gpg --armor --export-secret-key differ on last 4 characters

Question

I created a backup of a gpg key by doing:

gpg -a --export-secret-keys foo@bar > private.key
gpg -a --export foo@bar > public.key

Then on another system, I import them:

gpg --import private.key
gpg --import public.key

I trusted the key as ultimate, and the backup seems to be working, the only thing that I notice is that when doing:

gpg --armor --export-secret-key foo@bar

The last 4 characters differ for example:

dutrV4c4hoPc6ntI3n9VztsL4LmmvoCcH969nJD6bTh4H1VMH98r8zECshtCSfVE
tMIIhXjA9xO1IZ6vMqHJU8TNhV2ttOE1Z/sUjcB46X4=
=TGyi
-----END PGP PRIVATE KEY BLOCK-----

In the new computer:

dutrV4c4hoPc6ntI3n9VztsL4LmmvoCcH969nJD6bTh4H1VMH98r8zECshtCSfVE
tMIIhXjA9xO1IZ6vMqHJU8TNhV2ttOE1Z/sUjcB46X4=
=/eDz
-----END PGP PRIVATE KEY BLOCK-----

Wondering why the last characters differ, in this case =TGyi and =/eDz

Answer 1

TO THE ASCII ARMOR SPEC! -- RFC 4880. The ASCII ARMOR specification is given in Section 6.2:

Concatenating the following data creates ASCII Armor:

• An Armor Header Line, appropriate for the type of data
• Armor Headers
• A blank (zero-length, or containing only whitespace) line
• The ASCII-Armored data
• An Armor Checksum
• The Armor Tail, which depends on the Armor Header Line

So the last 5 characters (=TGyi and =/eDz) are a checksum of the armored data. Oddly Section 6.2 doesn't define the checksum format, but an older version of the spec, the 1995 Internet Draft for PGP, does:

The Armor Checksum is a 24-bit CRC converted to four bytes of radix-64 encoding, prepending an equal-sign (=) to the four-byte code.

Checksums are used in a number of other places is the RFC, always defined as two-octet sums modulo 65536:

Then a two-octet checksum is appended, which is equal to the sum of the preceding session key octets, not including the algorithm identifier, modulo 65536.

---

It does seem a bit odd that two copies of the same data would have different checksums, ... maybe there's enough ambiguity in the spec that different versions of openpgp use different methods to compute the checksum?

(Disclaimer: this is my first time diving into the PGP spec, perhaps someone more familiar with it can explain properly)