11.16 Compressing Data with Entropy into a Fixed-Size Seed

11.16.1 Problem

You are collecting data that may contain entropy, and you will need to output a fixed-size seed that is smaller than the input. That is, you have a lot of data that has a little bit of entropy, yet you need to produce a fixed-size seed for a pseudo-random number generator. At the same time, you would like to remove any statistical biases (patterns) that may be lingering in the data, to the extent possible.

Alternatively, you have data that you believe contains one bit of entropy per bit of data (which is generally a bad assumption to make, even if it comes from a hardware generator; see Recipe 11.19), but you'd like to remove any patterns in the data that could facilitate analysis if you're wrong about how much entropy is there. The process of removing patterns is called whitening.

11.16.2 Solution

You can use a cryptographic hash function such as SHA1 to process data into a fixed-size seed. It is generally a good idea to process data incrementally, so that you do not need to buffer potentially arbitrary amounts of data with entropy.

11.16.3 Discussion

 Be sure to estimate entropy conservatively. ( See Recipe 11.19.)

It is a good idea to use a cryptographic algorithm to compress the data from the entropy source into a seed of the right size. This helps preserve entropy in the data, up to the output size of the message digest function. If you need fewer bytes for a seed than the digest function produces, you can always truncate the output. In addition, cryptographic processing effectively removes any patterns in the data (assuming that the hash function is a pseudo-random function). Patterns in the data can help facilitate breaking an entropy source (in part or in full), particularly when that source does not actually produce as much entropy as was believed.

Most simpler compression methods are not going to do as good a job at preserving entropy. For example, suppose that your compression function is simply XOR. More concretely, suppose you need a 128-bit seed, and you XOR data in 16-byte chunks into a single buffer. Suppose also that you believe you have collected 128 bits of entropy from numerous calls to a 128-bit timestamp operation.

In any particular timestamp function, all of the entropy is going to live in a few of the least significant bits. Now suppose that only two or three of those bits are likely to contain any entropy. The XOR-everything strategy will leave well over 120 bits of the result trivial to guess. The remaining eight bits can be attacked via brute force. Therefore, even if the input had 128 bits of entropy, the XOR-based compression algorithm destroyed most of the entropy.

SHA1 is good for these purposes. See Recipe 6.5 for how to use SHA1.

Recipe 6.5, Recipe 11.19

 Foreword
 Preface
 Chapter 1. Safe Initialization
 Chapter 2. Access Control
 Chapter 3. Input Validation
 Chapter 4. Symmetric Cryptography Fundamentals
 Chapter 5. Symmetric Encryption
 Chapter 6. Hashes and Message Authentication
 Chapter 7. Public Key Cryptography
 Chapter 8. Authentication and Key Exchange
 Chapter 9. Networking
 Chapter 10. Public Key Infrastructure
 Chapter 12. Anti-Tampering
 Chapter 13. Other Topics
 Colophon