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Traces of EDHOCEricssonSE-164 40 StockholmSwedengoran.selander@ericsson.comEricssonSE-164 40 StockholmSwedenjohn.mattsson@ericsson.comASSA ABLOY32-080 ZabierzówPolandmarek.serafin@assaabloy.comRISESE-164 40 StockholmSwedenmarco.tiloca@ri.seThis document contains some example traces of Ephemeral Diffie-Hellman Over COSE (EDHOC).EDHOC is a lightweight authenticated key exchange protocol designed for highly constrained settings. This document contains annotated traces of EDHOC protocol runs, with input, output and intermediate processing results to simplify testing of implementations.The document contains two traces:Section 3. Authentication with signature keys identified by the hash value of the X.509 certificates (provided in ). The endpoints use EdDSA for authentication and X25519 for ephemeral-ephemeral Diffie-Hellman key exchange.Section 4. Authentication with static Diffie-Hellman keys identified by short key identifiers labelling CWT Claim Sets (CCSs) . The endpoints use NIST P-256 (FIPS PUB 186-4) for both ephemeral-ephemeral and static-ephemeral Diffie-Hellman key exchange. This trace also illustrates the cipher suite negotiation, and provides an example of low protocol overhead, with messages sizes of (39, 45, 19) bytes.The traces in this draft are valid for version -14 and -15 of .Editor’s note: update reference to test vectors below:The test vector for trace 2 can be found at: https://github.com/lake-wg/edhoc/tree/master/test-vectors-15/EDHOC is run between an Initiator (I) and a Responder (R). The private/public key pairs and credentials of I and R required to produce the protocol messages are shown in the traces when needed for the calculations.EDHOC messages and intermediate results are encoded in CBOR and can therefore be displayed in CBOR diagnostic notation using, e.g., the CBOR playground , which makes them easy to parse for humans.NOTE 1. The same name is used for hexadecimal byte strings and their CBOR encodings. The traces contain both the raw byte strings and the corresponding CBOR encoded data items.NOTE 2. If not clear from the context, remember that CBOR sequences and CBOR arrays assume CBOR encoded data items as elements.NOTE 3. When the protocol transporting EDHOC messages does not inherently provide correlation across all messages, like CoAP, then some messages typically are prepended with connection identifiers and potentially a message_1 indicator (see Section 3.4.1 and Appendix A.3 of ). Those bytes are not included in the traces in this document.In this example the Initiator (I) and Responder (R) are authenticated with digital signatures (METHOD = 0). Both I and R support cipher suite 0, which determines the algorithms:EDHOC AEAD algorithm = AES-CCM-16-64-128EDHOC hash algorithm = SHA-256EDHOC MAC length in bytes (Static DH) = 8EDHOC key exchange algorithm (ECDH curve) = X25519EDHOC signature algorithm = EdDSAApplication AEAD algorithm = AES-CCM-16-64-128Application hash algorithm = SHA-256The public keys are represented with X.509 certificates identified by the COSE header parameter ‘x5t’.Both endpoints are authenticated with signatures, i.e. METHOD = 0:I selects cipher suite 0. A single cipher suite is encoded as an int:I creates an ephemeral key pair for use with the EDHOC key exchange algorithm:I selects its connection identifier C_I to be the byte string 0x2d, which since it is represented by the 1-byte CBOR int -14 is encoded as 0x2d:No external authorization data:I constructs message_1:R supports the most preferred and selected cipher suite 0, so SUITES_I is acceptable.R creates an ephemeral key pair for use with the EDHOC key exchange algorithm:R selects its connection identifier C_R to be the byte string 0x18, which since it is not represented as a 1-byte CBOR int is encoded as h’18’ = 0x4118:The transcript hash TH_2 is calculated using the EDHOC hash algorithm:TH_2 = H( G_Y, C_R, H(message_1) )The input to calculate TH_2 is the CBOR sequence:G_Y, C_R, H(message_1)PRK_2e is specified in Section 4.1.1.1 of .First, the ECDH shared secret G_XY is computed from G_X and Y, or G_Y and X:Then, PRK_2e is calculated using Extract() determined by the EDHOC hash algorithm:where salt is the zero-length byte string:Since METHOD = 0, R authenticates using signatures. Since the selected cipher suite is 0, the EDHOC signature algorithm is EdDSA.R’s signature key pair using EdDSA:PRK_3e2m is specified in Section 4.1.1.2 of .Since R authenticates with signatures PRK_3e2m = PRK_2e.R constructs the remaining input needed to calculate MAC_2:MAC_2 = EDHOC-KDF( PRK_3e2m, 2, context_2, mac_length_2 )context_2 = « ID_CRED_R, TH_2, CRED_R, ? EAD_2 »CRED_R is identified by a 64-bit hash:where the COSE header value 34 (‘x5t’) indicates a hash of an X.509 certficate,
and the COSE algorithm -15 indicates the hash algorithm SHA-256 truncated to 64 bits.ID_CRED_R (CBOR Data Item) (14 bytes)
a1 18 22 82 2e 48 79 f2 a4 1b 51 0c 1f 9bCRED_R is a CBOR byte string of the DER encoding of the X.509 certificate in :No external authorization data:context_2 = « ID_CRED_R, TH_2, CRED_R, ? EAD_2 »MAC_2 is computed through Expand() using the EDHOC hash algorithm, see Section 4.1.2 of :MAC_2 = HKDF-Expand(PRK_3e2m, info, mac_length_2), whereinfo = ( 2, context_2, mac_length_2 )Since METHOD = 0, mac_length_2 is given by the EDHOC hash algorithm.info for MAC_2 is:where the last value is the output size of the EDHOC hash algorithm.Since METHOD = 0, Signature_or_MAC_2 is the ‘signature’ of the COSE_Sign1 object.R constructs the message to be signed:R signs using the private authentication key SK_RR constructs the plaintext without padding:The input needed to calculate KEYSTREAM_2 is defined in Section 4.1.2 of
, using Expand() with the EDHOC hash algorithm:where plaintext_length is the length of PLAINTEXT_2, and info for KEYSTREAM_2 is:where the last value is the length of PLAINTEXT_2.R calculates CIPHERTEXT_2 as XOR between PLAINTEXT_2 and KEYSTREAM_2:R constructs message_2:where G_Y_CIPHERTEXT_2 is the bstr encoding of the concatenation of
the raw values of G_Y and CIPHERTEXT_2.Since METHOD = 0, I authenticates using signatures. Since the selected cipher suite is 0, the EDHOC signature algorithm is EdDSA.I’s signature key pair using EdDSA:PRK_4e3m is specified in Section 4.1.1.3 of .Since I authenticates with signatures PRK_4e3m = PRK_3e2m.The transcript hash TH_3 is calculated using the EDHOC hash algorithm:TH_3 = H(TH_2, PLAINTEXT_2)I constructs the remaining input needed to calculate MAC_3:whereCRED_I is identified by a 64-bit hash:where the COSE header value 34 (‘x5t’) indicates a hash of an X.509 certficate,
and the COSE algorithm -15 indicates the hash algorithm SHA-256 truncated to 64 bits.CRED_I is a CBOR byte string of the DER encoding of the X.509 certificate in :No external authorization data:context_3 = « ID_CRED_I, TH_3, CRED_I, ? EAD_3 »MAC_3 is computed through Expand() using the
EDHOC hash algorithm, see Section 4.1.2 of :info = ( 6, context_3, mac_length_3 )where context_3 = « ID_CRED_I, TH_3, CRED_I, ? EAD_3 »Since METHOD = 0, mac_length_3 is given by the EDHOC hash algorithm.info for MAC_3 is:where the last value is the output size of the EDHOC hash algorithm.Since METHOD = 0, Signature_or_MAC_3 is the ‘signature’ of the
