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{SECT 0 {EXCHG {PARA 3 "" 0 "" {TEXT -1 58 "Maple Summer Workshop 2004
: Programming in Maple Tutorial." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 
26 "RSA Public Key Encryption." }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 27 "Michael Monagan, June 2004." }}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 256 "" 0 "" {TEXT -1 124 "These Maple programs \+
 illustrate strings in Maple, tables, and modular arithmetic.  Then we
 make the routines into a module." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 87 "Here \+
is a string, the letters in the alphabet that we'll use for encryption
/decryption." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "alphabet :=
 \"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz .,!\";" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)alphabetGQYABCDEFGHIJKLMNOPQRSTUVWX
YZabcdefghijklmnopqrstuvwxyz~.,!6\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "length(alphabet);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
\"#c" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Here are the operations o
n strings that we will use. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 12 "alphabet[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q\"B6\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "alphabet[2..3];" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#Q#BC6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 31 "cat(\"I'm\", \" \", \"hungry\", \"!\");" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#Q,I'm~hungry!6\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
36 "Now encoding the letters as integers" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 84 "for i to length(alphabet) do\n    l := alphabet[i]; C
ode[l] := i; Letter[i] := l \nod:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "Letter[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q\"B6\"
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "Code[\"B\"];" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
54 "The alphabet does include a space in position 53 note." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "Code[\" \"];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"#`" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 250 "Now here \+
is the encryption function for encrypting a message.  We convert the s
tring to a list of single letters (one must to encrypt this way but th
is is for illustration).  Then we  encrypt the codes one at a time usi
ng the RSA encryption exponent " }{TEXT 256 1 "e" }{TEXT -1 13 " and m
odulus " }{TEXT 257 1 "n" }{TEXT -1 63 ".  Decryption is the reverse u
sing the RSA decryption exponent " }{TEXT 258 1 "d" }{TEXT -1 13 " and
 modulus " }{TEXT 259 1 "n" }{TEXT -1 64 ", and then converting the co
des back to the letters and message." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 242 "encrypt := proc(message,e,n) local letters,codes,cyp
hertext,i,x;\n    letters := [seq(message[i],i=1..length(message))];\n
    codes := [seq( Code[letters[i]], i=1..length(message) )];\n    cyp
hertext := [seq( x &^ e mod n, x = codes )];\n    end:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 217 "decrypt := proc(cyphertext,d,n)\nl
ocal codes, letters, y, i, message;\n    codes := [seq( y &^ d mod n, \+
y = cyphertext )];\n    letters := [seq( Letter[codes[i]], i=1..nops(c
odes) )];\n    message := cat(op(letters))\nend:" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 219 "In RSA, one finds two (large) primes, p and q, co
mputes their product n, and pubishes n together with e as the public k
ey.  A user converts a message into a sequence of numbers and encodes \+
a number x using the function." }}}{EXCHG {PARA 11 "" 1 "" {XPPMATH 
20 "6#/%\"mG-%$modG6$)%\"xG%\"eG%\"nG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 37 "p := 101; q := 103; n := p*q; e := 7;" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"pG\"$,\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"qG\"$.\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"&./\"" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"eG\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "message := \"hello\";\n" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%(messageGQ&hello6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
15 "trace(encrypt);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%(encryptG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "encoding := encrypt(message,
e,n);" }}{PARA 9 "" 1 "" {TEXT -1 44 "\{--> enter encrypt, args = \"he
llo\", 7, 10403" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(lettersG7'Q\"h6
\"Q\"eF'Q\"lF'F)Q\"oF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&codesG7'
\"#M\"#J\"#QF(\"#T" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+cyphertextG7'
\"%\\v\"%r!)\"%<wF(\"%l@" }}{PARA 9 "" 1 "" {TEXT -1 69 "<-- exit encr
ypt (now at top level) = [7549, 8071, 7617, 7617, 2165]\}" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%)encodingG7'\"%\\v\"%r!)\"%<wF(\"%l@" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 " To get " }{XPPEDIT 18 0 "x;" "6#%
\"xG" }{TEXT -1 6 " from " }{XPPEDIT 18 0 "m;" "6#%\"mG" }{TEXT -1 20 
" we have to compute " }{XPPEDIT 18 0 "`mod`(m^(1/e),n);" "6#-%$modG6$
)%\"mG*&\"\"\"F)%\"eG!\"\"%\"nG" }{TEXT -1 34 " .  To do this we need \+
to compute " }{XPPEDIT 18 0 "`mod`(1/e,phi(n));" "6#-%$modG6$*&\"\"\"F
'%\"eG!\"\"-%$phiG6#%\"nG" }{TEXT -1 43 " where, since we know the fac
torization of " }{XPPEDIT 18 0 "n;" "6#%\"nG" }{TEXT -1 16 " , we know
 that " }{XPPEDIT 18 0 "phi(n) = (p-1)*(q-1);" "6#/-%$phiG6#%\"nG*&,&%
\"pG\"\"\"F+!\"\"F+,&%\"qGF+F+F,F+" }{TEXT -1 35 ".  Thus the secret d
ecryption key  " }{XPPEDIT 18 0 "d = `mod`(1/e,(p-1)*(q-1));" "6#/%\"d
G-%$modG6$*&\"\"\"F)%\"eG!\"\"*&,&%\"pGF)F)F+F),&%\"qGF)F)F+F)" }
{TEXT -1 23 " .  This requires that " }{XPPEDIT 18 0 "GCD(e,(p-1)*(q-1
)) = 1;" "6#/-%$GCDG6$%\"eG*&,&%\"pG\"\"\"F+!\"\"F+,&%\"qGF+F+F,F+F+" 
}{TEXT -1 11 " .  We have" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
23 "igcd( e, (p-1)*(q-1) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 101 "We now calculate the secret \+
decryption key which the user keeps secret, along with the primes p & \+
q. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "d := 1/e mod (p-1)*(
q-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG\"%V()" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "e*d mod (p-1)*(q-1);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 15 "trace(decrypt);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%(decryptG" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "decrypt( encoding, d, n );
" }}{PARA 9 "" 1 "" {TEXT -1 70 "\{--> enter decrypt, args = [7549, 80
71, 7617, 7617, 2165], 8743, 10403" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%&codesG7'\"#M\"#J\"#QF(\"#T" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(le
ttersG7'Q\"h6\"Q\"eF'Q\"lF'F)Q\"oF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%(messageGQ&hello6\"" }}{PARA 9 "" 1 "" {TEXT -1 46 "<-- exit decryp
t (now at top level) = \"hello\"\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
Q&hello6\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 385 "We remark that today, one can factor one hundred digit n
umbers.  It is considered safe if the primes are both of the order of \+
one hundred digits.  So n is two hundred digits long.  No known factor
ization algorithms would be able to factor a two hundred digit number \+
in a reasonable length of time.  Now we redo this encrypting a bock of
 10 letters at a time using a 20 digits modulus.\n" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 27 "p := nextprime(8113120951);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"pG\"+j578\")" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "q := nextprime(4766101972);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"qG\"+\")>5mZ" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 9 "n := p*q;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"5.e7d/Pizm
