A chaos generator for accumulating stream entropy is disclosed. The chaos
generator includes a random source coupled to an entropy accumulator that
is configurable for generating a binary random input sequence. The
entropy accumulator is configurable for accumulating entropy of the input
sequence and providing a binary random output sequence based on the
accumulated entropy. The binary random output sequence is reduced by a
modular reduction operation having a modulus that is set equal to a
cryptographic prime (e.g., the order of an elliptic curve). The number of
iterations performed by the entropy accumulator on the binary random
input sequence is selected to provide a binary random output sequence
having a desired cryptographic strength. The chaos generator can be part
of a signing and verification system that uses fast elliptic encryption
for small devices.