Narrow Results

Rabbit is a stream cipher proposed by M. Boesgaard et al., and has been selected into the final portfolio after three evaluation phases of the ECRYPT Stream Cipher Project (eSTREAM). So far only a few papers studied its security besides a series of white papers by the designers of Rabbit. Recently we presented a new idea to evaluate the security of a word-oriented stream cipher algorithm from a smaller data granularity instead of its original data granularity and applied it successfully to the stream cipher SOSEMANUK. In this work we apply the same idea to the Rabbit algorithm and analyze its security in resistance against the guess and determine attack from the view point of byte units. As a result, we present two new approaches of solving all x_j,t+1's and g_j,t's from the next-state function and the extraction scheme of Rabbit, whose complexities are 2¹⁶⁶ and 2^140.68 respectively, which are dramatically lower than those proposed by Lu et al. (2¹⁹² and 2¹⁷⁴ resp.) at ISC 2008. Finally based on the above new results we propose a byte-based guess and determine attack on Rabbit, which only needs a small segment of known keystream to recover the whole internal state of Rabbit with time complexity 2²⁴². Though the complexity of our attack is far higher than that of a brute force (2¹²⁸), we believe that some new techniques adopted in this paper are of interest for future work on Rabbit.

Recently, Tang, Carlet and Tang presented a combinatorial conjecture about binary strings, allowing proving that all balanced functions in some infinite class they introduced have optimal algebraic immunity. Later, Cohen and Flori completely proved that the conjecture is true. These functions have good (provable or at least observable) cryptographic properties but they are not 1-resilient, which represents a drawback for their use as filter functions in stream ciphers. We propose a construction of an infinite class of 1-resilient Boolean functions with optimal algebraic immunity by modifying the functions in this class. The constructed functions have optimal algebraic degree, that is, meet the Siegenthaler bound, and high nonlinearity. We prove a lower bound on their nonlinearity, but as for the Carlet-Feng functions and for the functions mentioned above, this bound is not enough for ensuring a nonlinearity sufficient for allowing resistance to the fast correlation attack. Nevertheless, as for previously found functions with the same features, there is a gap between the bound that we can prove and the actual values computed for small numbers of variables. Our computations show that the functions in this class have very good nonlinearity and also good immunity to fast algebraic attacks. This is the first time that an infinite class of functions gathers all of the main criteria allowing these functions to be used as filters in stream ciphers.

In this paper, we propose a new necessary condition for feedback functions of de Bruijn sequences and discuss its application in constructing de Bruijn sequences. It is shown that a large number of de Bruijn sequences could be easily constructed by precomputing an $n$-stage nonlinear feedback shift register (NFSR) with a special cycle structure—that is, if a state $s$ is on a cycle generated by this NFSR, then all the states with the same Hamming weight as $s$ are also on this cycle. Moreover, if there are $s+1$ different cycles in the state graph of the precomputed NFSR, then we can construct $\left(\genfrac{}{}{0.0pt}{}{n-1}{k_1}\right)\left(\genfrac{}{}{0.0pt}{}{n-1}{k_2}\right)\cdots \left(\genfrac{}{}{0.0pt}{}{n-1}{k_s}\right)$ de Bruijn sequences by the different choices of conjugate state pairs, where $0\le k_1<k_2<\cdots <k_s\le n-1$.

In this paper, we present a pseudo-random bit generator (PRBG) based on two lag time series of the logistic map using positive and negative values in the bifurcation parameter. In order to hidden the map used to build the pseudo-random series we have used a delay in the generation of time series. These new series when they are mapped x_n against x_n+1 present a cloud of points unrelated to the logistic map. Finally, the pseudo-random sequences have been tested with the suite of NIST giving satisfactory results for use in stream ciphers.

A one-way coupled chaotic map lattice is used for generating pseudo-random numbers. It is shown that with suitable cooperative applications of both chaotic and conventional approaches, the output of the spatiotemporally chaotic system can easily meet the practical requirements of random numbers, i.e., excellent random statistical properties, long periodicity of computer realizations, and fast speed of random number generations. This pseudo-random number generator system can be used as ideal synchronous and self-synchronizing stream cipher systems for secure communications.

The General Packet Radio Service (GPRS) uses the GPRS Encryption Algorithm 3 (GEA3) for data encryption. In this paper, alternative hardware implementations of the GEA3 algorithm are described. GEA3 algorithm is based on the KASUMI block cipher. Various KASUMI block cipher hardware implementations have been examined in order to provide information about the required silicon area and throughput. In order to achieve a significant performance improvement, Double Edge Triggered pipeline technique is used. The S-BOXes, which are fundamental elements of the KASUMI cipher, have been implemented by using combinational logic and ROM memories. The proposed GEA3 algorithm hardware implementation achieves throughput up to 837Mbps, which is much faster comparing to the previous designs. The whole system is implemented and evaluated by using Field Programmable Gate Array (FPGA) devices.

The use of quantum-dot cellular automata (QCA) technology for the design of logic circuits has shown to increase data transfer rates up to 2 THz. In QCA technology, circuits are designed to have an ultra-small feature size as well as ultra-low power consumption. Grain-128 is one of the best stream ciphers in the final list of the eSTREAM project. In this paper, we have designed and simulated the main blocks of this algorithm including XOR gate, linear-feedback shift register (LFSR) and nonlinear-feedback shift register (NLFSR) using QCA technology. The designs of these blocks using the QCA Designer simulator are given and the main factors such as area, complexity and delay are estimated. Furthermore, ModelSim software is used to simulate HDLQ model of the QCA Grain-128 stream cipher algorithm. The results indicate that the main parameters of the proposed Grain-128, such as area and throughput, are improved as well.

Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudo-random properties. The linear complexity of a period sequence plays a fundamental role in the randomness of sequences. In this paper, we construct a new family of quaternary generalized cyclotomic sequences with order $2d$ and length $2p^m$, which generalize the sequences constructed by Ke et al. in 2012. In addition, we determine its linear complexity using cyclotomic theory. The conclusions reveal that these sequences have high linear complexity, which means they can resist linear attacks.

Several reasonably cyclotomic sequences are constructed by cyclotomic classes having good pseudo-randomness property. In this paper, we derive the linear complexity of an extended binary cyclotomic sequences of order $2^{l}t$ over finite field having period $pq$. Our result shows that these sequences have higher linear complexity, which can resist linear attack.

The problem of software generation of the Generalized Self-Shrinking (GSS) sequence is considered. An efficient algorithm with low space complexity is proposed, which takes advantage of the special structure of the GSS. Several methods are discussed and a new block-oriented method is introduced. Then, a two-sequences-combined model is explored to make the algorithm more efficient. A comparison of the experiment result shows that it is competitive with other stream ciphers.

Single cycle invertible functions(SCIF) are studied in this paper. We show that if β + γ = k2^n-a, 2^aβ + α ≡ 1 (mod 4), and α + k ≡ C ≡ 1 (mod 2), g(x) = αx + β(x ⋙ b) + γ(x ≫ b) + C is a single cycle invertible function and some cryptographic properties are studied; new ways based on SCIF and linear feedback shift registers are introduced to generate longer periods state which can be used as the state transition function in stream ciphers. At last, a new stream cipher proposal which is based on SCIF and LFSR is introduced and its cryptographic properties are studied.