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Asked: 2026-05-15T09:11:14+00:00

I need to know the cost of succeeding with a Preimage attack (In cryptography,

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I need to know the cost of succeeding with a Preimage attack (“In cryptography, a preimage attack on a cryptographic hash is an attempt to find a message that has a specific hash value.”, Wikipedia).

The message I want to hash consists of six digits (the date of birth), then four random digits. This is a social security number.

Is there also a possibility to hash something using a specific password. This would introduce another layer of security as one would have to know the password in order to produce the same hash values for a message.

I am thinking about using SHA-2.

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  1. Editorial Team

    If you want to know how expensive it is to find a preimage for the string you’re describing, you need to figure out how many possible strings there are. Since the first 6 digits are a date of birth, their value is even more restricted than the naive assumption of 10^6 – we have an upper bound of 366*100 (every day of the year, plus the two digit year).

    The remaining 4 ‘random’ digits permit another 10^4 possibilities, giving a total number of distinct hashes of 366 * 100 * 10^4 = 366,000,000 hashes.

    With that few possibilities, it ought to be possible to find a preimage in a fraction of a second on a modern computer – or, for that matter, to build a lookup table for every possible hash.

    Using a salt, as Tom suggests, will make a lookup table impractical, but with such a restricted range of valid values, a brute force attack is still eminently practical, so it alone is not sufficient to make the attack impractical.

    One way to make things more expensive is to use iterative hashing – that is, hash the hash, and hash that, repeatedly. You have to do a lot less hashing than your attacker does, so increases in cost affect them more than they do you. This is still likely to be only a stopgap given the small search space, however.

    As far as “using a password” goes, it sounds like you’re looking for an HMAC – a construction that uses a hash, but can only be verified if you have the key. If you can keep the key secret – no easy task if you’re assuming the hashes can only be obtained if your system is compromised in the first place – this is a practical system.

    Edit: Okay, so ‘fractions of a second’ may have been a slight exaggeration, at least with my trivial Python test. It’s still perfectly tractable to bruteforce on a single computer in a short timeframe, however.

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