Cryptobench

wycheproof-x448-edge-case-multiplication

X448: Edge case multiplication

The public key in this test vector has been constructed, so that an edge case during the multiplication with a small k occurs. I.e., these are cases where during the multiplication one of the internal variables has a values such as -1, 0 or 1. This checks for errors in the integer arithmetic.

ACCEPT

Your service should accept this one.

Stated as the outcome to assert against, so a suite compares with this rather than hardcoding a result and getting it backwards.

The effect of arithmetic errors in the multiplication is that information about the private key is leaked. In the worst case such an error could be exploited to find the private key. Demonstrated by 1624 test vectors across 4 vector documents in Project Wycheproof.

Provenance

Kind
vulnerabilityA published weakness exists for this. Failing it is a known exploit path.
Source
wycheproof
Clause
RFC 7748 §5
CVE
none
Weakness
none
Produce this on the benchTake a token apart

Test keys only. Nothing here is a statement about any particular service: the expected outcome above is what an application ought to do, not evidence that yours does.

Reference

URL or embedded key?

Your app needs the public key to check a token. It can fetch it from a URL at runtime, or carry it as a file. Both are normal. The trade is always the same one: who controls rotation.

Fetch from the URLEmbed the key
RotationAutomatic on next fetchNeeds a redeploy
NetworkDepends on the URLNone
TrustWhatever the endpoint servesPinned to one key
SuitsA signer that rotates keysOffline, air-gapped, or pinned

Use the URL when the signer rotates its keys, which is what every identity provider does. That is why it became the norm, and it is usually a one-line config change.

Embed the key when you cannot make a network call while checking a token, or when you want your app pinned to one key so a compromised endpoint could not introduce another. Export the PEM from the Keysets tab.

One catch worth knowing: Spring Boot's public-key-location only loads RSA keys. An ES256 or EdDSA key needs a custom decoder, or the URL.