CryptographywithLB103

=Cryptology=Cryptography with Liberty BASIC : 103= 
//author//103 RSA Algorithm= 
Onur Alver (//CryptoMan//)
[[toc|flat]]
----
=First Part Title= 
Text here.**RSA ALGORITHM**
RSA Algorithm is based on the assumption on the difficulty of factoring large composite numbers.
Demonstration Program


[[code format="lb"]]
dim stats(11)
dim SmallPrimes(1000)

[begin]
    print "Liberty Basic RSA Demonstration"
    print "Loading Small Primes"
    for i=1 to 1000
        read x
        SmallPrimes(i)=x
    next
    NoOfSmallPrimes=1000
    print NoOfSmallPrimes;" Primes Loaded"
    print"Generating Random Primes"

    for i=1 to 2
        t1=time$("ms")

        [TryAnother]
        print
        print "Prime No ";i
        if i=1 then x=Random(30) else x=Random(30)
        iterations=0

        [Loop]
        iterations=iterations+1
        if MillerRabin(x,7)=1 then
            'print "Composite"
            x=x+2
            goto [Loop]
        else
            t2=time$("ms")
            print x;" Probably Prime. Generated in ";t2-t1;" milliseconds"
        end if
        if p then q=x else p=x
    next i
    print
    print "p=";dechex$(p)

[Retry]
    restore
    print "q=";dechex$(q)

    'Common modulus N=(p)(q)
    n=p*q
    print "Key Length ";len(dechex$(n))*4;" bits "
    print

    'Euler Totient Number M=(p-1)(q-1)
    m=(p-1)*(q-1)

    'Choose a suitable prime E relatively prime to M
    for i=1 to 12
        read e
        if (GCD(e,m)=1) then goto [Start]
    next i

[Start]
    print "Common Modulus, n=";dechex$(n)
    print "Euler-Totient No, m=";dechex$(m)
    print "Public Exponent, e=";dechex$(e)
    d=ExtBinEuclid( e, m )
    print "Secret Exponent, d=";dechex$(d)


    DIM TEST(10)
    DIM ENCR(10)
    DIM DECR(10)
    TEST(1)=TEXT2DEC("LIBERTY BASIC IS THE BEST")
    TEST(2)=TEXT2DEC("WHICH BASIC CAN DO THIS ")
    TEST(3)=TEXT2DEC("WITHOUT CALLING EXT DLL ?")
    TEST(4)=TEXT2DEC("LB CAN DO BIG INTEGERS ! ")
    TEST(5)=TEXT2DEC("UNDOCUMENTED LB FEATURE. ")
    print
    print "RSA ENCRYPTION DEMO"
    for i=1 to 5
        t1=time$("ms")
        ENCR(i)=FastExp(TEST(i), e, n)
        t2=time$("ms")
        print TEST(i);
        print " ";ENCR(i);
        print " ";t2-t1;" ms"
        print DEC2TEXT$( TEST(i) );" --> ";DEC2TEXT$( ENCR(i) )
        print
    next i
    print
    print ""
    print
    print "RSA DECRYPTION DEMO"
    for i=1 to 5
        t1=time$("ms")
        DECR(i)=FastExp(ENCR(i), d, n)
        t2=time$("ms")
        print ENCR(i);
        print " ";DECR(i);
        print " ";t2-t1;" ms"
        print DEC2TEXT$( ENCR(i) );" --> ";DEC2TEXT$( DECR(i) )
        print
    next i
    print " "
    print
    print "RSA Demo Finished."

[stop]
END

Function GCD( m,n )
    ' Find greatest common divisor with Extend Euclidian Algorithm
    ' Knuth Vol 1 P.13 Algorithm E
    ap =1 :b =1 :a =0 :bp =0: c =m :d =n
    [StepE2]
    q = int(c/d) :r = c-q*d
    if r<>0 then
        c=d :d=r :t=ap :ap=a :a=t-q*a :t=bp :bp=b :b=t-q*b
        'print ap;" ";b;" ";a;" ";bp;" ";c;" ";d;" ";t;" ";q
        goto [StepE2]
    end if
    GCD=a*m+b*n
    'print ap;" ";b;" ";a;" ";bp;" ";c;" ";d;" ";t;" ";q

End Function 'Extended Euclidian GCD

Function ExtBinEuclid( u, v )
    k=0 :t1=0 :t2=0 :t3=0
    if u<v then
        temp=u
        u=v
        v=temp
    end if
    while (IsEven( u ) and IsEven( v ))
        k = k+1
        u = int(u/2)
        v = int(v/2)
    wend
    u1 = 1: u2 = 0: u3 =u: t1 =v: t2 =u-1: t3 =v

    [Loop1]
    'two labels with no code!

    [Loop2]
    ' print "*"
    if (IsEven(u3)) then
        if IsOdd(u1) or IsOdd(u2) then
            u1=u1+v
            u2=u2+u
        end if
        u1=int(u1/2)
        u2=int(u2/2)
        u3=int(u3/2)
    end if
    if IsEven(t3) or (u3<t3) then
        temp=u1: u1=t1: t1=temp
        temp=u2: u2=t2: t2=temp
        temp=u3: u3=t3: t3=temp
    end if
    if IsEven(u3) then
        goto [Loop2]
    end if

    while u1<t1 OR u2<t2
        u1=u1+v: u2=u2+u
    wend
    u1=u1-t1: u2=u2-t2: u3=u3-t3
    if (t3>0) then
        goto [Loop1]
    end if

    while u1>=v AND u2>=u
        u1=ul-v: u2=u2-u
    wend
    ExtBinEuclid=u-u2
End Function

function IsEven( x )
    if ( x MOD 2 )=0 then
        IsEven=1
    else
        IsEven=0
    end if
end function

function IsOdd( x )
    if ( x MOD 2 )=0 then
        IsOdd=0
    else
        IsOdd=1
    end if
end function


