Encoding Program
This program will accept sender blocks of size 2 and will encrypt and convert to receiver
blocks of size 3. The user needs to enter the integer digits into the integer list. After
choosing values for p, q and i the program converts those integer digits to base 10,
encrypts and then converts back to integer digits.
Choosing p, q, and i:
> restart;
> p:=ithprime(35);
p := 149
> q:=ithprime(29);
q := 109
> n:=p*q;
n := 16241
> i:=43;
i := 43
>
Entering integer digits:
The list integers contains the integer digits from the message that is to be encrypted.
The list integersencrypted is set to the original integers but they will be changed later.
>
integers:=[[2,14],[13,6],[18,0],[19,20],[11,0],[19,8],[14,1
3],[18,26],[24,14],[20,26],[6,14],[19,26],[0,13],[26,0],[27
,29],[28,29]]:
> num:=nops(integers);
num := 16
>
integersencrypted:=[[2,14],[13,6],[18,0],[19,20],[11,0],[19
,8],[14,13],[18,26],[24,14],[20,26],[6,14],[19,26],[0,13],[
26,0],[27,29],[28,29]]:
> numenc:=nops(integersencrypted);
numenc := 16
>
Converting integer digits to base 10:
This procedure and loop converts the integer digits in the list integers to base 10
assuming they were in base 30.
It returns all the converted values.
> base:= proc(L,k)
local T, x, y:
T:= op(L):
x:=T[k,1]:
y:=T[k,2]:
x*30+y:
end;
base :=
proc(L, k) local T, x, y; T := op( L ) ; x := T[ k, 1 ] ; y := T[ k, 2 ] ; 30xy end proc
> for k from 1 to num do
conv[k]:=base(integers,k):
od;
conv 1 := 74
conv 2 := 396
conv 3 := 540
conv 4 := 590
conv 5 := 330
conv 6 := 578
conv 7 := 433
conv 8 := 566
conv 9 := 734
conv 10 := 626
conv 11 := 194
conv 12 := 596
conv 13 := 13
conv 14 := 780
conv 15 := 839
conv 16 := 869
>
Encryption:
The encryption function h will be used to encrypt all the values in the array conv.
> h:=x->x^i mod n;
h := xx i mod n
> for k from 1 to num do
encry[k]:=h(conv[k]):
od;
encry 1 := 10122
encry 2 := 7688
encry 3 := 10920
encry 4 := 9964
encry 5 := 13630
encry 6 := 4436
encry 7 := 6535
encry 8 := 14684
encry 9 := 15575
encry 10 := 9454
encry 11 := 2438
encry 12 := 4023
encry 13 := 6047
encry 14 := 2505
encry 15 := 13767
encry 16 := 11222
>
Converting back to integer digits:
This loop converts all the encrypted values back to integer digit blocks of size 3 and
stores them in the list integersencrypted.
> for k from 1 to num do
x1:=trunc(encry[k]/30^2):
x2:=trunc((encry[k]-(x1*30^2))/30):
x3:=encry[k] mod 30:
integersencrypted:=subsop(k=[x1,x2,x3],integersencrypted):
od:
> integersencrypted;
[ [ 11, 7, 12 ], [ 8, 16, 8 ], [ 12, 4, 0 ], [ 11, 2, 4 ], [ 15, 4, 10 ], [ 4, 27, 26 ], [ 7, 7, 25 ],
[ 16, 9, 14 ], [ 17, 9, 5 ], [ 10, 15, 4 ], [ 2, 21, 8 ], [ 4, 14, 3 ], [ 6, 21, 17 ], [ 2, 23, 15 ],
[ 15, 8, 27 ], [ 12, 14, 2 ] ]
>