##########################################################################
#
#                    RSA Encryption Algorithm
#
#                   (Miguel A. Lerma, 8/15/95)
#
# This file contains a function to compute large random primes, and two 
# functions to convert a string of text into a number and vice versa. 
#
##########################################################################


# Load Number Theory library.

with(numtheory):


# This function generates an n-digit random prime number by the 
# probabilistic Solovay and Strassen's method.

large_random_prime := 
       proc(n_digits) local m1,m2,a,b,n:
          m2 := (10^n_digits)/2:
          m1 := m2/10+1:
          is_prime := `false`:
          while(not is_prime) do
             b := 2*rand(m1..m2)()-1:
             is_prime := `true`:
             for n from 1 to 100 do
                a := rand(1..b-1)():
                if gcd(a,b) <> 1 or (J(a,b) - a&^((b-1)/2)) mod b <> 0 
                   then is_prime := `false`: break:
                fi:
             od:
          od:
          RETURN(b):
       end:


# Next function transforms a string into a number.

text_to_number := 
    proc(T1) local k1,M1,l1:
       M1 := 0:
       for k1 to length(T1) do 
          l1 :=  substring(T1,k1..k1):
          if l1 = '_' then d1:=10 
          elif l1 = 'a' then d1 := 11
          elif l1 = 'b' then d1 := 12
          elif l1 = 'c' then d1 := 13
          elif l1 = 'd' then d1 := 14
          elif l1 = 'e' then d1 := 15
          elif l1 = 'f' then d1 := 16
          elif l1 = 'g' then d1 := 17
          elif l1 = 'h' then d1 := 18
          elif l1 = 'i' then d1 := 19
          elif l1 = 'j' then d1 := 20
          elif l1 = 'k' then d1 := 21
          elif l1 = 'l' then d1 := 22
          elif l1 = 'm' then d1 := 23
          elif l1 = 'n' then d1 := 24
          elif l1 = 'o' then d1 := 25
          elif l1 = 'p' then d1 := 26
          elif l1 = 'q' then d1 := 27
          elif l1 = 'r' then d1 := 28
          elif l1 = 's' then d1 := 29
          elif l1 = 't' then d1 := 30
          elif l1 = 'u' then d1 := 31
          elif l1 = 'v' then d1 := 32
          elif l1 = 'w' then d1 := 33
          elif l1 = 'x' then d1 := 34
          elif l1 = 'y' then d1 := 35
          elif l1 = 'z' then d1 := 36
          else ERROR(`Use only lower case letters or underscore.`)
          fi:
          M1 := 100*M1+d1:
       od: 
       M1:
    end:


# List of letters used to transform a number into text.

L1 :=  ['_',''a'',''b'',''c'',''d'',''e'',''f'',''g'',''h'',''i'',''j'',
''k'',''l'',''m'',''n'',''o'',''p'',''q'',''r'',''s'',''t'',''u'',''v'',
''w'',''x'',''y'',''z'']:


# Next function trasforms a number into a string of text.

number_to_text :=
      proc(M1) local T1, r1, M2:
         M2 := M1:
         T1 := ``:
         while(M2 > 0) do
            M2 := iquo(M2,100,'r1'):
            T1 := cat(L1[r1-9],T1):
         od:
         T1:
      end: