A common approach to protect confidential information is to use a stream cipher which combines plain text bits with a pseudo-random bit sequence. Among the existing stream ciphers, Non-Linear Feedback Shift Register (NLFSR)based ones provide the best trade-off between cryptographic security and hardware efficiency. In this paper, we show how to further improve the hardware efficiency of Grain s...

We give a polynomial time algorithm for computing the Igusa local zeta function Z(s, f) attached to a polynomial f(x) ∈ Z[x], in one variable, with splitting field Q, and a prime number p. We also propose a new class of linear feedback shift registers based on the computation of Igusa’s local zeta function.

Nonlinear filter generators are common components used in the keystream generators for stream ciphers and more recently for authentication mechanisms. They consist of a Linear Feedback Shift Register (LFSR) and a nonlinear Boolean function to mask the linearity of the LFSR output. Properties of the output of a nonlinear filter are not well studied. Anderson noted that the m-tuple output of a no...

Clock control is one of the mechanisms employed to introduce non-linearity into key stream generators built from linear feedback shift registers. The earliest devices were built from stop-and-go registers while the most recent example, the Shrinking Generator proposed in [2], has an irregular clocking scheme where the number of steps between successive outputs is linked to the length of zero-ru...

We describe a solution for physically obfuscating the representation of a cipher, to augment chips resistance against physical threats, by combining ideas from masking techniques and Physical Obfuscated Keys (POKs). With embedded chips – like RFID tags – as main motivation, we apply this strategy to the representation of a Linear Feedback Shift Register (LFSR). The application of this technique...

Delft In this paper the problem of finding the absolutely shortest (possibly nonlinear) feedback shift register, which can generate a given sequence with characters from some arbitrary finite alphabet, is considered. To this end, a new complexity measure is defined, called the maximum order complexity. A new theory of the nonlinear feedback shift register is developed, concerning elementary com...

An arithmetic or with-carry analog of Blahut’s theorem is presented. This relates the length of the smallest feedback with carry shift register to the number of nonzero classical Fourier coefficients of a periodic binary sequence.

We give the results of a computer search for maximally equidistributed combined linear feedback shift register (or Tausworthe) random number generators, whose components are trinomials of degrees slightly less than 32 or 64. These generators are fast and have good statistical properties.

In this paper, a lemma in algebraic coding theory is established, which is frequently appeared in the encoding and decoding for algebraic codes such as Reed–Solomon codes and algebraic geometry codes. This lemma states that two vector spaces, one corresponds to information symbols and the other is indexed by the support of Gröbner basis, are canonically isomorphic, and moreover, the isomorphism...

Many proposals of pseudorandom sequence generators and stream ciphers employ linear feedback shift registers with dynamic feedback (DLFSR) as the main module to increase the period and linear span of the involved msequences. In this paper, we present a theoretical model that allows the design of longer sequences with higher linear span than in previous DLFSR schemes. The model determines the co...