The entropy of a hex string generated by `openssl rand` is influenced by the output length, but not in a straightforward manner. Here's a detailed explanation:
Entropy and Output Length
- Entropy Source: `openssl rand` uses a cryptographically secure pseudo-random number generator (CSPRNG), which is seeded from system entropy sources. The quality of the generated random numbers depends on the available entropy[7][9].
- Output Length: The command generates a specified number of random bytes. For example, `openssl rand -hex 16` generates 16 bytes of random data, which is then encoded in hexadecimal format, resulting in a 32-character string[1][4].
- Entropy per Byte: Each byte generated by `openssl rand` is intended to have high entropy. However, the actual entropy level can be limited by the system's entropy pool and how well the CSPRNG is seeded[2][10].
Impact of Output Length on Entropy
- Increasing Output Length: Generating more bytes (e.g., increasing from 16 to 32 bytes) does not necessarily increase the entropy per byte. Instead, it increases the total amount of entropy in the output, assuming the system's entropy pool is sufficient to maintain high-quality randomness throughout the generation process[10].
- Entropy Limitations: OpenSSL's RNG has a design limitation where the output may only achieve an entropy level of 240 bits for up to several hundred output bytes, even if seeded with 256 bits of entropy initially[2]. This means that while longer outputs can provide more total entropy, the entropy per byte may not increase beyond a certain point.
- Practical Considerations: For most cryptographic purposes, generating more bytes increases the overall security of the output, as it provides more unpredictable data. However, in environments with limited entropy (e.g., embedded systems or virtual machines), additional measures may be necessary to ensure sufficient randomness[10].
Conclusion
The entropy of a hex string generated by `openssl rand` does not directly increase with output length in terms of entropy per byte. Instead, longer outputs provide more total entropy, assuming the system can maintain high-quality randomness. The actual entropy level is influenced by the system's entropy pool and the limitations of OpenSSL's CSPRNG. For high-security applications, ensuring sufficient system entropy and using appropriate output lengths (e.g., at least 32 bytes for AES-256 keys) is crucial[10].
Citations:
[1] https://www.d12frosted.io/posts/2018-01-31-random-bytes-generation-with-openssl
[2] https://www.iacr.org/archive/eurocrypt2016/96650118/96650118.pdf
[3] https://docs.python.org/3/library/secrets.html
[4] https://jameshfisher.com/2017/03/10/openssl-rand/
[5] https://crypto.stackexchange.com/questions/12571/good-entropy-source-for-generating-openssl-keys
[6] https://learnmeabitcoin.com/technical/keys/hd-wallets/mnemonic-seed/
[7] https://docs.openssl.org/1.1.1/man1/rand/
[8] https://stackoverflow.com/questions/6475462/how-many-bytes-of-the-random-input-are-actually-read-by-openssl-for-the-genrsa-c
[9] https://docs.openssl.org/3.0/man1/openssl-rand/
[10] https://dev.to/mochafreddo/a-deep-dive-into-cryptographic-random-number-generation-from-openssl-to-entropy-16e6