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- Feedback_with_Carry_Shift_Registers abstract "In sequence design, a Feedback with Carry Shift Register (or FCSR) is the arithmetic or with carry analog of a Linear feedback shift register (LFSR). If is an integer, then an N-ary FCSR of length is a finite state device with a state consisting of a vector of elements in and an integer . The state change operation is determined by a set of coefficients and is defined as follows: compute . Express s as with in . Then the new state is . By iterating the state change an FCSR generates an infinite, eventually period sequence of numbers in .FCSRs have been used in the design of stream ciphers (such as the F-FCSR generator), in the cryptanalyis of the summation combiner stream cipher (the reason Goresky and Klapper invented them), and in generating pseudorandom numbers for quasi-Monte Carlo (under the name Multiply With Carry (MWC) generator - invented by Couture and L'Ecuyer,) generalizing work of Marsaglia and Zaman.FCSRs are analyzed using number theory. Associated with the FCSR is a connection integer . Associated with the output sequence is the N-adic number The fundamental theorem of FCSRs says that there is an integer so that , a rational number. The output sequence is strictly periodic if and only if is between and . It is possible to express u as a simple quadratic polynomial involving the initial state and the qi.There is also an exponential representation of FCSRs: if is the inverse of , and the output sequence is strictly periodic, then , where is an integer. It follows that the period is at most the order of N in the multiplicative group of units modulo q. This is maximized when q is prime and N is a primitive element modulo q. In this case, the period is . In this case the output sequence is called an l-sequence (for "long sequence").l-sequences have many excellent statistical properties that make them candidates for use in applications, including near uniform distribution of sub-blocks, ideal arithmetic autocorrelations, and the arithmetic shift and add property. They are the with-carry analog of m-sequences or maximum length sequences.There are efficient algorithms for FCSR synthesis. This is the problem: given a prefix of a sequence, construct a minimal length FCSR that outputs the sequence. This can be solved with a variant of Mahler and De Weger's lattice based analysis of N-adic numbers when by a variant of the Euclidean algorithm when N is prime; and in general by Xu's adaptation of the Berlekamp-Massey algorithm. If L is the size of the smallest FCSR that outputs the sequence (called the N-adic complexity of the sequence), then all these algorithms require a prefix of length about to be successful and have quadratic time complexity. It follows that, as with LFSRs and linear complexity, any stream cipher whose N-adic complexity is low should not be used for cryptography.FCSRs and LFSRs are special cases of a very general algebraic construction of sequence generators called Algebraic Feedback Shift Registers (AFSRs) in which the integers are replaced by an arbitrary ring R and N is replaced by an arbitrary non-unit in R. A general reference on the subject of LFSRs, FCSRs, and AFSRs is the book.".
- Feedback_with_Carry_Shift_Registers wikiPageID "24737769".
- Feedback_with_Carry_Shift_Registers wikiPageRevisionID "601887949".
- Feedback_with_Carry_Shift_Registers hasPhotoCollection Feedback_with_Carry_Shift_Registers.
- Feedback_with_Carry_Shift_Registers subject Category:Cryptographic_algorithms.
- Feedback_with_Carry_Shift_Registers subject Category:Cryptography.
- Feedback_with_Carry_Shift_Registers subject Category:Digital_registers.
- Feedback_with_Carry_Shift_Registers subject Category:Pseudorandom_number_generators.
- Feedback_with_Carry_Shift_Registers subject Category:Stream_ciphers.
- Feedback_with_Carry_Shift_Registers type Abstraction100002137.
- Feedback_with_Carry_Shift_Registers type Act100030358.
- Feedback_with_Carry_Shift_Registers type Activity100407535.
- Feedback_with_Carry_Shift_Registers type Algorithm105847438.
- Feedback_with_Carry_Shift_Registers type Cipher106254239.
- Feedback_with_Carry_Shift_Registers type Communication100033020.
- Feedback_with_Carry_Shift_Registers type CryptographicAlgorithms.
- Feedback_with_Carry_Shift_Registers type DigitalRegisters.
- Feedback_with_Carry_Shift_Registers type Event100029378.
- Feedback_with_Carry_Shift_Registers type Evidence106643408.
- Feedback_with_Carry_Shift_Registers type Indication106797169.
- Feedback_with_Carry_Shift_Registers type Message106253690.
- Feedback_with_Carry_Shift_Registers type Procedure101023820.
- Feedback_with_Carry_Shift_Registers type PsychologicalFeature100023100.
- Feedback_with_Carry_Shift_Registers type Record106647206.
- Feedback_with_Carry_Shift_Registers type Register106507041.
- Feedback_with_Carry_Shift_Registers type Rule105846932.
- Feedback_with_Carry_Shift_Registers type StreamCiphers.
- Feedback_with_Carry_Shift_Registers type WrittenRecord106502378.
- Feedback_with_Carry_Shift_Registers type YagoPermanentlyLocatedEntity.
- Feedback_with_Carry_Shift_Registers comment "In sequence design, a Feedback with Carry Shift Register (or FCSR) is the arithmetic or with carry analog of a Linear feedback shift register (LFSR). If is an integer, then an N-ary FCSR of length is a finite state device with a state consisting of a vector of elements in and an integer . The state change operation is determined by a set of coefficients and is defined as follows: compute . Express s as with in . Then the new state is .".
- Feedback_with_Carry_Shift_Registers label "Feedback with Carry Shift Registers".
- Feedback_with_Carry_Shift_Registers label "Registri a scorrimento a retroazione con riporto".
- Feedback_with_Carry_Shift_Registers label "Регистр сдвига с обратной связью по переносу".
- Feedback_with_Carry_Shift_Registers sameAs Registri_a_scorrimento_a_retroazione_con_riporto.
- Feedback_with_Carry_Shift_Registers sameAs m.080h9k_.
- Feedback_with_Carry_Shift_Registers sameAs Q3931998.
- Feedback_with_Carry_Shift_Registers sameAs Q3931998.
- Feedback_with_Carry_Shift_Registers sameAs Feedback_with_Carry_Shift_Registers.
- Feedback_with_Carry_Shift_Registers wasDerivedFrom Feedback_with_Carry_Shift_Registers?oldid=601887949.
- Feedback_with_Carry_Shift_Registers isPrimaryTopicOf Feedback_with_Carry_Shift_Registers.