Karim Belabas on Tue, 18 Jun 2013 10:42:49 +0200


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Re: windows 7 

* Ahmad Kamal [2013-06-18 10:34]:
> 2) I got a floating error when I run something like this " p^e mod n "
> given that p, e, n are 1024 bits, so I need to know If PARIGP can support
> such operations and if there are any solutions to overcome such errors

  ? p = random(2^1024);
  ? n = random(2^1024);
  ? e = random(2^1024);
  ? Mod(p, n)^e
  %4 = Mod(69385032932171365295186767408126928176586897311504613591152004442415063532730061006838433460706220938904331242995850061435657050104153421907843766557177258498633974305632563760704792595960240856897851599231039103059869590474298285801967182682928066860759258987208134612874193094162521278085114388471761193950, 105063345230616104657348013634297701786006542128941909083101185888832813981927541578449103885990606406091215423988641232290414368860661235234905516208831410002395649542617648887800946357680235133745987328106517234870888931439344639465469355722657253870347038180634028206997149618094761699250765049161158009075)

The error

  ? (p^e) % n
  ***   at top-level: (p^e)%n
  ***                  ^----
  *** _^_: overflow in lg().

is expected since the integer (p^e) cannot be represented in PARI,
and in fact on any physical computer: it has about 2^1034 bits,
i.e. almost 10^300 Terabytes of data :-)

Cheers,

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite Bordeaux 1          Fax: (+33) (0)5 40 00 69 50
351, cours de la Liberation    http://www.math.u-bordeaux1.fr/~kbelabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]
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