CryptographywithLB103

=Cryptology with Liberty BASIC : 103= 
//author//
[[toc|flat]]
----
=First Part Title= 
Text here.

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

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

    for i=1 to 2 t1=time$("ms")
[TryAnother] print print
        t1=time$("ms")

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

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

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

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

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

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

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


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

[stop]
END

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

End Function 'Extended Euclidian GCD
Function
Function ExtBinEuclid( u, v ) k=0
    k=0 :t1=0 :t2=0 :t3=0 if
    if u<v then temp=u u=v v=temp end
        temp=u
        u=v
        v=temp
    end if while
    while (IsEven( u ) and IsEven( v )) k
        k = k+1 u
        u = int(u/2) v
        v = int(v/2) wend u1
    wend
    u1 = 1: u2 = 0: u3 =u: t1 =v: t2 =u-1: t3 =v
[Loop1] 'two

    [Loop1]
    'two labels with no code!
[Loop2] '

    [Loop2]
    ' print "*" if
    if (IsEven(u3)) then if
        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
            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:
        temp=u1: u1=t1: t1=temp temp=u2:
        temp=u2: u2=t2: t2=temp temp=u3:
        temp=u3: u3=t3: t3=temp end if
    end if
    if IsEven(u3) then goto
        goto [Loop2] end
    end if
while

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

    while u1>=v AND u2>=u u1=ul-v:
        u1=ul-v: u2=u2-u wend ExtBinEuclid=u-u2End
    wend
    ExtBinEuclid=u-u2
End Function
function

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

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


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

    [ExitFunction]
end function
Function

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

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


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

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

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

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

[ExtFn]
End Function
Function


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

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

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


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

data 2, 3, 5, 7, 11, 13, 17, 19, 23, 29data29
data 31, 37, 41, 43, 47, 53, 59, 61, 67, 71data71
data 73, 79, 83, 89, 97, 101, 103, 107, 109, 113data113
data 127, 131, 137, 139, 149, 151, 157, 163, 167, 173data173
data 179, 181, 191, 193, 197, 199, 211, 223, 227, 229data229
data 233, 239, 241, 251, 257, 263, 269, 271, 277, 281data281
data 283, 293, 307, 311, 313, 317, 331, 337, 347, 349data349
data 353, 359, 367, 373, 379, 383, 389, 397, 401, 409data409
data 419, 421, 431, 433, 439, 443, 449, 457, 461, 463data463
data 467, 479, 487, 491, 499, 503, 509, 521, 523, 541data541
data 547, 557, 563, 569, 571, 577, 587, 593, 599, 601data601
data 607, 613, 617, 619, 631, 641, 643, 647, 653, 659data659
data 661, 673, 677, 683, 691, 701, 709, 719, 727, 733data733
data 739, 743, 751, 757, 761, 769, 773, 787, 797, 809data809
data 811, 821, 823, 827, 829, 839, 853, 857, 859, 863data863
data 877, 881, 883, 887, 907, 911, 919, 929, 937, 941data941
data 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013data1013
data 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069data1069
data 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151data1151
data 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223data1223
data 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291data1291
data 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373data1373
data 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451data1451
data 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511data1511
data 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583data1583
data 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657data1657
data 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733data1733
data 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811data1811
data 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889data1889
data 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987data1987
data 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053data2053
data 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129data2129
data 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213data2213
data 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287data2287
data 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357data2357
data 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423data2423
data 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531data2531
data 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617data2617
data 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687data2687
data 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741data2741
data 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819data2819
data 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903data2903
data 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999data2999
data 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079data3079
data 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181data3181
data 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257data3257
data 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331data3331
data 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413data3413
data 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511data3511
data 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571data3571
data 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643data3643
data 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727data3727
data 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821data3821
data 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907data3907
data 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989data3989
data 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057data4057
data 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139data4139
data 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231data4231
data 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297data4297
data 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409data4409
data 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493data4493
data 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583data4583
data 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657data4657
data 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751data4751
data 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831data4831
data 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937data4937
data 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003data5003
data 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087data5087
data 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179data5179
data 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279data5279
data 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387data5387
data 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443data5443
data 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521data5521
data 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639data5639
data 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693data5693
data 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791data5791
data 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857data5857
data 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939data5939
data 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053data6053
data 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133data6133
data 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221data6221
data 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301data6301
data 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367data6367
data 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473data6473
data 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571data6571
data 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673data6673
data 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761data6761
data 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833data6833
data 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917data6917
data 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997data6997
data 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103data7103
data 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207data7207
data 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297data7297
data 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411data7411
data 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499data7499
data 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561data7561
data 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643data7643
data 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723data7723
data 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829data7829
data 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919




[[code]]



[[toc|flat]]