COSE_Sign1 object.I constructs the message to be signed:I signs using the private authentication key SK_I:I constructs the plaintext without padding:I constructs the associated data for message_3:I constructs the input needed to derive the key K_3, see Section 4.1.2 of , using the EDHOC hash algorithm:where key_length is the key length of EDHOC AEAD algorithm, and info for K_3 is:where the last value is the key length of EDHOC AEAD algorithm.I constructs the input needed to derive the nonce IV_3, see Section 4.1.2 of , using the EDHOC hash algorithm:where iv_length is the nonce length of EDHOC AEAD algorithm, and info for IV_3 is:where the last value is the nonce length of EDHOC AEAD algorithm.I calculates CIPHERTEXT_3 as ‘ciphertext’ of COSE_Encrypt0 applied
using the EDHOC AEAD algorithm with plaintext PLAINTEXT_3, additional data
A_3, key K_3 and nonce IV_3.message_3 is the CBOR bstr encoding of CIPHERTEXT_3:The transcript hash TH_4 is calculated using the EDHOC hash algorithm:TH_4 = H(TH_3, PLAINTEXT_3)No external authorization data:R constructs the plaintext PLAINTEXT_4:R constructs the associated data for message_4:R constructs the input needed to derive the EDHOC message_4 key, see
Section 4.1.2 of , using the EDHOC hash algorithm:where key_length is the key length of the EDHOC AEAD algorithm,
and info for EDHOC_K_4 is:where the last value is the key length of EDHOC AEAD algorithm.R constructs the input needed to derive the EDHOC message_4 nonce, see Section 4.1.2 of , using the EDHOC hash algorithm:where length is the nonce length of EDHOC AEAD algorithm,
and info for EDHOC_IV_4 is:where the last value is the nonce length of EDHOC AEAD algorithm.R calculates CIPHERTEXT_4 as ‘ciphertext’ of COSE_Encrypt0 applied
using the EDHOC AEAD algorithm with plaintext PLAINTEXT_4, additional data
A_4, key K_4 and nonce IV_4.message_4 is the CBOR bstr encoding of CIPHERTEXT_4:PRK_out is specified in Section 4.1.2 of .where hash_length is the length of the output of the EDHOC hash algorithm, and info for PRK_out is:where the last value is the length of EDHOC hash algorithm.The OSCORE Master Secret and OSCORE Master Salt are derived with the EDHOC-Exporter as specified in 4.2.1 of .where PRK_exporter is derived from PRK_out:where hash_length is the length of the output of the EDHOC hash algorithm, and info for the PRK_exporter is:where the last value is the length of EDHOC hash algorithm.The derivation of OSCORE parameters is specified in Appendix A.1 of .The AEAD and Hash algorithms to use in OSCORE are given by the selected cipher suite:The mapping from EDHOC connection identifiers to OSCORE Sender/Recipient IDs is defined in Section 3.3.3 of .C_R is mapped to the Recipient ID of the server, i.e., the Sender ID of the client. The byte string 0x18, which as C_R is encoded as the CBOR byte string 0x4118, is converted to the server Recipient ID 0x18.C_I is mapped to the Recipient ID of the client, i.e., the Sender ID of the server. The byte string 0x2d, which as C_I is encoded as the CBOR integer 0x2d is converted to the client Recipient ID 0x2d.The OSCORE Master Secret is computed through Expand() using the
Application hash algorithm, see Appendix A.1 of :where oscore_key_length is by default the key length of the Application AEAD
algorithm, and info for the OSCORE Master Secret is:where the last value is the key length of Application AEAD algorithm.The OSCORE Master Salt is computed through Expand() using the Application hash algorithm, see Section 4.2 of :where oscore_salt_length is the length of the OSCORE Master Salt, and info for the OSCORE Master Salt is:where the last value is the length of the OSCORE Master Salt.Key update is defined in Section 4.2.2 of .where hash_length is the length of the output of the EDHOC hash function, context for KeyUpdate isand where info for key update is:After key update the PRK_exporter needs to be derived anew:where info and hash_length as unchanged as in .The OSCORE Master Secret is derived with the updated PRK_exporter:where info and key_length are unchanged as in .The OSCORE Master Salt is derived with the updated PRK_exporter:where info and salt_length are unchanged as in .In this example I and R are