Correlation-immunity of nonlinear combining functions for cryptographic applications (Corresp.)

Pseudonoise generators for cryptographic applications consisting of several linear feedback shift registers with a nonlinear combining function have been proposed as running key generators in stream ciphers. These running key generators eau sometimes be broken by (ciphertext-only) correlation attacks on individual subsequences. A new class of combining functions is presented, which provides better security against such attacks. The security is quantified by the smallest number
m + 1
of subsequences that must be simultaneously considered in a correlation attack. A necessary condition for such
m
th-order correlation-immunity is proved. A recursive construction is given that permits the construction of an
m
th-order immune combining function for
n
subsequences for any
m
and
n
with
1 \leq m < n
. Finally, the trade-off between the length of the linear equivalent of the nonlinear generator and the order
m
of its immunity against correlation attacks is considered.