jwt - How to convert a public key from a JWK into PEM for OpenSSL?

Question

There is an RSA key from an RFC:

https://www.rfc-editor.org/rfc/rfc7516#appendix-A.1

 {"kty":"RSA",
  "n":"oahUIoWw0K0usKNuOR6H4wkf4oBUXHTxRvgb48E-BVvxkeDNjbC4he8rUW
       cJoZmds2h7M70imEVhRU5djINXtqllXI4DFqcI1DgjT9LewND8MW2Krf3S
       psk_ZkoFnilakGygTwpZ3uesH-PFABNIUYpOiN15dsQRkgr0vEhxN92i2a
       sbOenSZeyaxziK72UwxrrKoExv6kc5twXTq4h-QChLOln0_mtUZwfsRaMS
       tPs6mS6XrgxnxbWhojf663tuEQueGC-FCMfra36C9knDFGzKsNa7LZK2dj
       YgyD3JR_MB_4NUJW_TqOQtwHYbxevoJArm-L5StowjzGy-_bq6Gw",
  "e":"AQAB",
  "d":"kLdtIj6GbDks_ApCSTYQtelcNttlKiOyPzMrXHeI-yk1F7-kpDxY4-WY5N
       WV5KntaEeXS1j82E375xxhWMHXyvjYecPT9fpwR_M9gV8n9Hrh2anTpTD9
       3Dt62ypW3yDsJzBnTnrYu1iwWRgBKrEYY46qAZIrA2xAwnm2X7uGR1hghk
       qDp0Vqj3kbSCz1XyfCs6_LehBwtxHIyh8Ripy40p24moOAbgxVw3rxT_vl
       t3UVe4WO3JkJOzlpUf-KTVI2Ptgm-dARxTEtE-id-4OJr0h-K-VFs3VSnd
       VTIznSxfyrj8ILL6MG_Uv8YAu7VILSB3lOW085-4qE3DzgrTjgyQ",
  "p":"1r52Xk46c-LsfB5P442p7atdPUrxQSy4mti_tZI3Mgf2EuFVbUoDBvaRQ-
       SWxkbkmoEzL7JXroSBjSrK3YIQgYdMgyAEPTPjXv_hI2_1eTSPVZfzL0lf
       fNn03IXqWF5MDFuoUYE0hzb2vhrlN_rKrbfDIwUbTrjjgieRbwC6Cl0",
  "q":"wLb35x7hmQWZsWJmB_vle87ihgZ19S8lBEROLIsZG4ayZVe9Hi9gDVCOBm
       UDdaDYVTSNx_8Fyw1YYa9XGrGnDew00J28cRUoeBB_jKI1oma0Orv1T9aX
       IWxKwd4gvxFImOWr3QRL9KEBRzk2RatUBnmDZJTIAfwTs0g68UZHvtc",
  "dp":"ZK-YwE7diUh0qR1tR7w8WHtolDx3MZ_OTowiFvgfeQ3SiresXjm9gZ5KL
       hMXvo-uz-KUJWDxS5pFQ_M0evdo1dKiRTjVw_x4NyqyXPM5nULPkcpU827
       rnpZzAJKpdhWAgqrXGKAECQH0Xt4taznjnd_zVpAmZZq60WPMBMfKcuE",
  "dq":"Dq0gfgJ1DdFGXiLvQEZnuKEN0UUmsJBxkjydc3j4ZYdBiMRAy86x0vHCj
       ywcMlYYg4yoC4YZa9hNVcsjqA3FeiL19rk8g6Qn29Tt0cj8qqyFpz9vNDB
       UfCAiJVeESOjJDZPYHdHY8v1b-o-Z2X5tvLx-TCekf7oxyeKDUqKWjis",
  "qi":"VIMpMYbPf47dT1w_zDUXfPimsSegnMOA1zTaX7aGk_8urY6R8-ZW1FxU7
       AlWAyLWybqq6t16VFd7hQd0y6flUK4SlOydB61gwanOsXGOAOv82cHq0E3
       eL4HrtZkUuKvnPrMnsUUFlfUdybVzxyjz9JF_XyaY14ardLSjf4L_FNY"
 }

I've tried jwk-to-pem:

https://stackoverflow.com/a/35995690/4742108

-----BEGIN RSA PUBLIC KEY-----
MIIBCgKCAQEAoahUIoWw0K0usKNuOR6H4wkf4oBUXHTxRvgb48E+BVvxkeDNjbC4
he8rUWcJoZmds2h7M70imEVhRU5djINXtqllXI4DFqcI1DgjT9LewND8MW2Krf3S
psk/ZkoFnilakGygTwpZ3uesH+PFABNIUYpOiN15dsQRkgr0vEhxN92i2asbOenS
ZeyaxziK72UwxrrKoExv6kc5twXTq4h+QChLOln0/mtUZwfsRaMStPs6mS6Xrgxn
xbWhojf663tuEQueGC+FCMfra36C9knDFGzKsNa7LZK2djYgyD3JR/MB/4NUJW/T
qOQtwHYbxevoJArm+L5StowjzGy+/bq6GwIDAQAB
-----END RSA PUBLIC KEY-----

Also had to replace "RSA PUBLIC KEY" with "PUBLIC KEY".

