Highly nonlinear balanced Boolean functions with a good correlation-immunity

Advances in Cryptology — EUROCRYPT 2000

Trabbia

2000

168

160

Abstract. This paper describes new techniques for fast correlation attacks, based on Gallager iterative decoding algorithm using parity-check equations of weight greater than 3. These attacks can be applied to any key-stream generator based on LFSRs and it does not require that the involved feedback polynomial have a low weight. We give a theoretical analysis of all fast correlation attacks, which shows that our algorithm with parity-check equations of weight 4 or 5 is usually much more efficient than correlation attacks based on convolutional codes or on turbo codes. Simulation results confirm the validity of this comparison. In this context, we also point out the major role played by the nonlinearity of the Boolean function used in a combination generator.

Section: Approximation Of a T-resilient Function By A Function With Tmentioning

confidence: 99%

Improved Fast Correlation Attacks Using Parity-Check Equations of Weight 4 and 5

Advances in Cryptology — EUROCRYPT 2000

Trabbia

2000

168

160

“…Since the bent function g can take any degree less than or equal to (n − 5)/2, the function defined in (2) can be obtained for any degree d, 4 ≤ d ≤ (n − 5)/2. Other almost optimal functions whose extended Walsh spectra have more than 3 values can be found in [10,11]. Proof: Recall that Proposition 3 asserts that f can be transformed into a 1-resilient function if and only if E CI (f) has rank n. We know from Theorem 2 that L(f) = 2 i for some i ≥ n/2 and that the number of zero Walsh coefficients of f is |E CI (f)| = 2 n − 2 2n−2i .…”

Section: -If N Is Even Then F Is Either Bent or It Satisfies L(f) = mentioning

confidence: 99%

Propagation Characteristics and Correlation-Immunity of Highly Nonlinear Boolean Functions

Advances in Cryptology — EUROCRYPT 2000

Carlet

Charpin

et al. 2000

Self Cite

Abstract. We investigate the link between the nonlinearity of a Boolean function and its propagation characteristics. We prove that highly nonlinear functions usually have good propagation properties regarding different criteria. Conversely, any Boolean function satisfying the propagation criterion with respect to a linear subspace of codimension 1 or 2 has a high nonlinearity. We also point out that most highly nonlinear functions with a three-valued Walsh spectrum can be transformed into 1-resilient functions.

“…It is well-known that a combining function must fulfill some criteria to yield a cryptographically secure combination generator (see e.g. [3]). Most notably, combination generators are vulnerable to "divide-and-conquer" attacks, called correlation attacks [17].…”

Section: Mod 2 Wherē U Denotes the Bitwise Completion To 1 And Wt(u) mentioning

confidence: 99%

Ciphertext only Reconstruction of Stream Ciphers Based on Combination Generators

Fast Software Encryption

Filiol

2001

Self Cite

Abstract. This paper presents an operational reconstruction technique of most stream ciphers. We primarily expose it for key-stream generators which consist of several linear feedback shift registers combined by a nonlinear Boolean function. It is shown how to completely recover the different feedback polynomials and the combining function, when the algorithm is totally unknown. This attack only requires the knowledge of some ciphertexts, which may be generated from different secret keys. Estimates of necessary ciphertext length and experimental results are detailed.