• Journal of Communications and Networks
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• v.13 no.1
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• pp.1-5
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• 2011

Feedback with carry shift registers (FCSRs) over 2-adic number would be suitable in hardware implementation, but the are not efficient in software implementation since their basic unit (the size of register clls) is 1-bit. In order to improve the efficiency we consider FCSRs over $2^{\ell}$-adic number (i.e., FCSRs with register cells of size ${\ell}$-bit) that produce ${\ell}$ bits at every clocking where ${\ell}$ will be taken as the size of normal words in modern CPUs (e.g., ${\ell}$ = 32). But, it is difficult to deal with the carry that happens when the size of summation results exceeds that of normal words. We may use long variables (declared with 'unsigned _int64' or 'unsigned long long') or conditional operators (such as 'if' statement) to handle the carry, but both the arithmetic operators over long variables and the conditional operators are not efficient comparing with simple arithmetic operators (such as shifts, maskings, xors, modular additions, etc.) over variables of size ${\ell}$-hit. In this paper, we propose some conditions for FCSRs over $2^{\ell}$-adic number which admit fast software implementations using only simple operators. Moreover, we give two implementation examples for the FCSRs. Our simulation result shows that the proposed methods are twice more efficient than usual methods using conditional operators.

• The KIPS Transactions:PartC
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• v.8C no.1
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• pp.12-15
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• 2001

A summation generator creates sequence from addition with carry of LFSR (Linear Feedback Shift Register) sequences. Similarly, it is possible to generate keystream by bitwise exclusive-oring on two FCSR sequences. In this paper, we described the cryptographic properties of a sequence generated by the FCSRs.

• Journal of KIISE:Computer Systems and Theory
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• v.32 no.10
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• pp.507-511
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• 2005

We have derived the linear complexity of a binary sequence generated by a Feedback with Carry Shift Regiater(FCSR) under the following condition: q is a power of a prime such that $q=r^e,\;(e{\geq}2)$ and r=2p+1, where both r and p are 2-prime. Also, a summation generator creates sequence from addition with carry of LFSR(Linear Feedback Shift Register) sequences. Similarly, it is possible to generate keystream by bitwise exclusive-oring on two FCSR sequences. In this paper, we described the cryptographic properties of a sequence generated by the FCSRs in view of the linear complexity.