Research On Several Driven Components In Stream Ciphers

Driven component is an important part in stream cipher, which provides source sequencefor stream cipher with large period and good pseudorandomness properties. It influences thesecurity of stream cipher directly. With the development of NESSIE and ECRYPT projects,several new designs of stream ciphers and driven components have appeared. Hardware orientedstream ciphers are usually based on feedback shift register, such as NFSR used in Grain andTrivium. Software oriented stream ciphers are usually based on driven components over finitefield, such as LFSR over finite field used in Snow and round function of block cipher used inLEX. The research on these new driven components and structures are not mature, and needfurther analysis. In this paper, we focus on several driven components, and our contributionsmainly include the following parts:1. For the Fibonacci NFSR-based combiner with memory, we give the necessary andsufficient conditions where the update transformation of inner state are bijective, and give threestructures with such property.2. For Grain-like cascade model and Trivium-like cascade model based on Fibonacci NFSR,we analyze the bijectivity of their state update transformations, show the constructions of suchmodel with bijective state update transformations. Moreover, we give the necessary andsufficient condition where the state update transformation of bit-oriented Trivium-like cascademode is bijective.3. For Galois NFSR over finite field, the necessary and sufficient condition for thenonsingularity of Galois NFSR is proposed, and three constructions of nonsingular Galois NFSRare proposed. And for combiner with memory and cascade model based on Galois NFSR, wegive the constructions with bijective state update transformation.4. For Galois NFSR and Fibonacci NFSR over finite field, we show the necessary andsufficient conditions of state update transformations being orthomorphic permutation. Then, theconstructions of such Galois NFSRs and Fibonacci NFSR are proposed.5. For leak extraction model which uses the round function of block cipher as state updatetransformation, we investigate how the extract locations influence the security of LEX cipher.We analyze the ability of such cipher whose extract locations are the same in both even and oddround against guess and determine attack, and prove that LEX whoes extract locations aredifferent in even and odd round may provide higher security level.6. A related key attack on LEX cipher is presented, if239.5bytes keysteams under tworelated keys are obtained, we can recover the entire key of LEX with only2100.3AES encryptoperations, and the success rate is1.