 for information on how new value
   assignments are added.

   A client compliant with this specification that supports no other
   curves MUST send the following octets; note that the first two octets
   indicate the extension type (Supported Point Formats Extension):

           00 0B 00 02 01 00

5.1.3.  The signature_algorithms Extension and EdDSA

   The signature_algorithms extension, defined in Section 7.4.1.4.1 of
   [RFC5246], advertises the combinations of signature algorithm and
   hash function that the client supports.  The pure (non-prehashed)
   forms of EdDSA do not hash the data before signing it.  For this
   reason, it does not make sense to combine them with a hash function
   in the extension.

   For bits-on-the-wire compatibility with TLS 1.3, we define a new
   dummy value in the "TLS HashAlgorithm" registry that we call
   "Intrinsic" (value 8), meaning that hashing is intrinsic to the
   signature algorithm.

   To represent ed25519 and ed448 in the signature_algorithms extension,
   the value shall be (8,7) and (8,8), respectively.

5.2.  Server Hello Extension

   This section specifies a TLS extension that can be included with the
   ServerHello message as described in [RFC4366], the Supported Point
   Formats Extension.

   When this extension is sent:

   The Supported Point Formats Extension is included in a ServerHello
   message in response to a ClientHello message containing the Supported
   Point Formats Extension when negotiating an ECC cipher suite.

   Meaning of this extension:

   This extension allows a server to enumerate the point formats it can
   parse (for the curve that will appear in its ServerKeyExchange
   message when using the ECDHE_ECDSA, ECDHE_RSA, or ECDH_anon key
   exchange algorithm.

   Structure of this extension:

   The server's Supported Point Formats Extension has the same structure
   as the client's Supported Point Formats Extension (see
   Section 5.1.2).  Items in ec_point_format_list here are ordered
   according to the server's preference (favorite choice first).  Note
   that the server MAY include items that were not found in the client's
   list.  However, without extensions, this specification allows exactly
   one point format, so there is not really any opportunity for
   mismatches.

   Actions of the sender:

   A server that selects an ECC cipher suite in response to a
   ClientHello message including a Supported Point Formats Extension
   appends this extension (along with others) to its ServerHello
   message, enumerating the point formats it can parse.  The Supported
   Point Formats Extension, when used, MUST contain the value 0
   (uncompressed) as one of the items in the list of point formats.

   Actions of the receiver:

   A client that receives a ServerHello message containing a Supported
   Point Formats Extension MUST respect the server's choice of point
   formats during the handshake (cf.  Sections 5.6 and 5.7).  If no
   Supported Point Formats Extension is received with the ServerHello,
   this is equivalent to an extension allowing only the uncompressed
   point format.

5.3.  Server Certificate

   When this message is sent:

   This message is sent in all non-anonymous, ECC-based key exchange
   algorithms.

   Meaning of this message:

   This message is used to authentically convey the server's static
   public key to the client.  The following table shows the server
   certificate type appropriate for each key exchange algorithm.  ECC
   public keys MUST be encoded in certificates as described in
   Section 5.9.

   NOTE: The server's Certificate message is capable of carrying a chain
   of certificates.  The restrictions mentioned in Table 2 apply only to
   the server's certificate (first in the chain).

   +-------------+-----------------------------------------------------+
   | Algorithm   | Server Certificate Type                             |
   +-------------+-----------------------------------------------------+
   | ECDHE_ECDSA | Certificate MUST contain an ECDSA- or EdDSA-capable |
   |             | public key.                                         |
   | ECDHE_RSA   | Certificate MUST contain an RSA public key.         |
   +-------------+-----------------------------------------------------+

                     Table 2: Server Certificate Types

   Structure of this message:

   Identical to the TLS Certificate format.

   Actions of the sender:

   The server constructs an appropriate certificate chain and conveys it
   to the client in the Certificate message.  If the client has used a
   Supported Elliptic Curves Extension, the public key in the server's

   certificate MUST respect the client's choice of elliptic curves.  A
   server that cannot satisfy this requirement MUST NOT choose an ECC
   cipher suite in its ServerHello message.)

   Actions of the receiver:

   The client validates the certificate chain, extracts the server's
   public key, and checks that the key type is appropriate for the
   negotiated key exchange algorithm.  (A possible reason for a fatal
   handshake failure is that the client's capabilities for handling
   elliptic curves and point formats are exceeded; cf. Section 5.1.)

