We study algebraic feedback shift registers (AFSRs) based on quotients of polynomial rings in several variables over a finite field. These registers are natural generalizations of linear feedback shift registers. We describe conditions under which such AFSRs produce sequences with various ideal randomness properties. We also show that there is an efficient algorithm which, given a prefix of a s...

Feedback with carry shift registers (FCSRs) are a class of finite state devices that are similar to linear feedback shift registers (LFSRs) in their simplicity and statistical randomness, and in that they have algebraic tools for the analysis of their output. In this paper we describe and analyze an alternative architecture for FCSRs that is similar to the Galois architecture for LFSRs. We also...

Recently, a new class of feedback shift registers (FCSRs) was introduced, based on algebra over the 2-adic numbers. The sequences generated by these registers have many algebraic properties similar to those generated by linear feedback shift registers. However, it appears to be significantly more difficult to find maximal period FCSR sequences. Jn this paper we exhibit a tpchnique for easily fi...

Recently, a new class of feedback shift registers (FCSRs) was introduced, based on algebra over the 2-adic numbers. The sequences generated by these registers have many algebraic properties similar to those generated by linear feedback shift registers. However, it appears to be significantly more difficult to find maximal period FCSR sequences. In this paper we exhibit a technique for easily fi...

Arithmetic function modules which are available in many circuits can be utilized to generate test patterns and compact test responses. Recently, it was shown that an adder or an accumulator cannot be used as a bit serial test pattern generator due to the poor random properties of the generated sequences. Thus, accumulator-multiplier or adder-multiplier structures have been proposed. In this pap...

Anewsoftware-baseddtestvectorcompressionn technique is proposedd for usingg ann embeddedd processor too test the other components of aa system-on-a-chipp (SOC). The tester transfers compressedd test dataa too the processor's on-chipp memory, andd the processor executes aa small program whichh decompresses the dataa andd applies it too the scann chains of eachh core-under-test. The proposedd dec...

An algorithm is given for the reconstruction of the initial state of a key–stream generator (KSG) consisting of a short linear feedback shift register (length ≤ 30), whose clock is controlled by an algebraically simple internal KSG. The algorithm is based on the fact that the expected number of possible LFSR initial states exponentially decreases with the length of the known part of the output ...

Using the structure of Singer cycles in general linear groups, we prove that a conjecture of Zeng, Han and He (2007) holds in the affirmative in a special case, and outline a plausible approach to prove it in the general case. This conjecture is about the number of primitive σ-LFSRs of a given order over a finite field, and it generalizes a known formula for the number of primitive LFSRs, which...

In this correspondence we determine the linear complexity of all Legendre sequences and the (monic) feedback polynomial of the shortest linear feedback shift register that generates such a Legendre sequence. The result of this correspondence shows that Legendre sequences are quite good from the linear complexity viewpoint.