JWK to PEM

Two formats for the same key

A JWK is a JSON object describing a cryptographic key, common in OAuth and OpenID Connect where a server publishes its keys at a JWKS endpoint. PEM is the older Base64-and-headers format most libraries and command-line tools expect. Converting JWK to PEM lets you take a key fetched from a JWKS URL and feed it to tooling that only speaks PEM.

What actually gets converted

The conversion is a repackaging, not a cryptographic transform. For an RSA key, the JWK fields n (modulus) and e (exponent) are Base64URL-decoded and re-encoded as DER inside a PEM envelope. For an EC key, the curve and the x/y coordinates are mapped into the equivalent structure. No key material changes; only the serialization does.

Example

{
  "kty": "RSA",
  "n": "0vx7agoebGcQ...",
  "e": "AQAB",
  "kid": "2024-key"
}

-> -----BEGIN PUBLIC KEY-----
   MIIBIjANBgkqhkiG9w0BAQEF...
   -----END PUBLIC KEY-----

AQAB is the famous 65537 public exponent, which decodes to the bytes 01 00 01. The resulting PEM can be inspected structurally with the ASN.1 parser.

Public and private pieces

A public JWK has only n and e (or the curve point). A private JWK adds d and, for RSA, the prime factors p, q, and the CRT values. If those fields are present, the PEM you produce is a private key and must be handled as a secret, not shared like the public half.

FAQ

Which PEM header will I get? A public key yields a PUBLIC KEY block; a private key yields a PRIVATE KEY block. The header reflects whether private fields were present in the JWK.

Does the kid matter for conversion? No. The key id is just a label for selecting the right key from a set; it is not part of the math and is dropped in the PEM.