5.4.  Server Key Exchange

   When this message is sent:

   This message is sent when using the ECDHE_ECDSA, ECDHE_RSA, and
   ECDH_anon key exchange algorithms.

   Meaning of this message:

   This message is used to convey the server's ephemeral ECDH public key
   (and the corresponding elliptic curve domain parameters) to the
   client.

   The ECCurveType enum used to have values for explicit prime and for
   explicit char2 curves.  Those values are now deprecated, so only one
   value remains:

   Structure of this message:

           enum {
               deprecated (1..2),
               named_curve (3),
               reserved(248..255)
           } ECCurveType;

   The value named_curve indicates that a named curve is used.  This
   option is now the only remaining format.

   Values 248 through 255 are reserved for private use.

   The ECCurveType name space (now titled "TLS EC Curve Types") is
   maintained by IANA.  See Section 9 for information on how new value
   assignments are added.

   RFC 4492 had a specification for an ECCurve structure and an
   ECBasisType structure.  Both of these are omitted now because they
   were only used with the now deprecated explicit curves.

           struct {
               opaque point <1..2^8-1>;
           } ECPoint;

   point: This is the byte string representation of an elliptic curve
   point following the conversion routine in Section 4.3.6 of
   [ANSI.X9-62.2005].  This byte string may represent an elliptic curve
   point in uncompressed, compressed, or hybrid format, but this
   specification deprecates all but the uncompressed format.  For the
   NIST curves, the format is repeated in Section 5.4.1 for convenience.
   For the X25519 and X448 curves, the only valid representation is the
   one specified in [RFC7748], a 32- or 56-octet representation of the u
   value of the point.  This structure MUST NOT be used with Ed25519 and
   Ed448 public keys.

           struct {
               ECCurveType    curve_type;
               select (curve_type) {
                   case named_curve:
                       NamedCurve namedcurve;
               };
           } ECParameters;

   curve_type: This identifies the type of the elliptic curve domain
   parameters.

   namedCurve: Specifies a recommended set of elliptic curve domain
   parameters.  All those values of NamedCurve are allowed that refer to
   a curve capable of Diffie-Hellman.  With the deprecation of the
   explicit curves, this now includes all of the NamedCurve values.

           struct {
               ECParameters    curve_params;
               ECPoint         public;
           } ServerECDHParams;

   curve_params: Specifies the elliptic curve domain parameters
   associated with the ECDH public key.

   public: The ephemeral ECDH public key.

   The ServerKeyExchange message is extended as follows.

           enum {
               ec_diffie_hellman
           } KeyExchangeAlgorithm;

   o  ec_diffie_hellman: Indicates the ServerKeyExchange message
      contains an ECDH public key.

      select (KeyExchangeAlgorithm) {
          case ec_diffie_hellman:
              ServerECDHParams    params;
              Signature           signed_params;
      } ServerKeyExchange;

   o  params: Specifies the ECDH public key and associated domain
      parameters.

   o  signed_params: A hash of the params, with the signature
      appropriate to that hash applied.  The private key corresponding
      to the certified public key in the server's Certificate message is
      used for signing.

        enum {
            ecdsa(3),
            ed25519(7)
            ed448(8)
        } SignatureAlgorithm;
        select (SignatureAlgorithm) {
           case ecdsa:
                digitally-signed struct {
                    opaque sha_hash[sha_size];
                };
           case ed25519,ed448:
                digitally-signed struct {
                    opaque rawdata[rawdata_size];
                };
        } Signature;
      ServerKeyExchange.signed_params.sha_hash
          SHA(ClientHello.random + ServerHello.random +
                                 ServerKeyExchange.params);
      ServerKeyExchange.signed_params.rawdata
          ClientHello.random + ServerHello.random +
                                 ServerKeyExchange.params;

   NOTE: SignatureAlgorithm is "rsa" for the ECDHE_RSA key exchange
   algorithm and "anonymous" for ECDH_anon.  These cases are defined in
   TLS.  SignatureAlgorithm is "ecdsa" or "eddsa" for ECDHE_ECDSA.

