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What type of certificate is this?

pe flag

I have been reading papers about authentication in VANETS and some of them mention a certificate that a trusted authority generates for a vehicle and has the following form: $${C_{V_i}}=S_{TA}+H(PID_{V_i}|PID_{TA}|P_{TA}|P_{V_I})*x_i$$
Here $S_{TA}$ is a secret that belongs to Trusted Authority.
$H()$ is a hash function.
$PID_{V_i}$ is the pseudo-identity of vehicle $V_i$.
$PID_{TA}$ is the pseudo-identity of $TA$.
$P_{TA}$ is the public key of $TA$.
$P_{V_i}$ is the public of of vehicle $V_i$.
and $x_i$ is a random secret generated by the $TA$.
the form is TA's secret plus some hash value times another random secret. They also mention that they are working with elliptic curve cryptography for their works.

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ru flag

Rather than a certificate, this looks to be part of an Ed25519 signature.

The value in question is usually denoted $S$ rather than $C$. The long-term and ephemeral secrets $S_{TA}$ and $x_i$ respectively are reversed from their usual usage ($r$ and $s$ in the usual Ed25519 equation are the ephemeral and long-term secrets. The value can only be verified if also presented with a curve point $R=x_iG$ and if there is a system owners public signing key $P=S_{TA}G$. If this is the case then the verfifier can check that $$C_VG=P+H({\rm identifiers/keys})R.$$

I sit in a Tesla and translated this thread with Ai:

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