Code change:
NAME Good point about being more explicit. I actually think is valuable to reference an existing encoding of public keys providing also key type and curve, like CREDX in URL Also, there is a discussion about format for public keys in COSE, which if it is specified probably will be referenced by EDHOC instead of CREDX. I would be good if there is a common format used in all these instances. For the time being I propose that we reference CRED_X with empty text string subject name, and keep track of the COSE activity.
We should consider replace the NIST reference with SECG [1] to harmonize with EDHOC [2]. [1] URL [2] URL (edit) ... but the commits in [3] mainly refers to the NIST spec. so I propose we keep it as is for the time being. [2] URL
It looks good to me; we can give more details on one point. For the two HKDF invocations in Section 2.3.1, we can define more explicitly how the public keys are expressed when concatenated to form IKM-Sender and IKM-Recipient. Given a public key, that can simply be: For OKP signature keys, the compressed 'x' coordinate, i.e. what would be expressed in the key parameter -2 of a corresponding COSE Key. For EC2 signature keys, the 'x' coordinate followed by the 'y' coordinate in this order, i.e. what would be expressed in the key parameters -2 and -3 of a corresponding COSE Key. This should be sufficient, i.e. it shouldn't be needed to have a more structured encoding of public keys providing also key type and curve, e.g. like done for CRED_X in URL

Related discussion:
text: 2.3.2. <ins> 2.3.2.1. The y-coordinate of the other endpoint's Ed25519 public key is decoded as specified in Section 5.1.3 of RFC8032.  The Curve25519 u-coordinate is recovered as u = (1 + y) / (1 - y) (mod p) following the map in Section 4.1 of RFC7748.  Note that the mapping is not defined for y = 1, and that y = -1 maps to u = 0 which corresponds to the neutral group element and thus will result in a degenerate shared secret.  Therefore implementations MUST abort if the y-coordinate of the other endpoint's Ed25519 public key is 1 or -1 (mod p). The private signing key byte strings (= the lower 32 bytes used for generating the public key, see step 1 of Section 5.1.5 of RFC8032) are decoded the same way for signing in Ed25519 and scalar multiplication in X25519.  Hence, to compute the shared secret the endpoint applies the X25519 function to the Ed25519 private signing key byte string and the encoded u-coordinate byte string as specified in Section 5 of RFC7748. 2.3.2.2. The y-coordinate of the other endpoint's Ed448 public key is decoded as specified in Section 5.2.3. of RFC8032.  The Curve448 u-coordinate is recovered as u = y^2 * (d * y^2 - 1) / (y^2 - 1) (mod p) following the map from "edwards448" in Section 4.2 of RFC7748, and also using the relation x^2 = (y^2 - 1)/(d * y^2 - 1) from the curve equation. Note that the mapping is not defined for y = 1 or -1.  Therefore implementations MUST abort if the y-coordinate of the peer endpoint's Ed448 public key is 1 or -1 (mod p). The private signing key byte strings (= the lower 57 bytes used for generating the public key, see step 1 of Section 5.2.5 of RFC8032) are decoded the same way for signing in Ed448 and scalar multiplication in X448.  Hence, to compute the shared secret the endpoint applies the X448 function to the Ed448 private signing key byte string and the encoded u-coordinate byte string as specified in Section 5 of RFC7748. 2.3.3. </ins> When using any of its Pairwise Sender Keys, a sender endpoint including the 'Partial IV' parameter in the protected message MUST use the current fresh value of the Sender Sequence Number from its