Q" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "e := 34781001071047370
39;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"eG\"4Rqt/r5+\"yM" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "d := 1/e mod (p-1)*(q-1);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG\"5fxSa8eHqeI" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 545 "encrypt := proc(message,e,n,BL) \nlocal \+
letters,codes,cyphertext,i,x,N,block,q,blocks,r;\n    letters := [seq(
message[i],i=1..length(message))];\n    N := length(alphabet)+1;\n    \+
codes := [seq( Code[letters[i]], i=1..length(message) )];\n    block :
= L -> add(L[i]*N^(i-1),i=1..BL);\n    q := iquo(nops(codes),BL,'r');
\n    if r>0 then # pad with BL-r blanks \n       codes := [op(codes),
Code[\" \"]$(BL-r)]; \n       q := q+1 \n    fi;\n    blocks := [seq( \+
block(codes[5*(i-1)+1..BL*i]), i=1..q )];\n    cyphertext := [seq( x &
^ e mod n, x = blocks )];\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 15 "trace(encrypt);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%(encryptG
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "cyphertext := encrypt(m
essage,e,n,5);" }}{PARA 9 "" 1 "" {TEXT -1 148 "\{--> enter encrypt, a
rgs = \"This is the day that the Lord has made, let us rejoice and be \+
glad in it!\", 3478100107104737039, 38667962370457125803, 5" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#>%(lettersG7eoQ\"T6\"Q\"hF'Q\"iF'Q\"sF'Q\"~F
'F)F*F+Q\"tF'F(Q\"eF'F+Q\"dF'Q\"aF'Q\"yF'F+F,F(F/F,F+F,F(F-F+Q\"LF'Q\"
oF'Q\"rF'F.F+F(F/F*F+Q\"mF'F/F.F-Q\",F'F+Q\"lF'F-F,F+Q\"uF'F*F+F3F-Q\"
jF'F2F)Q\"cF'F-F+F/Q\"nF'F.F+Q\"bF'F-F+Q\"gF'F6F/F.F+F)F:F+F)F,Q\"!F'
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG\"#d" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%&codesG7eo\"#?\"#M\"#N\"#X\"#`F(F)F*\"#YF'\"#JF*\"#I
\"#F\"#^F*F+F'F.F+F*F+F'F,F*\"#7\"#T\"#WF-F*F'F.F)F*\"#RF.F-F,\"#bF*\"
#QF,F+F*\"#ZF)F*F2F,\"#OF1F(\"#HF,F*F.\"#SF-F*\"#GF,F*\"#LF5F.F-F*F(F9
F*F(F+\"#c" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&blockGf*6#%\"LG6\"6$%
)operatorG%&arrowGF(-%$addG6$*&&9$6#T#\"\"\")T%,&F3F4F4!\"\"F4/F3;F4T(
F(F(6(%\"iG%\"iG%\"NG%\"NG%#BLG\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%\"qG\"#9" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&codesG7go\"#?\"#M\"
#N\"#X\"#`F(F)F*\"#YF'\"#JF*\"#I\"#F\"#^F*F+F'F.F+F*F+F'F,F*\"#7\"#T\"
#WF-F*F'F.F)F*\"#RF.F-F,\"#bF*\"#QF,F+F*\"#ZF)F*F2F,\"#OF1F(\"#HF,F*F.
\"#SF-F*\"#GF,F*\"#LF5F.F-F*F(F9F*F(F+\"#cF*F*" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"qG\"#:" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'blocks
G71\"*6u\"zc\"*4xfn$\"*%ycMa\"*)R*o!\\\"*x@Kl&\"*[\"p^c\"*Yqk@%\"*Chvp
&\"*N&)41&\"*TI!fQ\"*$H0`c\"*MI[0$\"*I'f@H\"*RD*pc\"*$)yYp&" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#>%+cyphertextG71\"5#z$3)*pLU&)eB\"5$>kjw)em6
@E\"5@%o.!R!H9$RM\"5-R=+eWh;XH\"41M)pXnbW)3$\"5L;5]br@K<I\"3\\.bd1(Hq/
*\"4&)3#zBji1'\\(\"5+-%HNl^*f5L\"5+jxUa4[0[G\"5AV'Hh[7\"GfG\"5)>s6u-A3
f<#\"5<zqAm%=G.s\"\"4OhN7*>np)3%\"5yEsI%))y9$QH" }}{PARA 9 "" 1 "" 
{TEXT -1 364 "<-- exit encrypt (now at top level) = [23588542336998083
792, 26211166588766364193, 34393142903900368421, 29451661445800183902,
 3088445567456983406, 30173221715550101633, 904702970657550349, 749606
6263237920885, 33105995165352940200, 28480548095442776300, 28592811248
612964322, 21759082202741172198, 17203281846622707917, 408869671991235
6136, 29383147888430722678]\}" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%+cy
phertextG71\"5#z$3)*pLU&)eB\"5$>kjw)em6@E\"5@%o.!R!H9$RM\"5-R=+eWh;XH
\"41M)pXnbW)3$\"5L;5]br@K<I\"3\\.bd1(Hq/*\"4&)3#zBji1'\\(\"5+-%HNl^*f5
L\"5+jxUa4[0[G\"5AV'Hh[7\"GfG\"5)>s6u-A3f<#\"5<zqAm%=G.s\"\"4OhN7*>np)
3%\"5yEsI%))y9$QH" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 167 "Here is a r
outine to convert an integer to an integer in base B, N digits base B.
