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#1 2011-01-03 08:22:42

calccrypto
Member
Registered: 2010-03-06
Posts: 96

Whats a fast way to find generator g in Zp?

Is there some way to find a generator for a large prime number without checking each number individually?


Visit calccrypto.wikidot.com for detailed descriptions of algorithms and other crypto related stuff (not much yet, so help would be appreciated).

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#2 2011-01-03 08:27:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,444

Re: Whats a fast way to find generator g in Zp?

Hi calccrypto;

What do you mean by a generator?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#3 2011-01-03 08:35:03

calccrypto
Member
Registered: 2010-03-06
Posts: 96

Re: Whats a fast way to find generator g in Zp?

Hi bobbym. Its been a long time

totient(x) = {1,2, 3,...,etc.}, for some number (ignore prime p for now)
im looking for integer g (that is in totient(x) ) such that:
the set of {for 1 <= i < x: g ^ i mod x (removing all duplicates)} will equal the totient of x

since x = p = prime, totient(p) = {1,2, ... p-1}
since p is big, testing all those values will take forever

Last edited by calccrypto (2011-01-03 08:35:56)


Visit calccrypto.wikidot.com for detailed descriptions of algorithms and other crypto related stuff (not much yet, so help would be appreciated).

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#4 2011-01-03 10:21:07

calccrypto
Member
Registered: 2010-03-06
Posts: 96

Re: Whats a fast way to find generator g in Zp?

Any ideas on how to get g for a big p?


Visit calccrypto.wikidot.com for detailed descriptions of algorithms and other crypto related stuff (not much yet, so help would be appreciated).

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#5 2011-01-03 10:28:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,444

Re: Whats a fast way to find generator g in Zp?

I am still asking questions. For totient(7) you would get {1,2,3,4,5,6}. What do you get for totient(10)?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#6 2011-01-03 10:35:12

calccrypto
Member
Registered: 2010-03-06
Posts: 96

Re: Whats a fast way to find generator g in Zp?

10 would be {1, 3, 7, 9}. However, since 10 is not prime, theres no need for it


Visit calccrypto.wikidot.com for detailed descriptions of algorithms and other crypto related stuff (not much yet, so help would be appreciated).

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#7 2011-01-03 10:42:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,444

Re: Whats a fast way to find generator g in Zp?

I know what you want now, the generator. Offhand I do not know of anything faster than trying them all. The expected time is ( p - 1 ) / 2. Let me do a search around.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#8 2011-01-03 10:54:21

calccrypto
Member
Registered: 2010-03-06
Posts: 96

Re: Whats a fast way to find generator g in Zp?

Darn.


Visit calccrypto.wikidot.com for detailed descriptions of algorithms and other crypto related stuff (not much yet, so help would be appreciated).

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#9 2011-01-03 11:47:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,444

Re: Whats a fast way to find generator g in Zp?

Hi calccrypto;

I am sorry.

The only thing I found out is that T(7) and T(11) both have more than one generator. I could find nothing faster than trying them all. Maybe someone else can do more.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#10 2011-01-03 12:35:34

calccrypto
Member
Registered: 2010-03-06
Posts: 96

Re: Whats a fast way to find generator g in Zp?

Darn. Oh well. I will keep on searching. Thanks for looking!


Visit calccrypto.wikidot.com for detailed descriptions of algorithms and other crypto related stuff (not much yet, so help would be appreciated).

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