   ECDSA signatures are generated and verified as described in
   Section 5.10.  SHA, in the above template for sha_hash, may denote a
   hash algorithm other than SHA-1.  As per ANSI X9.62, an ECDSA
   signature consists of a pair of integers, r and s.  The digitally-
   signed element is encoded as an opaque vector <0..2^16-1>, the
   contents of which are the DER encoding corresponding to the following
   ASN.1 notation.

              Ecdsa-Sig-Value ::= SEQUENCE {
                  r       INTEGER,
                  s       INTEGER
              }

   EdDSA signatures in both the protocol and in certificates that
   conform to [RFC8410] are generated and verified according to
   [RFC8032].  The digitally-signed element is encoded as an opaque
   vector <0..2^16-1>, the contents of which include the octet string
   output of the EdDSA signing algorithm.

   Actions of the sender:

   The server selects elliptic curve domain parameters and an ephemeral
   ECDH public key corresponding to these parameters according to the
   ECKAS-DH1 scheme from IEEE 1363 [IEEE.P1363].  It conveys this
   information to the client in the ServerKeyExchange message using the
   format defined above.

   Actions of the receiver:

   The client verifies the signature (when present) and retrieves the
   server's elliptic curve domain parameters and ephemeral ECDH public
   key from the ServerKeyExchange message.  (A possible reason for a
   fatal handshake failure is that the client's capabilities for
   handling elliptic curves and point formats are exceeded; cf.
   Section 5.1.)

5.4.1.  Uncompressed Point Format for NIST Curves

   The following represents the wire format for representing ECPoint in
   ServerKeyExchange records.  The first octet of the representation
   indicates the form, which may be compressed, uncompressed, or hybrid.
   This specification supports only the uncompressed format for these
   curves.  This is followed by the binary representation of the X value
   in "big-endian" or "network" format, followed by the binary
   representation of the Y value in "big-endian" or "network" format.
   There are no internal length markers, so each number representation
   occupies as many octets as implied by the curve parameters.  For

   P-256 this means that each of X and Y use 32 octets, padded on the
   left by zeros if necessary.  For P-384, they take 48 octets each, and
   for P-521, they take 66 octets each.

   Here's a more formal representation:

             enum {
                 uncompressed(4),
                 (255)
               } PointConversionForm;

             struct {
                 PointConversionForm  form;
                 opaque               X[coordinate_length];
                 opaque               Y[coordinate_length];
             } UncompressedPointRepresentation;

5.5.  Certificate Request

   When this message is sent:

   This message is sent when requesting client authentication.

   Meaning of this message:

   The server uses this message to suggest acceptable client
   authentication methods.

   Structure of this message:

   The TLS CertificateRequest message is extended as follows.

           enum {
               ecdsa_sign(64),
               deprecated1(65),  /* was rsa_fixed_ecdh */
               deprecated2(66),  /* was ecdsa_fixed_ecdh */
               (255)
           } ClientCertificateType;

   o  ecdsa_sign: Indicates that the server would like to use the
      corresponding client authentication method specified in Section 3.

   Note that RFC 4492 also defined RSA and ECDSA certificates that
   included a fixed ECDH public key.  These mechanisms saw very little
   implementation, so this specification is deprecating them.

   Actions of the sender:

   The server decides which client authentication methods it would like
   to use and conveys this information to the client using the format
   defined above.

   Actions of the receiver:

   The client determines whether it has a suitable certificate for use
   with any of the requested methods and whether to proceed with client
   authentication.

5.6.  Client Certificate

   When this message is sent:

   This message is sent in response to a CertificateRequest when a
   client has a suitable certificate and has decided to proceed with
   client authentication.  (Note that if the server has used a Supported
   Point Formats Extension, a certificate can only be considered
   suitable for use with the ECDSA_sign authentication method if the
   public key point specified in it is uncompressed, as that is the only
   point format still supported.

   Meaning of this message:

   This message is used to authentically convey the client's static
   public key to the server.  ECC public keys must be encoded in
   certificates as described in Section 5.9.  The certificate MUST
   contain an ECDSA- or EdDSA-capable public key.

   NOTE: The client's Certificate message is capable of carrying a chain
   of certificates.  The restrictions mentioned above apply only to the
   client's certificate (first in the chain).

