SecureRandom: init once or every time it is needed

Question

Our team is using a SecureRandom to generate a list of key pairs (the SecureRandom is passed to a KeyPairGenerator). We cannot agree on which of the following two options to use:

1. Create a new instance every time we need to generate a key pair

2. Initialize a static instance and use it for all key pairs

Which approach is generally better and why?

ADDED: My gut feeling is that the second option is more secure. But my only argument is a theoretical attack based on the assumption that the pseudorandomness is derived from the current timestamp: someone may see the creation time of the key pair, guess timestamps in the surrounding time interval, compute the possible pseudorandom sequences, and obtain the key material.

ADDED: My assumption about determinism based on a timestamp was wrong. That's the difference between Random and SecureRandom. So, it looks like the answer is: in terms of security it doesn't really matter.

Answer 1

I would not rely on SecureRandom to be anything other than a cryptographically secure PRNG. The complete quote that Gowri is using from the javadocs is:

Additionally, SecureRandom must produce non-deterministic output and therefore it is required that the seed material be unpredictable and that output of SecureRandom be cryptographically strong sequences as described in RFC 1750: Randomness Recommendations for Security.

It's less than clear from this what the real expectation is - RFC 1750 details the use of hardware to enhance random number generation, but the javadocs say "therefore it is required that the seed material be unpredictable", which would seem to contradict this.

The safest assumption to work on is that your implementation of SecureRandom is simply a cryptographically-secure PRNG, and therefore that your keys are no more secure than the random seed that you use. Thus, initializing a new SecureRandom with a new (unique, truly random) seed for each key would be the safest bet.