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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 47 "Parsing text into r-digi
t numbers to given base" }}{PARA 19 "" 0 "" {TEXT -1 55 "Mike O'Sulliv
an\nSan Diego State University\nJanuary 2005" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 87 " With some cryptosystems it is useful to combine severa
l  letters into a single number." }}{PARA 0 "" 0 "" {TEXT -1 96 "If th
ere are N letters in the alphabet, we may combine r of these letters t
o produce an integer " }}{PARA 0 "" 0 "" {TEXT -1 68 "between 0 and N^
r.  The letters x_\{r-1\}, ...,x_0 become the integer " }}{PARA 0 "" 
0 "" {TEXT -1 30 "x_\{r-1\}*N^\{r-1\}+...+x_1*N +x_0" }}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 14 "The procedures" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 96 "These following two proce
duress allow us to take a list of numbers between 0 and N and produce \+
a" }}{PARA 0 "" 0 "" {TEXT -1 107 "Vector that will be  input to a cry
ptosystem.  Parse_rgraphs() takes as input the list of numbers, p_nums
; " }}{PARA 0 "" 0 "" {TEXT -1 245 " the base, N and  the number of di
gits, r,  in which the vector components are to be written.  We assume
 that the entries in p_nums are  nonnegative integers less than N.  Th
e output of Psrse_rgraphs() is a Vector of integers  between 0 and N^r
." }}{PARA 0 "" 0 "" {TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 179 "Th
e reverse procedure is Decompose_rgraphs() which takes a vector--whose
 components are positive integers less than N^r-- and returns a list o
f positive integers all less than N. " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 375 "Parse_rgraphs := proc (p_nums, N, r) \nlocal i, j, k
, len, p_vec, new_digit; \n\nlen := ceil(nops(p_nums)/r); #Find the  \+
\np_vec := Vector(len); \nk := 0; \nfor i to len do \n   k := (i-1)*r;
 \n   for j to r do \n     if k+j <= nops(p_nums) then \n        new_d
igit := p_nums[k+j] \n     else new_digit := 0 end if; \n   p_vec[i] :
= p_vec[i]*N+new_digit \n   od; \nod;\nRETURN(p_vec); \nend;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 366 "Decompose_rgraphs := proc (
d_vec, N, r) \nlocal i, j, temp_list, d_nums, temp; \n\nd_nums := []; \+
\ntemp_list := [seq(0,i = 1 .. r)]; \nfor i to LinearAlgebra[Dimension
](d_vec) do \n   temp := d_vec[i]; \n   for j from 0 to r-1 do \n     \+
 temp_list[r-j] := irem(temp,N); \n      temp := iquo(temp,N);\n    od
; \n   d_nums := [op(d_nums), op(temp_list)];\nod;\nRETURN(d_nums);\ne
nd;" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 
3 "" 0 "" {TEXT -1 7 "Example" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 46 "h:=[12, 3, 12, 43, 54, 66, 54, 67, 82, 45,12];" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 24 "Parse_rgraphs(h, 100,2);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Decompose_ngraphs(%,100,2);" }}}}
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