Function FastExp(x, y, N)
    if (y=1) then 'MOD(x,N)
        FastExp=x-int(x/N)*N
        goto [ExitFunction]
    end if
    if ( y and 1) = 0 then
        dum1=y/2
        dum2=y-int(y/2)*2 'MOD(y,2)
        temp=FastExp(x,dum1,N)
        z=temp*temp
        FastExp=z-int(z/N)*N 'MOD(temp*temp,N)
        goto [ExitFunction]
    else
        dum1=y-1
        dum1=dum1/2
        temp=FastExp(x,dum1,N)
        dum2=temp*temp
        temp=dum2-int(dum2/N)*N 'MOD(dum2,N)
        z=temp*x
        FastExp=z-int(z/N)*N 'MOD(temp*x,N)
        goto [ExitFunction]
    end if

    [ExitFunction]
end function

Function PowMod( a, n, m)
    r = 1
    while (n > 0)
        if (n AND 1) then '/* test lowest bit */
            r = MulMod(r, a, m) '/* multiply (mod m) */
        end if
        a = MulMod(a, a, m) '/* square */
        n = int(n/2) '/* divided by 2 */
    wend
    PowMod=r
End Function

Function MulMod( a, b, m)
    if (m = 0) then
        MulMod=a * b ' /* (mod 0) */
    Else
        r = 0
        while (a > 0)
            if (a AND 1) then ' /* test lowest bit */
                r= r+b
                if (r > m) then
                    r = (r MOD m) ' /* add (mod m) */
                end if
            end if
            a = int(a/2) ' /* divided by 2 */
            b = b*2
            if (b > m) then
                b = (b MOD m) ' /* times 2 (mod m) */
            end if
        wend
        MulMod=r
    End If
End Function


Function rand( x )
    x=x*5
    x=x+1
    rand=x
End Function

Function MillerRabin(n,b)
    'print "Miller Rabin"
    't1=time$("ms")
    if IsEven(n) then
        MillerRabin=1
        goto [ExtFn]
    end if
    i=0

    [Loop]
    i=i+1
    if i>1000 then goto [Continue]
    if ( n MOD SmallPrimes(i) )=0 then
        MillerRabin=1
        goto [ExtFn]
    end if
    goto [Loop]

    [Continue]
    if GCD(n,b)>1 then
        MillerRabin=1
        goto [ExtFn]
    end if
    q=n-1
    t=0
    while (int(q) AND 1 )=0
        t=t+1
        q=int(q/2)
    wend
    r=FastExp(b, q, n)
    if ( r <> 1 ) then
        e=0
        while ( e < (t-1) )
            if ( r <> (n-1) ) then
                r=FastExp(r, r, n)
            else
                Exit While
            end if
            e=e+1
        wend
        [ExitLoop]
    end if
    if ( (r=1) OR (r=(n-1)) ) then
        MillerRabin=0
    else
        MillerRabin=1
    end if

[ExtFn]
End Function


Function Random( Digits )
' x=INT(RND(1)*TIME$("ms")*9912812828239112219) * INT(RND(1)*9912166437771297131373) *
' INT(RND(1)*71777126181142123) * INT(RND(1)*7119119672435637981) *
' INT(RND(1)*991216643912127789) * INT(RND(1)*79126181142123) *
' INT(RND(1)*711911128376332417) * INT(RND(1)*991216643123129) *
' INT(RND(1)*79126181142123) * INT(RND(1)*6661912727312317)
' Random=INT(VAL(RIGHT$(STR$(x,1)))

    x=INT(RND(1)*TIME$("ms")*9912812828239112219) * INT(RND(1)*9912166437771297131373) *_
    INT(RND(1)*71777126181142123) * INT(RND(1)*7119119672435637981) *_
    INT(RND(1)*991216643912127789) * INT(RND(1)*79126181142123) *_
    INT(RND(1)*711911128376332417)
    x=x*x+x+41
    y$=mid$(str$(x),INT(rnd(1)*30+1),Digits )
    ldg=val(right$(y$,1))
    z=0
    if ldg=0 then z=1
    if ldg=2 then z=1
    if ldg=4 then z=1
    if ldg=6 then z=1
    if ldg=8 then z=1
    Random=val(y$)+z
End Function

FUNCTION TEXT2DEC( x$ )
    a$=UPPER$(x$)
    y$=""
    FOR i=1 TO LEN(a$)
        y$=y$+STR$(ASC(MID$(a$,i,1)))
    NEXT
    TEXT2DEC=VAL(y$)
END FUNCTION


FUNCTION DEC2TEXT$( n )
    a$=STR$(n)
    y$=""
    FOR i=1 TO LEN(a$)-1 STEP 2
        m=VAL(MID$(a$,i,2))
        if m>30 and m<99 then y$=y$+CHR$(m) else y$=y$+"."
    NEXT
    DEC2TEXT$=y$
END FUNCTION

data 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
data 31, 37, 41, 43, 47, 53, 59, 61, 67, 71
data 73, 79, 83, 89, 97, 101, 103, 107, 109, 113
data 127, 131, 137, 139, 149, 151, 157, 163, 167, 173
data 179, 181, 191, 193, 197, 199, 211, 223, 227, 229
data 233, 239, 241, 251, 257, 263, 269, 271, 277, 281
data 283, 293, 307, 311, 313, 317, 331, 337, 347, 349
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data 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919




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[[toc|flat]]