  The example shows the number 00012345 base 100 being converted to 5 \+
base 100 digits." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "base :
= proc(a,B,N) local L,b;\n       b := a;\n       L := NULL; to N do L \+
:= L,irem(b,B,'b') od; [L];\n    end: " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "base(12345,100,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#7&\"#X\"#B\"\"\"\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 305 "
decrypt := proc(cyphertext,d,n,BL)\nlocal blocks,codes,letters,message
;\n    blocks := [seq( x &^ d mod n, x = cyphertext )];\n    blocks :=
 map(base,blocks,1+length(alphabet),BL);\n    codes := map(op,blocks);
\n    letters := [seq( Letter[codes[i]], i=1..nops(codes) )];\n    mes
sage := cat(op(letters));\nend: " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "trace(decrypt);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%(
decryptG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "decrypt(cyphert
ext,d,n,5);" }}{PARA 9 "" 1 "" {TEXT -1 399 "\{--> enter decrypt, args
 = [23588542336998083792, 26211166588766364193, 34393142903900368421, \+
29451661445800183902, 3088445567456983406, 30173221715550101633, 90470
2970657550349, 7496066263237920885, 33105995165352940200, 284805480954
42776300, 28592811248612964322, 21759082202741172198, 1720328184662270
7917, 4088696719912356136, 29383147888430722678], 30587029581354407759
, 38667962370457125803, 5" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'blocks
G71\"*6u\"zc\"*4xfn$\"*%ycMa\"*)R*o!\\\"*x@Kl&\"*[\"p^c\"*Yqk@%\"*Chvp
&\"*N&)41&\"*TI!fQ\"*$H0`c\"*MI[0$\"*I'f@H\"*RD*pc\"*$)yYp&" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#>%'blocksG717'\"#?\"#M\"#N\"#X\"#`7'F)F*F+\"
#YF(7'\"#JF+\"#I\"#F\"#^7'F+F-F(F1F-7'F+F-F(F/F+7'\"#7\"#T\"#WF0F+7'F(
F1F*F+\"#R7'F1F0F/\"#bF+7'\"#QF/F-F+\"#Z7'F*F+F8F/\"#O7'F7F)\"#HF/F+7'
F1\"#SF0F+\"#G7'F/F+\"#LF>F17'F0F+F)FEF+7'F)F-\"#cF+F+" }}{PARA 12 "" 
1 "" {XPPMATH 20 "6#>%&codesG7go\"#?\"#M\"#N\"#X\"#`F(F)F*\"#YF'\"#JF*
\"#I\"#F\"#^F*F+F'F.F+F*F+F'F,F*\"#7\"#T\"#WF-F*F'F.F)F*\"#RF.F-F,\"#b
F*\"#QF,F+F*\"#ZF)F*F2F,\"#OF1F(\"#HF,F*F.\"#SF-F*\"#GF,F*\"#LF5F.F-F*
F(F9F*F(F+\"#cF*F*" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(lettersG7goQ
\"T6\"Q\"hF'Q\"iF'Q\"sF'Q\"~F'F)F*F+Q\"tF'F(Q\"eF'F+Q\"dF'Q\"aF'Q\"yF'
F+F,F(F/F,F+F,F(F-F+Q\"LF'Q\"oF'Q\"rF'F.F+F(F/F*F+Q\"mF'F/F.F-Q\",F'F+
Q\"lF'F-F,F+Q\"uF'F*F+F3F-Q\"jF'F2F)Q\"cF'F-F+F/Q\"nF'F.F+Q\"bF'F-F+Q
\"gF'F6F/F.F+F)F:F+F)F,Q\"!F'F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%(messageGQfoThis~is~the~day~that~the~Lord~has~made,~let~us~rejoice~an
d~be~glad~in~it!~~6\"" }}{PARA 9 "" 1 "" {TEXT -1 116 "<-- exit decryp
t (now at top level) = \"This is the day that the Lord has made, let u
s rejoice and be glad in it!  \"\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
