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The Joy of Cryptography

joyofcryptography.com

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Re: The Joy of Cryptography

#41

Post by garmaine »

marcan_42 wrote: post #36
garmaine wrote: post #32

Earlier quoted context omitted.

Almost no cryptography being deployed today uses prime numbers. (Not because of any weakness, but because there are better, more efficient algorithms instead.)

RSA is still in wide use in both old and new deployments (e.g. it is still the majority of TLS handshakes). Elliptic curves are faster and use smaller keys, but they're also a more fragmented ecosystem; plus, in particular for the older NIST curves, there is the unshakable fear that they're backdoored by the NSA (since they use magic unexplainable numbers, which RSA does not). Thankfully ed25519 gave us an alternativ…

By cryptography being deployed today I meant new protocols. Like if the people who are actually in the position of picking cryptographic primitives, virtually no one reaches for RSA. Sorry if that wasn’t clear.

Re: The Joy of Cryptography

#43

Post by BossingAround »

This looks excellent. I tried to go through the Introduction to Cryptography by Christof Paar [1] and that material was not really suitable for me, personally. I found it too dense, and written in not very interesting manner.

Thank you for posting this book, I'll give it a go! Crypto is one of those things I have on my shameful "how-come-you-don't-know-it-yet" to-learn list :).

[1] https://www.youtube.com/channel/UC1usFRN4LCMcfIV7UjHNuQg

Re: The Joy of Cryptography

#44

Post by anjanb »

le-mark wrote: post #5

> All the sensible textbook titles were already taken. Actual joy not guaranteed. Like a lot of people (I imagine) I made it through a CS bachelors program not really ‘getting’ the discrete math combinatorics part. Crypto is an area where those concepts really really matter. It’s great to see this resource available!

Is there a good text book/resource to (re) learn 'discrete math combinatorics' ?

Re: The Joy of Cryptography

#46

Post by marcan_42 »

tptacek wrote: post #40
marcan_42 wrote: post #36

Earlier quoted context omitted.

RSA is still in wide use in both old and new deployments (e.g. it is still the majority of TLS handshakes). Elliptic curves are faster and use smaller keys, but they're also a more fragmented ecosystem; plus, in particular for the older NIST curves, there is the unshakable fear that they're backdoored by the NSA (since they use magic unexplainable numbers, which RSA does not). Thankfully ed25519 gave us an alternativ…

No cryptography engineer seriously believes the NIST P-curves are backdoored, and they are in widespread use. Ed25519 is a signing scheme; it isn't a replacement for the RSA in classic TLS --- you'd be thinking of Curve25519, its sibling. The benefit of the 25519s isn't "no magic numbers", it's a structure that makes it easy to implement relatively safely. And all these curves work over prime subfields. This is all 1…

No magic numbers is certainly one of the advantages of curve25519 and its siblings. The NSA already gave us one backdoored elliptic curve algorithm (Dual EC DRBG); there is no reason to trust them with magic numbers. They may be backdoored or they may not be, but every serious cryptography engineer knows there's no good reason for algorithm constants not to be generated according to public criteria if you aren't hiding anything. Sometimes they're hiding that they picked numbers that made the algorithm stronger against secret attacks they discovered (DES). Sometimes they're hiding a backdoor (Dual EC DRBG). We'd all rather they not hide anything.

More info: https://safecurves.cr.yp.to/rigid.html

Ed25519 is a replacement for RSA in the x.509 WebPKI, which is what I was trying to refer to when I said TLS. Classic TLS (as in non-PFS, the one that also used RSA to encrypt the session secret) is dead and nobody cares about replacing it with anything. There is no public key encryption involved in modern TLS; instead all you need is a signature scheme (for the certificate and for the final server to authenticate itself) and a key exchange scheme. The former can be ed25519. The latter can be curve25519 (specifically, the retroactively named X25519 ECDH key exchange).

My point is precisely that there's no inherent distrust in RSA (and some concerns with NIST EC, both the magic numbers and secure implementation difficulty), which is why we haven't abandoned it yet. There is certainly no inherent issue with prime field cryptography.

Re: The Joy of Cryptography

#48

Post by cleemens »

BossingAround wrote: post #43

This looks excellent. I tried to go through the Introduction to Cryptography by Christof Paar [1] and that material was not really suitable for me, personally. I found it too dense, and written in not very interesting manner. Thank you for posting this book, I'll give it a go! Crypto is one of those things I have on my shameful "how-come-you-don't-know-it-yet" to-learn list :). [1] https://www.youtube.com/channel/UC1…

Really? The book might not be suitable to read it from cover to cover in bed, but still approachable. The videos are also really nice and easy going (I took the lecture at his uni, nice foundation).

Compared to this book you seem right, the glimps I had was easily digestable and still concise.

Re: The Joy of Cryptography

#49

Post by 123pie123 »

garmaine wrote: post #31
__MatrixMan__ wrote: post #27

Earlier quoted context omitted.

If the whole of math were represented by the surface of the planet, "discrete math" would be more than half of it. Calculus (i.e. differentiation/integration on the reals) on the other hand, would be a city. Perhaps a very populated city, but just one. It's a shame that match curriculum for non-math-majors is an all-roads-lead-to-calculus affair. I think we scare a lot of potentially talented people away from math wi…

I'm not sure why you think that? Basically all of physics, chemistry, and other physical sciences is calculus. Calculus is the mathematics of rates of change, and basically all physical science is the study of change. Discrete math is very important to computer science. But in the rest of the world, calculus (and differential equations) dominate.

Double integration - brings not very nice memories back of my hand aching from writing upto 5 pages of workings out
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