The command openssl rsa -inform PEM -pubin gives:

unable to load Public Key
139911798556312:error:0D0680A8:asn1 encoding routines:ASN1_CHECK_TLEN:wrong tag:tasn_dec.c:1197:
139911798556312:error:0D07803A:asn1 encoding routines:ASN1_ITEM_EX_D2I:nested asn1 error:tasn_dec.c:374:Type=X509_ALGOR
139911798556312:error:0D08303A:asn1 encoding routines:ASN1_TEMPLATE_NOEXP_D2I:nested asn1 error:tasn_dec.c:697:Field=algor, Type=X509_PUBKEY
139911798556312:error:0906700D:PEM routines:PEM_ASN1_read_bio:ASN1 lib:pem_oth.c:83:

How to get a usable key?

Answer 1

I developed a a PHP class that is able to convert public/private keys from JWK to PEM (and vice versa).

You will find that class here.

Basically, you have to decode each component from Base64UrlSafe to a binary string and assemble all of them according to the ASN.1 Structure described in the RFC3447.

Nevertheless, I recommend you to use a dedicated library/tool for that to ease your work. With my PHP library, your code will looks like:

use  JoseKeyConverterRSAKey;
$key = new RSAKey([
    "kty" => "RSA",
    "n"   => "oahUIoWw0K0usKNuOR6H4wkf4oBUXHTxRvgb48E-BVvxkeDNjbC4he8rUWcJoZmds2h7M70imEVhRU5djINXtqllXI4DFqcI1DgjT9LewND8MW2Krf3Spsk_ZkoFnilakGygTwpZ3uesH-PFABNIUYpOiN15dsQRkgr0vEhxN92i2asbOenSZeyaxziK72UwxrrKoExv6kc5twXTq4h-QChLOln0_mtUZwfsRaMStPs6mS6XrgxnxbWhojf663tuEQueGC-FCMfra36C9knDFGzKsNa7LZK2djYgyD3JR_MB_4NUJW_TqOQtwHYbxevoJArm-L5StowjzGy-_bq6Gw",
    "e"   => "AQAB",
    "d"   => "kLdtIj6GbDks_ApCSTYQtelcNttlKiOyPzMrXHeI-yk1F7-kpDxY4-WY5NWV5KntaEeXS1j82E375xxhWMHXyvjYecPT9fpwR_M9gV8n9Hrh2anTpTD93Dt62ypW3yDsJzBnTnrYu1iwWRgBKrEYY46qAZIrA2xAwnm2X7uGR1hghkqDp0Vqj3kbSCz1XyfCs6_LehBwtxHIyh8Ripy40p24moOAbgxVw3rxT_vlt3UVe4WO3JkJOzlpUf-KTVI2Ptgm-dARxTEtE-id-4OJr0h-K-VFs3VSndVTIznSxfyrj8ILL6MG_Uv8YAu7VILSB3lOW085-4qE3DzgrTjgyQ",
    "p"   => "1r52Xk46c-LsfB5P442p7atdPUrxQSy4mti_tZI3Mgf2EuFVbUoDBvaRQ-SWxkbkmoEzL7JXroSBjSrK3YIQgYdMgyAEPTPjXv_hI2_1eTSPVZfzL0lffNn03IXqWF5MDFuoUYE0hzb2vhrlN_rKrbfDIwUbTrjjgieRbwC6Cl0",
    "q"   => "wLb35x7hmQWZsWJmB_vle87ihgZ19S8lBEROLIsZG4ayZVe9Hi9gDVCOBmUDdaDYVTSNx_8Fyw1YYa9XGrGnDew00J28cRUoeBB_jKI1oma0Orv1T9aXIWxKwd4gvxFImOWr3QRL9KEBRzk2RatUBnmDZJTIAfwTs0g68UZHvtc",
    "dp"  => "ZK-YwE7diUh0qR1tR7w8WHtolDx3MZ_OTowiFvgfeQ3SiresXjm9gZ5KLhMXvo-uz-KUJWDxS5pFQ_M0evdo1dKiRTjVw_x4NyqyXPM5nULPkcpU827rnpZzAJKpdhWAgqrXGKAECQH0Xt4taznjnd_zVpAmZZq60WPMBMfKcuE",
    "dq"  => "Dq0gfgJ1DdFGXiLvQEZnuKEN0UUmsJBxkjydc3j4ZYdBiMRAy86x0vHCjywcMlYYg4yoC4YZa9hNVcsjqA3FeiL19rk8g6Qn29Tt0cj8qqyFpz9vNDBUfCAiJVeESOjJDZPYHdHY8v1b-o-Z2X5tvLx-TCekf7oxyeKDUqKWjis",
    "qi"  => "VIMpMYbPf47dT1w_zDUXfPimsSegnMOA1zTaX7aGk_8urY6R8-ZW1FxU7AlWAyLWybqq6t16VFd7hQd0y6flUK4SlOydB61gwanOsXGOAOv82cHq0E3eL4HrtZkUuKvnPrMnsUUFlfUdybVzxyjz9JF_XyaY14ardLSjf4L_FNY",
]);
$pem = $key->toPEM();