QfoThis~is~the~day~that~the~Lord~has~made,~let~us~rejoice~and~be~glad~
in~it!~~6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1351 "RSA := mod
ule()\n   export encrypt, decrypt;\n   local UnBlock,alphabet,Code,Let
ter,N,i,l,BlockLength;\n\nalphabet := \"ABCDEFGHIJKLMNOPQRSTUVWXYZabcd
efghijklmnopqrstuvwxyz .,!\";\nN := length(alphabet);\nfor i to N do l
 := alphabet[i]; Code[l] := i; Letter[i] := l; od;\nN := N+1;\n\nBlock
Length := proc(n) local B; for B from 1 while N^B < n do od; B-1 end;
\nUnBlock := proc(a,B) local L,b;\n       b := a;\n       L := NULL; t
o B do L := L,irem(b,N,'b') od; [L];\nend;\n\nencrypt := proc(message,
e,n) \nlocal letters,codes,cyphertext,i,x,block,q,blocks,r,BL;\n    BL
 := BlockLength(n);\n    letters := [seq(message[i],i=1..length(messag
e))];\n    codes := [seq( Code[letters[i]], i=1..length(message) )];\n
    block := proc(L) local i; add(L[i]*N^(i-1),i=1..BL) end;\n    q :=
 iquo(nops(codes),BL,'r');\n    if r>0 then # pad with BL-r blanks \n \+
      codes := [op(codes),Code[\" \"]$(BL-r)]; \n       q := q+1 \n   \+
 fi;\n    blocks := [seq( block(codes[BL*(i-1)+1..BL*i]), i=1..q )];\n
    cyphertext := [seq( x &^ e mod n, x = blocks )];\nend:\n\ndecrypt \+
:= proc(cyphertext,d,n)\nlocal blocks,codes,letters,message,BL;\n    B
L := BlockLength(n);\n    blocks := [seq( x &^ d mod n, x = cyphertext
 )];\n    blocks := map(UnBlock,blocks,BL);\n    codes := map(op,block
s);\n    letters := [seq( Letter[codes[i]], i=1..nops(codes) )];\n    \+
message := cat(op(letters));\nend:\n\nend module;\n      " }}{PARA 12 
"" 1 "" {XPPMATH 20 "6#>%$RSAG`6$%(encryptG%(decryptGb6#%+thismoduleG6
*%(UnBlockG%)alphabetG%%CodeG%'LetterG%\"NG%\"iG%\"lG%,BlockLengthG6\"
6$%(encryptG%(decryptGF5F5F5F56\"6*%(UnBlockG%)alphabetG%%CodeG%'Lette
rG%\"NG%\"iG%\"lG%,BlockLengthG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 10 "p,q,n,e,d;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'\"+j578\")\"+\")
>5mZ\"5.e7d/PizmQ\"4Rqt/r5+\"yM\"5fxSa8eHqeI" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 8 "message;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#QdoTh
is~is~the~day~that~the~Lord~has~made,~let~us~rejoice~and~be~glad~in~it
!6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "cyphertext := RSA:-
encrypt(message,e,n);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%+cyphertext
G7)\"4&HP$)e-<a&y#\"5m7))*G/hp2&H\"5&*pp$4pPZ+c\"\"5O]o(*)[(z/qE\"4)R%
Hvhk@)>&*\"5X&z\"G?z(4;?$\"5lF@%HL9@Fd#" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 29 "RSA:-decrypt(cyphertext,d,n);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#QhoThis~is~the~day~that~the~Lord~has~made,~let~us~rejoi
ce~and~be~glad~in~it!~~~~6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}}{MARK "4 0 0" 17 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
{PAGENUMBERS 0 1 2 33 1 1 }