This is a procedure for converting ordinary text (plaintext) to padded ASCII numbers. It takes as input a sentence written between ' and ', and also the size parameter "modulus". Then it chops the sentence into parts so that the padded versions of these parts will be smaller than the size parameter. Then it pads these parts one after another, and returns the padded parts as a list, listed in the order of occurrence of the parts. It 'pads' by adding 100 to each list item.

with(numtheory): ASCIIPad:=proc(Message,Modulus) local L, K, l, x, y, p, r, M, j, i, z; L:= length(Modulus); K:=convert(Message,bytes); l:=nops(K); ########################################################################## y:=floor(L/3)-1; #Correct here by inserting "-1". It was just floor(L/3). # April 4, 2007 # if ( l mod y = 0) then ########################################################################## p:= l/y; r:= 0; else p:= floor(l/y)+1; r:= 1; fi: M := [seq(x[i],i=1..p)]; ############################################################################# if (r = 0) then for j from 1 to p do x[j]:=0; for i from 1 to y do if (i < y) then x[j]:= (x[j] + (100 + K[(j-1)*y+i]))*1000; else x[j]:= (x[j] + (100 + K[j*y])); fi: od: od: ############################################################################# elif ( p = 1) then x[1]:=0; for i from 1 to l do if (i < l) then x[1]:= (x[1] + (100 + K[i]))*1000; else x[1]:= (x[1] + (100 + K[i])); fi: od: ############################################################################# else for j from 1 to p do x[j]:=0; if (j < p) then for i from 1 to y do if (i < y) then x[j]:= (x[j] + (100 + K[(j-1)*y+i]))*1000; else x[j]:= (x[j] + (100 + K[j*y])); fi: od: else z := l mod y; for i from 1 to z do if (i < z) then x[j]:= (x[j] + (100 + K[(p-1)*y+i]))*1000; else x[j]:= (x[j] + (100 + K[(p-1)*y+z])); fi: od: fi: od: fi: RETURN(M): end:

This procedure takes as input the output of ASCIIPad, and returns how many padded ASCII packets there are, as well as the individual packets.

ReadPadded:=proc(X) local j: printf("There are %d packets\134n",nops(X)): for j from 1 to nops(X) do printf("Packet %d: %d\134n",j, op(j,X)): od: end:

This procedure checks a packet in the Padded ASCII list produced by ASCIIPad to see if it really is padded ASCII. The output is "true" if it is padded ASCII, and "false" otherwise.

CheckPadding:=proc(X) local i, j, Y: Y:=X: if (length(X) mod 3 > 0) then RETURN(false) else for i from 1 to (length(X)/3) do j:= Y mod 1000; if (j < 100 or j > 355) then RETURN(false): fi: Y:= (Y - j)/1000: od: RETURN(true): fi: end:

The input is a sequence of padded ASCII numbers (packets), and the output is the original message of which these are the packets.

ASCIIDepad:=proc(Expression) local k, l, M, i, j, N, X, Y; l:=nops(Expression); Y:="": for j from 1 to l do if (CheckPadding(op(j,Expression)) = false) then printf(" This is not a padded ASCII string.\134n"); RETURN(NULL): else M:= op(j,Expression); k:=length(M): for i from 1 to (k/3) do X[i]:=((M mod 10^(k-3*(i-1)) - (M mod 10^(k-3*i)))/(10^(k-3*i)))-100; if (i = 1) then N:=[X[i]]; else N:=[op(N),X[i]]; fi: od: fi: Y:= cat(Y,convert(N,bytes)): od: RETURN(Y); end:

with(numtheory): usqrt:=proc(R) local ur: ur:=isqrt(R); if(ur^2<R) then ur:=ur+1: fi: RETURN(ur): end: FermatAttack:=proc(R,r) local x,y,st,sq: st:=usqrt(R): for x from st to (st+r) do sq:=x^2-R: if(issqr (sq)=true) then printf("Factor found in round %d rounds\134n",x-st+1); y:=isqrt(sq): RETURN(x+y): fi: od: printf("No factors found in %d rounds\134R",r): end:

p:=nextprime(9^51);q:=nextprime(9^51+199);n:=p*q:phin:=(p-1)*(q-1):x:=823727281201: e:=1/x mod phin: printf("PUBLIC KEY:\134n n=%d\134n e=%d\134n\134nPRIVATE KEY:%d\134n",n,e,x);

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PUBLIC KEY: n=21514733098945856316441287084898149773167909666891634793053927140101627434191087599176402926563077 e=5961845582634761597404254251537324648550729369485832117593700950678428573698903043708430160403681 PRIVATE KEY:823727281201

text:="Cyber Security":X:=ASCIIPad(text,n):printf("Cyber Security\134n"):E:=X[1]&^e mod n: printf("The encrypted message that Bob sends to Alice is %d\134n",E):

Cyber Security The encrypted message that Bob sends to Alice is 16154900154973686118089694866378698280069578812849295627767099236869952191142129985694743024950490

DD:=E&^x mod n:ASCIIDepad(DD);

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FermatAttack(n,e);

Factor found in round 1 rounds

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