"Prime"?

Der tales så vidt jeg kan se om primtal, så skal vi ikke bare skrive dét? :-)

Edit: Hov, jeg havde ikke bemærket foreslå rettelser-funktionen!

Enig - artiklen er hermed opdateret, også med mere viden om hvordan komprommiteringen mere præcist foregår.

Med venlig hilsen
Jakob Dam | Administrator

Super! 

Jeg blev indledningsvist snydt og tænkte, at det måtte dække over noget i, hvor man implicit skulle forstå, hvad det var - som når man omtaler en prime lens som bare en prime.

Oh well, tak for rettelsen.

Fra kilden skrives der følgende om de usikre primtal.

The condition for being able to use the faster form of the algorithm (the "special" in the special number field sieve) is that the prime has a particular property. For some primes that's easy to see, for example if a prime is very close to a power of 2. We found some implementations using primes like this, which are clearly vulnerable. We did discrete log computations for a couple of them, described in Section 6.2 of the paper.

But there are also primes for which this is impossible to detect. (Or, more precisely, would be as much work to detect as it is to just do the discrete log computation the hard way.) This is more distressing, since there's no way for any user to tell that a prime someone gives them has this special property or not, since it just looks like a large prime. We discuss in the paper how to construct primes that have this special property but the property is undetectable unless you know the trapdoor secret.

It's possible to give assurance that a prime does not contain a trapdoor like this. One way is to generate primes where most of the bits come from a "nothing up my sleeve" number like e or pi. Some standards do this. Another way is to give the seeds used for a verifiable random generation algorithm.

Selve artiklen som forskerne har skrevet.
http://eprint.iacr.org/2016/961

Side 13 i artiklen skriver at et usikkert primtal, x, kan udtrykkes på denne måde: 

and the trapdoor polynomial pair is 
f = 1155 x^6 + 1090 x^5 + 440 x^4 + 531 x^3 − 348 x^2 − 223 x − 1385

g = 567162312818120432489991568785626986771201829237408 x −663612177378148694314176730818181556491705934826717 .