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English

p.specht

Modulares Potenzieren
==================
at that RSA-Verschlüsselungsverfahren go two large Primzahlen multipliziert or. potentiated, to a Module for further Berechnungen. These Berechnungen wären because of the irrsinnigen Size the enstehenden numbers terrific costly. as remedy there whom Algorithmus "Modulares Potenzieren": one must then not first the Endergebnis calculate, separate can Zwischenergebnisse already "unterwegs" MODULO-take, speak: with the enstehenden Divisionsresten weiterrechnen, without that the Endergebnis changed would. the untenstehende Machwerk is though not Gültigkeitsgrenzen examined, it deals itself only circa a Prinzipstudie. Gegengeprüft watts through the Language "R".

an the founts: [...]

wished one objectively the RSA-take action emulate, should self-evident Assemblercode written go. and self the could too slow go, therefore becomes to Codierung and Decodierung in moderneren Geräten already The Grafikkarte (Parallelcomputing) herangezogen.

Compile Mark Separation

Window Title "Modulares Potenzieren (Prinzipstudie zB. for the RSA-take action)"
' (CL) CopyLeft 2018-05 P.woodpecker, Wien; without each Gewähr!  fountain: https://www.
' inf-school.de/communication/kryptologie/rsa/modpotenz/station_schnellespotenzieren
Windowstyle 24:font 2:set("decimals",17)
Declare w$,x!,y!,m!

Repeat

    Cls rgb(200+rnd(56),200+rnd(56),200+rnd(56)):w$=""
    print "\n\n (x ^ y) mod m  should accounts go:"
    Print "\n\n x = ";:input w$:x!=val(w$)
    Print "\n y = ";:input w$:y!=val(w$)
    Print "\n m = ";:input w$:m!=val(w$)
    print "\n ModPotf(x,y,m) = ";
    color 14,1:print " "+stature$("%g",ModPotf(x!,y!,m!))+" "
    color 0,15
    waitinput

Until %key=27

End

Proc modpotf :parameters x!,y!,m!

    var pot! = 1

    while y!>0

        if remodf(y!,2)=1

            pot!=remodf(pot!*x!,m!)
            y!=y!-1

        else

            x!=remodf(sqr(x!),m!)
            y!=y!/2

        endif

    endwhile

    return pot!

endproc

'-----------------------------
'Hilfsfunktionen from geplanter Include (work in progress):

proc floor :parameters x!

    case abs(x!)<(10^-35):return 0
    case x!>0:return intf(x!)
    return (abs(x!-intf(x!)) < 10^-35)-intf(abs(x!-1))

endproc

proc remodf :parameters x!,y!

    ' Q: https://de.wikipedia.org/wiki/Modulo , How in ADA
    case abs(x!)<(10^-35):return 0
    case abs(y!)<(10^-35):return x!
    return ((x!>0)-(x!<0))*abs(x!-y!*floor(x!/y!))

endproc

proc frac :parameters x!

    var s!=(x!>0)-(x!<0)
    x!=abs(x!)
    x!=x!-round(x!,0)
    case x!<0:x!=1+x!
    return s!*x!

endproc

proc intf :parameters x!

    var s!=(x!>0)-(x!<0)
    x!=abs(x!)
    x!=x!-frac(x!)
    return s!*x!

endproc