Is there a security difference between GPG signing a file directly or its SHA512SUM file?

Question

I am about to decide what SHA-512 hash sum and / or GPG verification scheme I will choose.

Let me present you with two options:

1. Signing the 25 GB ~ 23 GiB (one file fit to a Blu-Ray) directly with:

   $ gpg --local-user <my_gpg_fingerprint> \
         --sign --armor \
         --output       "${backup_file}.xz.enc.asc" \
         --detach-sign  "${backup_file}.xz.enc"
   

   which honestly takes a long time even on a higher-end laptop of mine; or

2. Create SHA512SUM of that big encrypted file and sing that one with:

   $ sha512sum --binary "${backup_file}.xz.enc" > \ 
         "${backup_file}.xz.enc.SHA512SUM"
   
   $ gpg --local-user <my_gpg_fingerprint> \
         --sign --armor \
         --output       "${backup_file}.xz.enc.SHA512SUM.asc" \
         --detach-sign  "${backup_file}.xz.enc.SHA512SUM"
   

   which has actually proven to be way a little faster.

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Please elaborate as to what security implications might the faster version have as a disadvantage to the direct signing the big file.

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Benchmark

$ time gpg --personal-digest-preferences sha512 \
    --local-user <my_gpg_fingerprint> \
    --sign --armor \
    --output test_file_23gib_random_data.asc \
    --detach-sign test_file_23gib_random_data

result:

real    1m25,444s
user    1m17,059s
sys     0m4,728s

As opposed to signing the SHA-512 file:

$ time sha512sum --binary test_file_23gib_random_data > \
    test_file_23gib_random_data.SHA512SUM

result:

real    1m7,568s
user    1m2,810s
sys     0m4,567s

and signing it in ~ 0.4 seconds.

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Final thoughts

So, there is a few seconds difference. Not really a big deal, but noticeable.

I am still interested in your view about the security implications, which this question was originally intended to be about.

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Hardware:

• Dell Inspiron 15 Gaming 7577, model number 7577-92774.

• Processor: I have an Intel Kaby Lake CPU: Intel Core i7-7700HQ.

• Storage: NVMe PCI-E drive.

System:

I am on Linux Mint 19.1; based on Ubuntu 18.04.

Answer 1

Most signature schemes already require hashing the data as part of the signing operation. Adding another hash before this shouldn't really be necessary (ie this likely indicates a performance issue in gpg), but as long as the hash used is at least as strong as the one used for the signature it shouldn't result in a reduction in security.

There is a minor difference in that sha512sum will output the filename as well as the hash, so your signature will be over the filename as well as the data.

Note that gpg allows you to specify the hash function with --personal-digest-preferences or --digest-algo, so selecting a different hash may be an alternate solution to your problem.