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What is the best (thoroughly covering) textbook for application of LFSRs in cryptography?

(Beside Cipher Systems by Beker & Piper)

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Requests for reference recommendations are off-topic here. For details, see: Do we want “literature recommendations” and similar “list/subjective questions”? –  e-sushi Dec 18 '13 at 16:51
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1 Answer

You can start with chapter 6 of the Handbook of Applied Cryptography (which can furthermore be downloaded for free). But a rough summary is that LFSR are much less used nowadays in cryptography than what they used to be; most LFSR-based stream ciphers turned out to be weak in some way. The main advantage of LFSR is that they are extremely cheap to implement in a circuit (e.g. a dedicated ASIC), but the World at large is increasingly shifting towards software: we now put full 32-bit ARM cores in smart cards, and encryption algorithms follow the trend by being optimized for low-end software platforms.

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Indeed, "the World at large is increasingly shifting towards software" and "we now put full 32-bit ARM cores in smart cards". But the later is a dubious example of the former. We shift to software except when a device which security matters could end in the hands of an adversary. Recent Smart Cards with ARM core tend to have hardware for 3DES, AES, RSA, and ECDSA, see e.g. this and this –  fgrieu Dec 18 '13 at 16:38
    
@fgrieu: perhaps it's better put this way: "transistors are currently real cheap, and so current designs tend to be tuned for things other than minimal transistor count". –  poncho Dec 18 '13 at 16:47
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@poncho: yes, "transistors are currently real cheap, and so current designs tend to be tuned for things other than minimal transistor count" is one the many good reasons why "LFSR are much less used nowadays in cryptography". –  fgrieu Dec 18 '13 at 16:58
    
@Thomas Pornin: It may be premature to be writing-off LFSR's for several reasons. There are several PRNG's based on LFSR's that we have no polynomial time algorithms for breaking (Alternating Step Generator for one). Also nonlinear feedback shift registers is still a relatively new field whose algebraic properties are still not completely understood , so it is a rich field to explore (my opinion). –  William Hird Dec 25 '13 at 16:01
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