In RFC 2409 does SIG_I and HASH_I refers to the same?

Question

In RFC 2409, IKE authentication by digital signature we see the following:

`Initiator              Responder
-----------                 -----------
HDR, SA             -->
                <--  HDR, SA
HDR, KE, Ni         -->
                <--     HDR, KE, Nr
HDR*, IDii, [ CERT, ] SIG_I     -->
                <--     HDR*, IDir, [ CERT, ] SIG_R
`

also, we see it's mentioned:

-In both modes, the signed data, SIG_I or SIG_R, is the result of the negotiated digital signature algorithm applied to HASH_I or HASH_R respectively.

-In general the signature will be over HASH_I and HASH_R as above using the negotiated prf, or the HMAC version of the negotiated hash function (if no prf is negotiated).

what does the above means? , how SIG_I and SIG_R are get calculated and verified?

I understand that the HASH_I and HASH_R are calculated like the following:

HASH_I = prf(SKEYID, g^xi | g^xr | CKY-I | CKY-R | SAi_b | IDii_b ) HASH_R = prf(SKEYID, g^xr | g^xi | CKY-R | CKY-I | SAi_b | IDir_b )

and the SKEYID is different depends on the authentication method in use, and for digital signatures it's like the following:

For signatures: SKEYID = prf(Ni_b | Nr_b, g^xy)

now, I would like to understand what does it mean by "SIG_I or SIG_R, is the result of the negotiated digital signature algorithm applied to HASH_I or HASH_R respectively." ? does this mean SIG_I = prf (HASH_I)?