authenticated with ephemeral-static Diffie-Hellman (METHOD = 3). I supports cipher suites 6 and 2 (in order of preference) and R only supports cipher suite 2. After an initial negotiation message exchange cipher suite 2 is used, which determines the algorithms:EDHOC AEAD algorithm = AES-CCM-16-64-128EDHOC hash algorithm = SHA-256EDHOC MAC length in bytes (Static DH) = 8EDHOC key exchange algorithm (ECDH curve) = P-256EDHOC signature algorithm = ES256Application AEAD algorithm = AES-CCM-16-64-128Application hash algorithm = SHA-256The public keys are represented as raw public keys (RPK), encoded in a CWT Claims Set (CCS) and identified by the COSE header parameter ‘kid’.Both endpoints are authenticated with static DH, i.e. METHOD = 3:I selects its preferred cipher suite 6. A single cipher suite is encoded as an int:I creates an ephemeral key pair for use with the EDHOC key exchange algorithm:I selects its connection identifier C_I to be the byte string 0x0e, which since it is represented by the 1-byte CBOR int 14 is encoded as 0x0e:No external authorization data:EAD_1 (CBOR Sequence) (0 bytes)I constructs message_1:R does not support cipher suite 6 and sends an error with ERR_CODE 2 containing SUITES_R as ERR_INFO. R proposes cipher suite 2, a single cipher suite thus encoded as an int.Same steps are performed as message_1 first time, , but with updated SUITES_I.Both endpoints are authenticated with static DH, i.e. METHOD = 3:I selects cipher suite 2 and indicates the more preferred cipher suite(s), in this case 6, all encoded as the array [6, 2]:I creates an ephemeral key pair for use with the EDHOC key exchange algorithm:I selects its connection identifier C_I to be the byte string 0x37, which since it is represented by the 1-byte CBOR int -24 is encoded as 0x37:No external authorization data:I constructs message_1:R supports the selected cipher suite 2 and not the by I more preferred cipher suite(s) 6, so SUITES_I is acceptable.R creates an ephemeral key pair for use with the EDHOC key exchange algorithm:R selects its connection identifier C_R to be the byte string 0x27, which since it is represented by the 1-byte CBOR int -8 is encoded as 0x27:The transcript hash TH_2 is calculated using the EDHOC hash algorithm:TH_2 = H( G_Y, C_R, H(message_1) )The input to calculate TH_2 is the CBOR sequence:G_Y, C_R, H(message_1)PRK_2e is specified in Section 4.1.1.1 of .First, the ECDH shared secret G_XY is computed from G_X and Y, or G_Y and X:Then, PRK_2e is calculated using Extract() determined by the EDHOC hash algorithm:where salt is the zero-length byte string:Since METHOD = 3, R authenticates using static DH. The EDHOC key exchange algorithm is based on the same curve as for the ephemeral keys, which is P-256, since the selected cipher suite is 2.R’s static Diffie-Hellman key pair for use with P-256:Since R authenticates with static DH (METHOD = 3), PRK_3e2m is derived
from SALT_3e2m and G_RX.The input needed to calculate SALT_3e2m is defined in Section 4.1.2 of , using Expand() with the EDHOC hash algorithm:.where hash_length is the length of the output of the EDHOC hash algorithm, and info for SALT_3e2m is:PRK_3e2m is specified in Section 4.1.1.2 of .PRK_3e2m is derived from G_RX using Extract() with the EDHOC hash algorithm:where G_RX is the ECDH shared secret calculated from G_X and R, or G_R and X.R constructs the remaining input needed to calculate MAC_2:MAC_2 = EDHOC-KDF( PRK_3e2m, 2, context_2, mac_length_2 )context_2 = « ID_CRED_R, TH_2, CRED_R, ? EAD_2 »CRED_R is identified by a ‘kid’ with byte string value 0x32:CRED_R is an RPK encoded as a CCS:No external authorization data:context_2 = « ID_CRED_R, TH_2, CRED_R, ? EAD_2 »MAC_2 is computed through Expand() using the EDHOC hash algorithm, see Section 4.1.2 of :MAC_2 = HKDF-Expand(PRK_3e2m, info, mac_length_2), whereinfo = ( 2, context_2, mac_length_2 )Since METHOD = 3, mac_length_2 is given by the EDHOC MAC length.info for MAC_2 is:where the last value is the EDHOC MAC length.Since METHOD = 3, Signature_or_MAC_2 is MAC_2:R constructs PLAINTEXT_2 without padding:Since ID_CRED_R contains a single ‘kid’ parameter, only the byte string value is included in the plaintext, represented as described in Section 3.3.2 of . The CBOR map { 4 : h’32’ } is thus replaced, not by the CBOR byte string 0x4132, but by the CBOR int 0x32, since that is a one byte encoding of a CBOR integer (-19).The input needed to calculate KEYSTREAM_2 is defined in Section 4.1.2 of
, using Expand() with the EDHOC hash algorithm:where plaintext_length is the length of PLAINTEXT_2, and info for KEYSTREAM_2 is:where last value is the length of PLAINTEXT_2.R calculates CIPHERTEXT_2 as XOR between PLAINTEXT_2 and KEYSTREAM_2:R constructs message_2:where G_Y_CIPHERTEXT_2 is the bstr encoding of the concatenation of
the raw values of G_Y and CIPHERTEXT_2.The transcript hash TH_3 is calculated using the EDHOC hash algorithm:TH_3 = H( TH_2, PLAINTEXT_2 )Since METHOD = 3, I authenticates using static DH. The EDHOC key exchange algorithm is based on the same curve as for the ephemeral keys, which is P-256, since the selected cipher suite is 2.I’s static Diffie-Hellman key pair for use with P-256:Since I authenticates with static DH (METHOD = 3), PRK_4e3m is derived
from SALT_4e3m and G_IY.The input needed to calculate SALT_4e3m is defined in Section 4.1.2 of , using Expand() with the EDHOC hash algorithm:.where hash_length is the length of the output of the EDHOC hash algorithm, and info for SALT_4e3m is:PRK_4e3m is specified in Section 4.1.1.3 of .PRK_4x3m is derived as specified in Section 4.1.3 of .
Since I authenticates with static DH (METHOD = 3), PRK_4x3m is derived
from G_IY using Extract() with the EDHOC hash algorithm:where G_IY is the ECDH shared secret calculated from G_I and Y, or G_Y and I.I constructs the remaining input needed to calculate MAC_3:MAC_3 = EDHOC-KDF( PRK_4e3m, 6, context_3, mac_length_3 )context_3 = « ID_CRED_I, TH_3, CRED_I, ? EAD_3 »CRED_I is identified by a ‘kid’ with byte string value 0x2b:ID_CRED_I (CBOR Data Item) (4 bytes)
a1 04 41 2bCRED_I is an RPK encoded as a CCS:No external authorization data:context_3 = « ID_CRED_I, TH_3, CRED_I, ? EAD_3 »MAC_3 is computed through Expand() using the EDHOC hash algorithm, see
Section 4.1.2 of :info = ( 6, context_3, mac_length_3 )Since METHOD = 3, mac_length_3 is given by the EDHOC MAC length.info for MAC_3 is:where the last value is the EDHOC MAC length.Since METHOD = 3, Signature_or_MAC_3 is MAC_3:I constructs PLAINTEXT_3 without padding:Since ID_CRED_I contains a single ‘kid’ parameter, only the byte string value is included in the plaintext, represented as described in Section 3.3.2 of . The CBOR map { 4 : h’2b’ } is thus replaced, not by the CBOR byte string 0x412b, but by the CBOR int 0x2b, since that is a one byte encoding of a CBOR integer (-12).I constructs the associated data for message_3:I constructs the input needed to derive the key K_3, see Section 4.1.2 of , using the EDHOC hash algorithm:where key_length is the key length of EDHOC AEAD algorithm, and info for K_3 is:where the last value is the key length of EDHOC AEAD algorithm.I constructs the input needed to derive the nonce IV_3, see Section 4.1.2 of
, using the EDHOC hash algorithm:where iv_length is the nonce length of EDHOC AEAD algorithm, and info for IV_3 is:where the last value is the nonce length of EDHOC AEAD algorithm.I calculates CIPHERTEXT_3 as ‘ciphertext’ of COSE_Encrypt0 applied
using the EDHOC AEAD algorithm with plaintext PLAINTEXT_3, additional data
