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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,938

Hi calccrypto;

What do you mean by a generator?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,938

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.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,938

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.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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

Darn.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,938

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.****If it ain't broke, fix it until it is.**

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

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

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