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I have generated one RSA-2048 signing key and one DSA-2048 signing key, using gpg command
gpg --full-generate-keys
I would expect the key to have size 2048 bits, however, running the command
gpg --export-secret-keys <key-id> | wc -c
gives a size of 1353Bytes for the RSA private key and 1103Bytes for the DSA private key. The public keys are 656Bytes and 1020Bytes.
Why is this? Is this because the exponent and primes, passphrases, my name etc are stored together with the keys?
Yes. There is a difference between key strength, key size and the size of the encoding of a key.
The modulus of the RSA private key determines the key size, for instance, but an RSA key commonly also contains the public, private exponent and CRT parameters, an encoding structure etc. etc.
In GPG indeed the "key" consists of many additional parts as well (as you can see from the size). You can packet-inspect the keys in GPG by simply performing gpg <exported-key>.
See here for more information (and note that the question really belongs on Superuser, but whatever).
