Long story short, I share a server with a few other people and store my backups there. All these backups are archived to a .7z file using AES-256 encryption, using a randomly-generated password of about 100 bits of entropy. Assuming my backups became public, how hard would it be to access their contents in 2018 and beyond?
All of the comments assume a brute force attack against the encrypted file. In cryptography, however, this is far from the only attack to consider.
As an example, AES-256 is generally considered 'computationally secure' by modern standards but there a lot of assumptions in just saying that. Computationally secure means that while it's secure by modern standards, history has proven it won't always be secure. AES operates in different modes (CBC, ECB, CFB, OFB, CTS) -- each with their own targeted attacks against each mode.
As an example in Cipher Block Chaining, after the first round, the cipher text from the previous round is xor'd with the plaintext in the current block but circling back to the first round, the encryptor must be provided the first bits of randomness (called the Initialization Vector or IV). If this isn't done properly, this can be used to systematically derive the ciphertext that's xor'd in all for each subsequent blocks and thus, providing the unCBC'd ciphertext that can be statistically analyzed or brute forced to derive the key.
Additionally, your password can be targeted. You already leaked some interesting information about it.
- You said it was randomly generated with 100-bits of entropy and around 20 chars. With that, I can roughly derive the keyspace and probably make an educated guess as to the randomness (uppers, lowers, numbers, and a handful of common specials).
- You said it was randomly generated... was it cryptographically randomly generated or did it use a pseudo-random number generator? Most PRNGs have significant weakness (e.g. based on atomic clock values) -- so if I know when the file was created, file metadata or in the filename itself, I might be able derive the seed and generate the same value you did at that time, thus significantly limiting the effectiveness of the 'randomness' almost to the point of negating it.
- You said it was a passphrase, and not a password. This also leaks information. If true, it means your password probably isn't really cryptographically secure (e.g. 1r5%vb9*?_ad!@KLvnd) and probably something closer to I<3G0ldenR3tri3v3rs!!. L337 speak is not cryptographically secure and good cracker will have dictionary files with common l337 speak variations on common words to significantly lower the time to crack.
So... to answer your question on how hard would it be to access their contents in 2018 and beyond? -- it highly depends on a number of factors.