Cryptanalysis of the "Grain" family of stream ciphers

Maximov, Alexander

doi:10.1145/1128817.1128859

Cited by 24 publications

(19 citation statements)

References 29 publications

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“…Linear Approximations. In [30] it is explained how to find a time-invariant biased linear relation between the LFSR bits and the keystream bits for Grain family of stream ciphers. This bias depends on the nonlinearity and the resiliency of the NLFSR update and of the output functions.…”

Section: Security Discussionmentioning

confidence: 99%

On Lightweight Stream Ciphers with Shorter Internal States

Armknecht

Mikhalev

2015

Lecture Notes in Computer Science

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Abstract. To be resistant against certain time-memory-data-tradeoff (TMDTO) attacks, a common rule of thumb says that the internal state size of a stream cipher should be at least twice the security parameter. As memory gates are usually the most area and power consuming components, this implies a sever limitation with respect to possible lightweight implementations. In this work, we revisit this rule. We argue that a simple shift in the established design paradigm, namely to involve the fixed secret key not only in the initialization process but in the keystream generation phase as well, enables stream ciphers with smaller area size for two reasons. First, it improves the resistance against the mentioned TMDTO attacks which allows to choose smaller state sizes. Second, one can make use of the fact that storing a fixed value (here: the key) requires less area size than realizing a register of the same length. We demonstrate the feasibility of this approach by describing and implementing a concrete stream cipher Sprout which uses significantly less area than comparable existing lightweight stream ciphers.

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Section: Security Discussionmentioning

confidence: 99%

On Lightweight Stream Ciphers with Shorter Internal States

Armknecht

Mikhalev

2015

Lecture Notes in Computer Science

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“…The Grain stream cipher [17,18] uses this structure to produce keystream output bits. Some security analyses have been published in [2,21,9]. Figure 3 shows the structure of the design, which combines a LF-NLFSR with a filter generator.…”

Section: Lf-nlfsr and Lfsrmentioning

confidence: 99%

Security analysis of linearly filtered NLFSRs

Orumiehchiha

Pieprzyk

Steinfeld

et al. 2013

Journal of Mathematical Cryptology

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Abstract. Our contributions are applying distinguishing attack on Linearly Filtered NLFSR as a primitive or associated with filter generators. We extend the attack on linear combinations of Linearly Filtered NLFSRs as well. Generally, these structures can be examined by the proposed techniques and the criteria will be achieved to design secure primitive. The attacks allow attacker to mount linear attack to distinguish the output of the cipher and recover its internal state. Also, we investigate security of the modified version of Grain stream cipher to present how invulnerable is the scheme against distinguishing attacks.

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“…For example, a (4, k)-NLFSR going through the following 16 states: 1, 3, 0, 2, 8,5,7,6,9,11,4,10,14,13,15,12 generates the output sequence 1100011011000110 which has the period 8. For the Fibonacci type of NLFSRs, the period is always equal to the length of the longest cycle of states.…”

Section: Relation Between the Length Of The Longest Cycle Ofmentioning

confidence: 99%

“…A number of different implementations of NLFSRbased stream ciphers for RFID and smartcards applications have been proposed, including Achterbahn [12], Grain [13], [14], KeeLoq [15], Trivium [16], VEST [17], and [18]. NLFSRs have been shown to be more resistant to cryptanalytic attacks than LFSRs [19], [20].…”

Section: Introductionmentioning

confidence: 99%

On analysis and synthesis of ( n, k )-non-linear feedback shift registers

Dubrova

Teslenko

Tenhunen

2008

Proceedings of the Conference on Design, Automation and Test in Europe

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Abstract-Non-Linear Feedback Shift Registers (NLFSRs) have been proposed as an alternative to Linear Feedback Shift Registers (LFSRs) for generating pseudo-random sequences for stream ciphers. In this paper, we introduce (n, k)-NLFSRs which can be considered a generalization of the Galois type of LFSR. In an (n, k)-NLFSR, the feedback can be taken from any of the n bits, and the next state functions can be any Boolean function of up to k variables. Our motivation for considering this type NLFSRs is that their Galois configuration makes it possible to compute each next state function in parallel, thus increasing the speed of output sequence generation. Thus, for stream cipher application where the encryption speed is important, (n, k)-NLFSRs may be a better alternative than the traditional Fibonacci ones. We derive a number of properties of (n, k)-NLFSRs. First, we demonstrate that they are capable of generating output sequences with good statistical properties which cannot be generated by the Fibonacci type of NLFSRs. Second, we show that the period of the output sequence of an (n, k)-NLFSR is not necessarily equal to the length of the largest cycle of its states. Third, we compute the period of an (n, k)-NLFSR constructed from several parallel NLFSRs whose outputs are XOR-ed and show how to maximize this period. We also present an algorithm for estimating the length of cycles of states of (n, k)-NLFSRs which uses Binary Decision Diagrams for representing the set of states and the transition relation on this set.

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Cryptanalysis of the "Grain" family of stream ciphers

Cited by 24 publications

References 29 publications

On Lightweight Stream Ciphers with Shorter Internal States

On Lightweight Stream Ciphers with Shorter Internal States

Security analysis of linearly filtered NLFSRs

On analysis and synthesis of ( n, k )-non-linear feedback shift registers

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