onuralver Oct 7, 2017

Submit Articles Here for Liberty BASIC Programmer's Encyclopedia

Liberty BASIC Programmer's Encyclopedia

Anybody can submit articles to the Liberty BASIC Programmer's Encyclopedia. You do not need to be a member of this site. The public may edit existing pages. Only persons with a Wikispaces account may create new pages. You may get a free Wikispaces account here.

License
By adding content to the Liberty BASIC Programmer's Encyclopedia, you are bound by the license. If you do not want to release your work under this license, do not submit articles. Click HERE to read the License.

Article Guidelines
The Liberty BASIC Programmer's Encyclopedia is a place for full-length technical articles. Authors should make sure that articles are well-structured, that words are spelled correctly, and that all code works properly. Click HERE for help on technical writing.

When you submit an article, be aware this is not the end of your involvement. Few of us get it Just Right the very first time. Expect an LBPE editor to contact you with questions, suggestions, possible edits, etcetera for you to look over and take the proper action.

Adding Articles

Click the edit button at the top of this page.
Add your article to the list at the bottom of this page . If you are using the formatted text editor, simply click the link button on the editing toolbar and invoke a dialog to add the link. Type the name of your new page in the "wiki link" area and click the "okay" button.If you are using the plain text editor, do this by typing a name for your page inside of double square brackets. If your article is called "Using Arrays", your link would look like this: * [[Using Arrays]] Save the editing of this page.
View this page and click on the link you just created.
On the new page, click the edit link and type or paste your article.
Please place your name and the date at the top of your article, along with a descriptive title.
Save your edits. That's all there is to it!

Having trouble submitting an article? Try Visual Directions for Submitting an Article

Editing Articles
To learn how to use WikiText markup to edit site content, click HERE. You don't need to know WikiText, though. When you are editing a page, there is a button near the bottom to "Use Visual Editor." If you want to try some editing in a safe place where you can do no harm, play in the Test Area. Before finalizing the article, you can click the "Preview" button to see how your article will appear, and make changes as needed.

Additional Files
If your article requires images or other additional files, simply upload them and include links in your article. When you are editing a page there is a link in the upper right for "Images". Click this to view a list of all available files and images.

Article Placement
One of the organizers of the Liberty BASIC Programmer's Encyclopedia will tag your article for editing. If the organizers find it to be a viable article for the encyclopedia, it will be added to all the appropriate categories.

Confirmation
Organizers of the Liberty BASIC Programmer's Encyclopedia will make any modifications they feel are needed. Authors may accept or reject these changes before articles are listed in the appropriate categories and locked.

Article Modification in the Future
One of the advantages of this format is that it affords us the ability to update and modify the information. Organizers reserve the right to modify, expand, or delete articles as they determine such actions to be appropriate.

Who Can Edit Articles
Articles can be edited by the original authors and by the site organizers. Others should suggest changes via the site's discussion feature.

CryptographyWithLB103

Edit 6…

Cryptography with Liberty Basic

103: Public Key Cryptography: RSA Algorithm

By Onur Alver (CryptoMan)

INTRODUCTION

Cryptography with Liberty Basic
103: Public Key Cryptography: RSA Algorithm
We will continue in our series of articles about Cryptography with Public Key Cryptography.

RSA ALGORITHM

RSA Algorithm is based on the assumption on the difficulty of factoring large composite numbers.

Code:

dim stats(11)

dim SmallPrimes(1000)

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

data 353, 359, 367, 373, 379, 383, 389, 397, 401, 409

data 419, 421, 431, 433, 439, 443, 449, 457, 461, 463

data 467, 479, 487, 491, 499, 503, 509, 521, 523, 541

data 547, 557, 563, 569, 571, 577, 587, 593, 599, 601

data 607, 613, 617, 619, 631, 641, 643, 647, 653, 659

data 661, 673, 677, 683, 691, 701, 709, 719, 727, 733

data 739, 743, 751, 757, 761, 769, 773, 787, 797, 809

data 811, 821, 823, 827, 829, 839, 853, 857, 859, 863

data 877, 881, 883, 887, 907, 911, 919, 929, 937, 941

data 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013

data 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069

data 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151

data 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223

data 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291

data 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373

data 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451

data 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511

data 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583

data 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657

data 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733

data 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811

data 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889

data 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987

data 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053

data 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129

data 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213

data 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287

data 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357

data 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423

data 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531

data 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617

data 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687

data 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741

data 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819

data 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903

data 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999

data 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079

data 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181

data 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257

data 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331

data 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413

data 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511

data 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571

data 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643

data 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727

data 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821

data 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907

data 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989

data 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057

data 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139

data 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231

data 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297

data 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409

data 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493

data 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583

data 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657

data 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751

data 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831

data 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937

data 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003

data 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087

data 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179

data 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279

data 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387

data 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443

data 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521

data 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639

data 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693

data 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791

data 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857

data 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939

data 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053

data 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133

data 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221

data 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301

data 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367

data 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473

data 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571

data 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673

data 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761

data 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833

data 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917

data 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997

data 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103

data 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207

data 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297

data 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411

data 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499

data 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561

data 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643

data 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723

data 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829

data 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919

playwave "ding.wav", async

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"

'goto [Jump]

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"

playwave "tada.wav", async

end if

if p then q=x else p=x

next i

print

playwave "tada.wav", async

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."

playwave "ding.wav", async

[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]

[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

Submit