Revisiting LFSMs

Linear Finite State Machines (LFSMs) are particular primitives widely used in information theory, coding theory and cryptography. Among those linear automata, a particular case of study is Linear Feedback Shift Registers (LFSRs) used in many cryptographic applications such as design of stream ciphers or pseudo-random generation. LFSRs could be seen as particular LFSMs without inputs. In this paper, we first recall the description of LFSMs using traditional matrices representation. Then, we introduce a new matrices representation with polynomial fractional coefficients. This new representation leads to sparse representations and implementations. As direct applications, we focus our work on the Windmill LFSRs case, used for example in the E0 stream cipher and on other general applications that use this new representation. In a second part, a new design criterion called diffusion delay for LFSRs is introduced and well compared with existing related notions. This criterion represents the diffusion capacity of an LFSR. Thus, using the matrices representation, we present a new algorithm to randomly pick LFSRs with good properties (including the new one) and sparse descriptions dedicated to hardware and software designs. We present some examples of LFSRs generated using our algorithm to show the relevance of our approach.Comment: Submitted to IEEE-I

Immunotronics - novel finite-state-machine architectures with built-in self-test using self-nonself differentiation

A novel approach to hardware fault tolerance is demonstrated that takes inspiration from the human immune system as a method of fault detection. The human immune system is a remarkable system of interacting cells and organs that protect the body from invasion and maintains reliable operation even in the presence of invading bacteria or viruses. This paper seeks to address the field of electronic hardware fault tolerance from an immunological perspective with the aim of showing how novel methods based upon the operation of the immune system can both complement and create new approaches to the development of fault detection mechanisms for reliable hardware systems. In particular, it is shown that by use of partial matching, as prevalent in biological systems, high fault coverage can be achieved with the added advantage of reducing memory requirements. The development of a generic finite-state-machine immunization procedure is discussed that allows any system that can be represented in such a manner to be "immunized" against the occurrence of faulty operation. This is demonstrated by the creation of an immunized decade counter that can detect the presence of faults in real tim