It is possible to repeatedly fold a standard letter-sized sheet of paper at the midway point about six to seven times. In 2012, some MIT students were able to fold an 1.2 kilometer long toilet paper 13 times. And every time the paper was folded, the number of layers on top of each other doubled. Therefore, the MIT students ended up with 2^13 = 8192 layers of paper on top of each other. And poor Eve's job was to manually count all layers one by one.
Please refer to this Wiki before asking questions that might have been asked before (use your common sense).
Cryptography is also usually more interesting than decrypting your random ciphertext, so consider that when posting, read what we are sharing first to see if it's really pertinent.
How to learn about Cryptography?
The first thing you should do, is to sign-up for Dan Boneh's course Crypto I on Coursera.
You do not have to finish it. Watching a few videos will already give you an idea of what is crypto and how easy/hard it is for you. If you can finish the course, and enjoy it at the same time, then you're in for a lot of fun.
Don't try signing-up for Crypto II though.
Alright, that was interesting, MOAR
There are many ways to learn more about crypto. Here's a non-exhaustive list:
But my favorite way: read whitepapers. Look at the ePrint archives and check what papers interest you. Often papers will come with an introduction section that explains the basics.
What about studying cryptography in a real school?
First, it's important to cultivate your new passion. Don't let your course get in the way of reading or building and doing side projects involving crypto.
Second, You need either a bachelor in mathematics or computer science. Depending on which part you find the more interesting in crypto. Usually Math => Theorical Cryptography, CS => Applied Cryptography.
Now either you don't have a master, and you could choose to do a cryptography master. There are a few: Rennes, Bordeaux, Limoges in France.Stanford, etc...
Or you can do a Computer Science or Number Theory oriented master and pick a crypto subject for a phd. Note that a phd will often lead you into theorical research in university, although some phd can be done within a company and might involve applied crypto. But companies around the world might find that relatively relevant (in France a phd will get you to some places).
It's important to know what you want to do, theorical or applied or in the middle? Usually finding an internship in a applied crypto company helps to get out of academia for a while. A good way to see what please you the most. And good news, in cryptography internships are pretty easy to find (at least at the moment).
Alright I'm studying crypto now, how to get more involved?
Cryptography is a big world, many things are happening and it's sometimes hard to follow everything. Especially some mediums give you a high noise-to-quality ratio. So here they are:
Now is your time to find an internship or a job? Apply everywhere, in the world. But where? Where other cryptographers are working, or have worked. You can find that on their published papers (usually written in the header), on Twitter, on Linkedin, etc...
First of all, we stress that SVP and its variants should all be considered easy when the lattice dimension is less than 70. Indeed, we will see in Section 4 that exhaustive search techniques can solve SVP within an hour up to dimension 60. But because such techniques have exponential running time, even a 100-dimensional lattice is out of reach. When the lattice dimension is beyond 100, only approximation algorithms like LLL, DEEP and BKZ can be run.
I can't remember from what article I got that from. Must have been something Phong Nguyen wrote.
It states that a lattice of dimension 60 could be easily solved, in an hour, by an exhaustive search (or similar techniques (enumeration?)). Something to dig into.
After defending my master thesis in Labri's amphitheatrum I thought I would never have to go back there again. Little did I know, ECC 2015 took place in the exact same room. I was back in school.
It was a first for me, but for many people it was only one more ECC. Most people knew each other, a few were wandering alone, mostly students. The atmosphere was serious although relaxed. People were mostly in their late 30s and 40s, a good part was french, others came from all over the world, a good minority were government people. Rumor has it that NSA was somewhere hidden.
Nothing really groundbreaking was introduced, as everybody knows ECC is more about politics than math these days. The content was so rare that a few talks were not even talking about ECC. Like that talk about Logjam (was a good talk though) or a few about lattices.