   Structure of this message:

   Identical to the TLS client Certificate format.

   Actions of the sender:

   The client constructs an appropriate certificate chain and conveys it
   to the server in the Certificate message.

   Actions of the receiver:

   The TLS server validates the certificate chain, extracts the client's
   public key, and checks that the key type is appropriate for the
   client authentication method.

5.7.  Client Key Exchange

   When this message is sent:

   This message is sent in all key exchange algorithms.  It contains the
   client's ephemeral ECDH public key.

   Meaning of the message:

   This message is used to convey ephemeral data relating to the key
   exchange belonging to the client (such as its ephemeral ECDH public
   key).

   Structure of this message:

   The TLS ClientKeyExchange message is extended as follows.

           enum {
               implicit,
               explicit
           } PublicValueEncoding;

   o  implicit, explicit: For ECC cipher suites, this indicates whether
      the client's ECDH public key is in the client's certificate
      ("implicit") or is provided, as an ephemeral ECDH public key, in
      the ClientKeyExchange message ("explicit").  The implicit encoding
      is deprecated and is retained here for backward compatibility
      only.

           struct {
               ECPoint ecdh_Yc;
           } ClientECDiffieHellmanPublic;

   ecdh_Yc: Contains the client's ephemeral ECDH public key as a byte
   string ECPoint.point, which may represent an elliptic curve point in
   uncompressed format.

           struct {
               select (KeyExchangeAlgorithm) {
                   case ec_diffie_hellman: ClientECDiffieHellmanPublic;
               } exchange_keys;
           } ClientKeyExchange;

   Actions of the sender:

   The client selects an ephemeral ECDH public key corresponding to the
   parameters it received from the server.  The format is the same as in
   Section 5.4.

   Actions of the receiver:

   The server retrieves the client's ephemeral ECDH public key from the
   ClientKeyExchange message and checks that it is on the same elliptic
   curve as the server's ECDH key.

5.8.  Certificate Verify

   When this message is sent:

   This message is sent when the client sends a client certificate
   containing a public key usable for digital signatures.

   Meaning of the message:

   This message contains a signature that proves possession of the
   private key corresponding to the public key in the client's
   Certificate message.

   Structure of this message:

   The TLS CertificateVerify message and the underlying signature type
   are defined in the TLS base specifications, and the latter is
   extended here in Section 5.4.  For the "ecdsa" and "eddsa" cases, the
   signature field in the CertificateVerify message contains an ECDSA or
   EdDSA (respectively) signature computed over handshake messages
   exchanged so far, exactly similar to CertificateVerify with other
   signing algorithms:

           CertificateVerify.signature.sha_hash
               SHA(handshake_messages);
           CertificateVerify.signature.rawdata
               handshake_messages;

   ECDSA signatures are computed as described in Section 5.10, and SHA
   in the above template for sha_hash accordingly may denote a hash
   algorithm other than SHA-1.  As per ANSI X9.62, an ECDSA signature
   consists of a pair of integers, r and s.  The digitally-signed
   element is encoded as an opaque vector <0..2^16-1>, the contents of
   which are the DER encoding [X.690] corresponding to the following
   ASN.1 notation [X.680].

           Ecdsa-Sig-Value ::= SEQUENCE {
               r       INTEGER,
               s       INTEGER
           }

   EdDSA signatures are generated and verified according to [RFC8032].
   The digitally-signed element is encoded as an opaque vector
   <0..2^16-1>, the contents of which include the octet string output of
   the EdDSA signing algorithm.

   Actions of the sender:

   The client computes its signature over all handshake messages sent or
   received starting at client hello and up to but not including this
   message.  It uses the private key corresponding to its certified
   public key to compute the signature, which is conveyed in the format
   defined above.

   Actions of the receiver:

   The server extracts the client's signature from the CertificateVerify
   message and verifies the signature using the public key it received
   in the client's Certificate message.

5.9.  Elliptic Curve Certificates

   X.509 certificates containing ECC public keys or signed using ECDSA
   MUST comply with [RFC3279] or another RFC that replaces or extends
   it.  X.509 certificates containing ECC public keys or signed using
   EdDSA MUST comply with [RFC8410].  Clients SHOULD use the elliptic
   curve domain parameters recommended in ANSI X9.62, FIPS 186-4, and
   SEC 2 [SECG-SEC2], or in [RFC8032].

