[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

*To*: [email protected]*Subject*: Diffie Hellman - logs in Galois fields*From*: [email protected]*Date*: Mon, 16 Sep 1996 14:42:41 +0000*CC*: [email protected]*Comments*: Authenticated sender is <[email protected]>*Priority*: normal*Sender*: [email protected]

Hi all, A question for the matematicians out there: I am looking at the Diffie Hellman public key exchange protocol and am trying to find out why it is computationally hard to take logs in a finite (Galois) field. My maths tutor has told me a bit about the construction of Galois fields (If I`m correct the construction is Z mod N, N some integer, then a transformation F(x) on the residue classes already in the field) I know also the definition is that there are P**k elements, p a prime. My questions are as follows: 1. How can a field be finite, as by definition it has to be closed under addition, subtraction, multiplication and division???? (sorry if this one is a bit of a no brainer, maybe the definition is different but I can`t seem to see how) 2. Why is taking logs in a finite field computationally hard? - Me and Alec (My maths tutor at college) guessed that it is because exponentiation and logs are each others inverse functions, and somehow this becomes a one way function in a finite field. 3. Are the Galois fields used in Diffie Hellman specially constructed in any way or are they just normal GF???? Thanks for any help anyone can give me.... Datacomms Technologies web authoring and data security Paul Bradley, [email protected] Http://www.fatmans.demon.co.uk/crypt/ "Don`t forget to mount a scratch monkey" -----BEGIN PGP PUBLIC KEY BLOCK----- Version: 2.6.3ia mQCNAjH9j+cAAAEEAMBvREiQR0ot9dFCO0TiSCSunAYLv2g1Bc6I3bz8FzKXNH53 6mieJf/W4rD+CxJpT0q9RQaaoRtkHJLwbjfK2il3D7mEahMAyqvF/xRJNqkXfhM3 sRJM0Jh43l+W0M5vwokbEbk25/bxWWGspTsLD3YHbzKnG6pOcL5OPIRbv66xAAUR tCdQYXVsIEJyYWRsZXkgPHBhdWxAZmF0bWFucy5kZW1vbi5jby51az6JAJUDBRAy NwfvNkCBjDT0xHEBATQPA/9TORmN/UjNecj03q4anpvdyCLiez5sKuNbnYK50RiP Jj4QpWWvST3smyQ0A86DrZY/re056MXwQmARESx0rFZxdnD0oORICl5r8dJLIy3b j8rbA5olXwZwKz73/X5s13v/pvHYX4cIsbVK8NHXqh5llSKt6TBAuGgkIGF29z5k C4kAlQMFEDI3B9mdtf/umVkv7QEBcRYD/1FBteLqsUmr81euxqqnnrpLlyHb58B/ 9sdATuua4uSjX46hXDZ264YozspNrzSB4NEdrmXOWVX3fiE0ga6XkSSkIeF23V90 En37Z0BdbFzgF00FRYTFyTq8eezQrdg/+rBPUsZUmG5wpq3e12FKHQsX01i+1mB2 YmqqwCV5e95eiQCVAgUQMh8uSb5OPIRbv66xAQEqJwP/fxQyiCasjFcbDpsFfsYp put5cCC/9pOx6X3DlbKShPMpUOS+A9HsTEmJQN8Iawv1nSwPdtc2cR/GhW6ilVjW LSloGdMVLabm9pGpZZMkRaZlXFUkOv7VhfgsUiL+vIDryBCAwUZCzQiWycjt/cPi mUqFH41Z7NkyO8ZFdi5GGX0= =CMZA -----END PGP PUBLIC KEY BLOCK-----

**Follow-Ups**:**Re: Diffie Hellman - logs in Galois fields***From:*Justin Card <[email protected]>

**Re: Diffie Hellman - logs in Galois fields***From:*"Vladimir Z. Nuri" <[email protected]>

- Prev by Date:
**Re: Snake Oil FAQ 0.4 [comments appreciated]** - Next by Date:
**Re: The Living and the Dead** - Prev by thread:
**Edited Edupage, 15 Sept 1996** - Next by thread:
**Re: Diffie Hellman - logs in Galois fields** - Index(es):