An Improved Time-Memory-Data Trade-Off Attack against Irregularly Clocked and Filtered Keystream Generators

In this paper, we propose a new key recovery attack against irregularly clocked keystream generators, using the approach of time-memory-data trade-offs. The main idea behind our attack is creating several look-up tables and finally recovering the initial states of

LFSR

d

and

LFSR

c

synchronously, by alternatively deriving the initial states of

LFSR

d

and

LFSR

c

along the chains. We show that our attack is more efficient, and improves the previous attacks on the cipher model. Especially, we prove that our attack almost always needs less complexity than that of the normal time-memory-data trade-off attack [3] on the cipher model. We test our attack on LILI-128, and find out that it can successfully break the cipher with 2

56.6

bit-comparison operations, 2

49

pairs of 89-bit words memory and 2

59

keystream bits. This result is better than those in [15,6], which possess the complexity of 2

62

parity checks and 2

63

bit operations respectively. Moreover, our attack can be divided and computed in parallel, and the actual runtime of the attack can be reduced depending on the number of computers we access.