Elaboration of selfish-mine strategy

As it was shown by Ittay Eyal and Emin Gun Sirer, the Bitcoin mining protocol is not incentive-compatible, because there exists an attack in which colluding miners obtain a revenue larger than their fair share. We describe an elaboration of Selfish-Mine Strategy and present an extended model of selfish mining based on independency hypothesis: both groups are made their work independently from each other. We describe a new state machine modelling selfish pool strategy. Let the selfish pool has mining power of p, 0 < p < 1/2, and the others of (1 - p). We also consider the situation in which the others mine a block on the previously private branch (frequency 7(1 - p)), and the others mine a block on the public branch (frequency (1 - 7)(1 - p)). Main result is an elaboration of an interval, in which selfish miners will earn more than their relative mining power: 1) for a given p, a pool of size p obtains a revenue larger than its relative size for p in the following range: 0 < p ^ 0.429 (the left bound coinsides with 7 =1, and the right bound coinsides with 7 = 0); 2) for a given p, a pool of size p obtains a revenue larger than a revenue of other group in the following range: 0.358 ^ p ^ 0.449. Keywords: blockchain, mining, Markov model, state machine. Bonich T.A., Panferov M.A., Tokareva N.N. ON THE NUMBER OF UNSUITABLE BOOLEAN FUNCTIONS IN CONSTRUCTIONS OF FILTER AND COMBINING MODELS OF STREAM CIPHERS. It is well known that every stream cipher is based on a good pseudorandom generator. For cryptographic purposes, we are interested in generation of pseudorandom sequences of the maximal possible period. A feedback register is one of the most known cryptographic primitives that is used in construction of stream generators. We analyze periodic properties of pseudorandom sequences produced by filter and combiner generators equipped with nonlinear Boolean functions. We determine which nonlinear functions in these schemes lead to pseudorandom sequences of not maximal possible period. We call such functions unsuitable and count the exact number of them for an arbitrary n.

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