How fast we generate a prime number is mostly a matter of luck. It
varies from miliseconds to seconds and depends how lucky we are with
drawing bytes.
With today's multicore processors, we can execute the process on
multiple cores concurrently, accept the first valid result and cancel
the rest of work. This way, with the same algorithm, we get the result
faster.
I've adapted a Go code for generating random numbers by inserting some
optimisations that will allow us to generate safe primes faster than
with the previous, naive approach.
First of all, having q which can be prime, we first check whether q%3=1.
If that's true, there is no chance p=2q+1 is prime. It lets us to reject
candidate numbers quicker without running an expensive primality tests.
Also, before we run a primality test for q, we may check p=2q+1 against
the primes between 3-53 (We are limited by Go's uint64 range).
If all those conditions are met and we know p is prime, it's enough to
check Pocklington criterion for q instead of running an expensive
primality test for it.
It's now possible to multiply Cypher by an integer.
Paillier is a homomorphic encryption scheme, where an encrypted
plaintext `m` raised to an integer `k` will decrypt to the product of
the plaintext `m` and `k`.
Function `EncryptWithR` lets to specify randomness `r` explicitely. For
some ZKPs based on the Paillier scheme, it's required to use the same
`r` for encryption and constructing ZKP. It wasn't possible previously,
because `r` was generated internally and never returned.
I did not want to modify `Encrypt` to return `r` because it would break
existing code using this API, as well as, I want to make sure person
using the specific `r` and using it somewhere else really knows what
he's doing.
`PublicKey.Add` accepts now an arbitrary number of `*Cypher`s.
Previously, it was possible to add only two `*Cypher*` instances and it
was quite unwieldy for a lot of use cases.
The current implementation is backward compatible. It's still possible
to pass just two `*Cypher` arguments, so every project referencing the
library will observe no compilation issues.
Piotr Dyraga