   EdDSA keys using the Ed25519 algorithm MUST use the ed25519 signature
   algorithm, and Ed448 keys MUST use the ed448 signature algorithm.
   This document does not define use of Ed25519ph and Ed448ph keys with
   TLS.  Ed25519, Ed25519ph, Ed448, and Ed448ph keys MUST NOT be used
   with ECDSA.

5.10.  ECDH, ECDSA, and RSA Computations

   All ECDH calculations for the NIST curves (including parameter and
   key generation as well as the shared secret calculation) are
   performed according to [IEEE.P1363] using the ECKAS-DH1 scheme with
   the identity map as the Key Derivation Function (KDF) so that the
   premaster secret is the x-coordinate of the ECDH shared secret
   elliptic curve point represented as an octet string.  Note that this
   octet string (Z in IEEE 1363 terminology), as output by FE2OSP (Field

   Element to Octet String Conversion Primitive), has constant length
   for any given field; leading zeros found in this octet string MUST
   NOT be truncated.

   (Note that this use of the identity KDF is a technicality.  The
   complete picture is that ECDH is employed with a non-trivial KDF
   because TLS does not directly use the premaster secret for anything
   other than for computing the master secret.  In TLS 1.0 and 1.1, this
   means that the MD5- and SHA-1-based TLS Pseudorandom Function (PRF)
   serves as a KDF; in TLS 1.2, the KDF is determined by ciphersuite,
   and it is conceivable that future TLS versions or new TLS extensions
   introduced in the future may vary this computation.)

   An ECDHE key exchange using X25519 (curve x25519) goes as follows:
   (1) each party picks a secret key d uniformly at random and computes
   the corresponding public key x = X25519(d, G); (2) parties exchange
   their public keys and compute a shared secret as x_S = X25519(d,
   x_peer); and (3), if either party obtains all-zeroes x_S, it MUST
   abort the handshake (as required by definition of X25519 and X448).
   ECDHE for X448 works similarly, replacing X25519 with X448 and x25519
   with x448.  The derived shared secret is used directly as the
   premaster secret, which is always exactly 32 bytes when ECDHE with
   X25519 is used and 56 bytes when ECDHE with X448 is used.

   All ECDSA computations MUST be performed according to ANSI X9.62 or
   its successors.  Data to be signed/verified is hashed, and the result
   runs directly through the ECDSA algorithm with no additional hashing.
   A secure hash function such as SHA-256, SHA-384, or SHA-512 from
   [FIPS.180-4] MUST be used.

   All EdDSA computations MUST be performed according to [RFC8032] or
   its successors.  Data to be signed/verified is run through the EdDSA
   algorithm with no hashing (EdDSA will internally run the data through
   the "prehash" function PH).  The context parameter for Ed448 MUST be
   set to the empty string.

   RFC 4492 anticipated the standardization of a mechanism for
   specifying the required hash function in the certificate, perhaps in
   the parameters field of the subjectPublicKeyInfo.  Such
   standardization never took place, and as a result, SHA-1 is used in
   TLS 1.1 and earlier (except for EdDSA, which uses identity function).
   TLS 1.2 added a SignatureAndHashAlgorithm parameter to the
   DigitallySigned struct, thus allowing agility in choosing the
   signature hash.  EdDSA signatures MUST have HashAlgorithm of 8
   (Intrinsic).

   All RSA signatures must be generated and verified according to
   Section 7.2 of [RFC8017].

5.11.  Public Key Validation

   With the NIST curves, each party MUST validate the public key sent by
   its peer in the ClientKeyExchange and ServerKeyExchange messages.  A
   receiving party MUST check that the x and y parameters from the
   peer's public value satisfy the curve equation, y^2 = x^3 + ax + b
   mod p.  See Section 2.3 of [Menezes] for details.  Failing to do so
   allows attackers to gain information about the private key to the
   point that they may recover the entire private key in a few requests
   if that key is not really ephemeral.

   With X25519 and X448, a receiving party MUST check whether the
   computed premaster secret is the all-zero value and abort the
   handshake if so, as described in Section 6 of [RFC7748].

   Ed25519 and Ed448 internally do public key validation as part of
   signature verification.