We got warmed up by a one hour cocktail party organized by Microsoft, by 6pm most people were "canard" as the belgium crypto people were saying. We left Bordeaux's Magnificient sun and sat back into the hot room with our wine glasses. Then every 5 minutes a random person would show up on stage and present something, sometimes serious, sometimes ridiculous, sometimes funny.
The panel was introduced by Benjamin Smith and was composed of 7 figures. Dan Bernstein that needs no introduction, Bos from NXP, Flori from the french government agency ANSSI, Hamburg from Cryptography Research (who was surprised that his company let him assist to the panel), Lochter from BSI (German government) and Moody from NIST.
It was short and about standardization, here are the notes I took then. Please don't quote anything from here, it's inexact and redacted after the fact.
Presenter: you have very different people in front of you, you have exactly 7 white people in front of you, hopefuly it will be different next year.
The consensus is that standardisation in ECC is not working at all. Maybe it should be more like the AES one. Also, people are disapointed that not enough academics were involved... general sadness.
Lochter: it's not good to change too much, things are working for now and Post-Quantum will replace ECC. We should start standardizing PQ. Because everything is slow, mathematics takes years to get standardized, then implemented, etc... maybe the problem is not in standardization but keeping software up-to-date.
Hamburg: PQ is the end of every DLP-based cryptosystem.
Bos: I agree we shouldn't do this (ECC2015) too often. Also we should have a framework where we can plugin different parameters and it would work with any kind of curves.
Someone: why build new standards if the old/current one is working fine. This is distracting implementers. How many crypto standards do we already have? (someone else: a lot)
Bos: Peter's talk was good (about formal verification, other panelists echoed that after). It would be nice for implementers to have tools to test. Even a database with a huge amount of test vectors would be nice
Flori: people don't trust NIST curves anymore, surely for good reasons, so if we do new curves we should make them trustable. Did anyone here tried generating nist, dan, brainpool etc...? (3 people raised their hands).
Bernstein: you're writing a paper? Why don't you put the Sage script online? Like that people won't make mistakes or won't run into a typo in your paper, etc...
Lochter: people have to implement around patents all the time (ranting).
Presenter: NSA said, if you haven't moved to ECC yet, since there will be PQ, don't get into too much trouble trying to move to ECC. Isn't that weird?
Bernstein: we've known for years that PQ computers are coming. There is no doubt. When? It is not clear. NSA's message is nice. Details are weird though.
We've talked to people at the NSA about that. Really weird. Everybody we've talked to has said "we didn't see that in advance" (the announcement). So who's behind that? No one knows. (someone in the audience says that maybe the NSA's website got hacked)
Flori: I agree it's hard to understand what the NSA is saying. So if someone in the audience wants to make some clarification... (waiting for some hidden NSA agent to speak. No one speaks. People laugh).
Hamburg: usually they say they do not deny, or they say they do not confirm. This time they said both (the NSA about Quantum computers).
Lochter: 30 years is the lifetime of secret data, could be 60 years if you double it (grace period?). We take the NSA's announcement seriously, satelites have stuff so we can upgrade them with curves (?)
Presenter: maybe they (the NSA) are scared of all the curve standardization happening and that we might find a curve by accident that they can't break. (audience laughing)
Bos: we have to follow standards when we implement in smartcards...
Lochter: we can't blame the standard. Look at Openssl, they did this mess themselves.
Moody: standards give a false sense a security but we are better with them than without (lochter looks at him weirdly, Moody seems embarassed that he doesn't have anything else to say about it).
Bernstein: we can blame it on the standard!
Lochter: blame the process instead. Implementers should get involved in the standardization process.
Bernstein: I'll give you an example of implementers participating in standardization, Rivest sent a huge comment to the NIST ("implementers have enough rope to hang themselve"). It was one scientific involved in the standardization.
Presenter: we got 55 minutes of the panel done before the first disagreement happened. Good. (everybody laughs)
Bos: we don't want every app dev to be able to write crypto. It is not ideal. We can't blame the standards. We need cryptographers to implement crypto.