Implicit certificate

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In cryptography, implicit certificates are a variant of public key certificate. A subject's public key is reconstructed from the data in an implicit certificate, and is then said to be "implicitly" verified. Tampering with the certificate will result in the reconstructed public key being invalid, in the sense that it is infeasible to find the matching private key value, as would be required to make use of the tampered certificate.

By comparison, traditional public-key certificates include a copy of the subject's public key, and a digital signature made by the issuing certificate authority (CA). The public key must be explicitly validated, by verifying the signature using the CA's public key. For the purposes of this article, such certificates will be called "explicit" certificates.

Elliptic Curve Qu-Vanstone (ECQV) is one kind of implicit certificate scheme. It is described in the document Standards for Efficient Cryptography 4 (SEC4).^[1]
This article will use ECQV as a concrete example to illustrate implicit certificates.