A_3, key K_3 and nonce IV_3.message_3 is the CBOR bstr encoding of CIPHERTEXT_3:The transcript hash TH_4 is calculated using the EDHOC hash algorithm:TH_4 = H( TH_3, PLAINTEXT_3 )No external authorization data:EAD_4 (CBOR Sequence) (0 bytes)R constructs the plaintext PLAINTEXT_4:PLAINTEXT_4 (CBOR Sequence) (0 bytes)R constructs the associated data for message_4:R constructs the input needed to derive the EDHOC message_4 key, see
Section 4.1.2 of , using the EDHOC hash algorithm:where key_length is the key length of the EDHOC AEAD algorithm,
and info for EDHOC_K_4 is:where the last value is the key length of EDHOC AEAD algorithm.R constructs the input needed to derive the EDHOC message_4 nonce, see Section 4.1.2 of , using the EDHOC hash algorithm:where iv_length is the nonce length of EDHOC AEAD algorithm,
and info for EDHOC_IV_4 is:where the last value is the nonce length of EDHOC AEAD algorithm.R calculates CIPHERTEXT_4 as ‘ciphertext’ of COSE_Encrypt0 applied
using the EDHOC AEAD algorithm with plaintext PLAINTEXT_4, additional data
A_4, key K_4 and nonce IV_4.message_4 is the CBOR bstr encoding of CIPHERTEXT_4:PRK_out is specified in Section 4.1.2 of .where hash_length is the length of the output of the EDHOC hash algorithm, and info for PRK_out is:where the last value is the length of EDHOC hash algorithm.The OSCORE Master Secret and OSCORE Master Salt are derived with the EDHOC-Exporter as specified in 4.2.1 of .where PRK_exporter is derived from PRK_out:where hash_length is the length of the output of the EDHOC hash algorithm, and info for the PRK_exporter is:where the last value is the length of EDHOC hash algorithm.The derivation of OSCORE parameters is specified in Appendix A.1 of
.The AEAD and Hash algorithms to use in OSCORE are given by the selected cipher suite:The mapping from EDHOC connection identifiers to OSCORE Sender/Recipient IDs
is defined in Section 3.3.3 of .C_R is mapped to the Recipient ID of the server, i.e., the Sender ID of the client. The byte string 0x27, which as C_R is encoded as the CBOR integer 0x27, is converted to the server Recipient ID 0x27.C_I is mapped to the Recipient ID of the client, i.e., the Sender ID of the server. The byte string 0x37, which as C_I is encoded as the CBOR integer 0x0e is converted to the client Recipient ID 0x37.The OSCORE Master Secret is computed through Expand() using the
Application hash algorithm, see Appendix A.1 of :where oscore_key_length is by default the key length of the Application AEAD
algorithm, and info for the OSCORE Master Secret is:where the last value is the key length of Application AEAD algorithm.The OSCORE Master Salt is computed through Expand() using the Application hash algorithm, see Section 4.2 of :where oscore_salt_length is the length of the OSCORE Master Salt, and info for the OSCORE Master Salt is:where the last value is the length of the OSCORE Master Salt.ey update is defined in Section 4.2.2 of .where hash_length is the length of the output of the EDHOC hash function, context for KeyUpdate isand where info for key update is:After key update the PRK_exporter needs to be derived anew:where info and hash_length as unchanged as in .The OSCORE Master Secret is derived with the updated PRK_exporter:where info and key_length are unchanged as in .The OSCORE Master Salt is derived with the updated PRK_exporter:where info and salt_length are unchanged as in .This document contains examples of EDHOC whose security considerations apply. The keys printed in these examples cannot be considered secret and must not be used.There are no IANA considerations.
&I-D.ietf-lake-edhoc;
&RFC7748;
&RFC8032;
&RFC8392;
&RFC8949;
CBOR PlaygroundThe authors want to thank all people verifying EDHOC test vectors and/or contributing to the interoperability testing including: Christian Amsüss, Timothy Claeys, Stefan Hristozov, Rikard Höglund, Christos Koulamas, Francesca Palombini, Lidia Pocero, Peter van der Stok, and Michel Veillette.