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Article overview
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Restricted linear congruences and an authenticated encryption scheme | | Khodakhast Bibak
; Bruce M. Kapron
; Venkatesh Srinivasan
; Roberto Tauraso
; László Tóth
; | | Date: |
5 Mar 2015 | | Abstract: | In this paper, using properties of Ramanujan sums and of the finite Fourier
transform of arithmetic functions, we give an explicit formula for the number
of solutions of the linear congruence $a_1x_1+cdots +a_kx_kequiv b pmod{n}$,
with $(x_i,n)=t_i$ ($1leq ileq k$), where $a_1,t_1,ldots,a_k,t_k, b,n$
($ngeq 1$) are arbitrary integers. Some special cases of this problem have
been studied in many papers, and have found very interesting applications in
number theory, combinatorics, and cryptography, among other areas. We also
propose an authenticated encryption scheme, and using our explicit formula,
analyze the integrity of this scheme. | | Source: | arXiv, 1503.1806 | | Services: | Forum | Review | PDF | Favorites | |
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