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Why is elliptic curve cryptography not widely used, compared to RSA?

crypto.stackexchange.com

21–30 of 31 posts

Re: Why is elliptic curve cryptography not widely used, compared to RSA?

#21
post #19
post #17

Not relevant to ECC, but if anyone here has spare time and any interest at all in crypto, please contribute to the linked site ( http://crypto.stackexchange.com )! In case anyone doesn't know, StackExchange is a network of Q&A websites, of which StackOverflow was the first. Sites go through a proposal process and, if enough people commit, a private and then public beta. The Cryptography StackExchange site is currentl…

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Re: Why is elliptic curve cryptography not widely used, compared to RSA?

#22
post #12

Earlier quoted context omitted.

You don't need to replace your entire anything, and it's not "just for fun". No, the question is really "EC has these benefits (lower CPU and memory usage) - why aren't these benefits attractive enough for someone to start experimenting with it?" - with those someones probably being companies like Google, Facebook, Dropbox etc that have very substantial amounts of SSL traffic and could surely benefit from saving on m…

"could surely benefit from saving on memory and CPU." ... at a certain labor cost. And memory and CPU prices are forever decreasing and labor cost is sorta increasing. So if it doesn't make sense as a system to do it today it probably never will, for an established organization anyway. Also its not "why aren't they experimenting" but "why aren't they publicly experimenting". And it would nearly be a first in the secu…

> Finally its highly unclear why anyone uses SSL for these apps

Huh? The reason you use SSL for Google and Facebook is so 15 random strangers don't get access to your accounts just because you go online for five minutes in Starbucks.

PRISM is awful and all but that doesn't mean non-state adversaries stopped being a thing overnight.

Re: Why is elliptic curve cryptography not widely used, compared to RSA?

#24
ECC is the emerging new standard for asymmetric crypto. It's misleading to say it's not widely used. It's not widely used in mainstream protocols, because those protocols were almost invariably designed in the 1990s. During the '90s, ECC was both patent-encumbered and a less conservative choice than RSA.

In 2013, the scales have tipped. RSA is now the less conservative choice. Classical number-theoretic asymmetric cryptography has been getting weaker and weaker with improvements both on factoring and the DLP. ECC has been deployed in more and more systems without patent debacles. Research has firmed up our confidence in ECC.

You should generally be distrustful of any new system that uses asymmetric crypto of any sort. Asymmetric crypto is very difficult to get right; it has more corner cases than AES/SHA constructions do. But you should be especially distrustful if you see a new system that uses RSA.

Re: Why is elliptic curve cryptography not widely used, compared to RSA?

#25
post #18

The top answer tries to brush off the difference in hardness assumptions as "semi-valid", and I think that's rather odd. Assumptions about hardness are pretty damned important in cryptography, and 25 years is not really all that long for mathematicians to have been thinking about a problem.

As another answer points out, the mathematics of the discrete logarithm on elliptic curves is closely related to factoring, and most factoring algorithms have close analogs for the discrete logarithm, so the difference is actually not that great. However it does have a subtle consequence. We've developed some very good sieve based algorithms for factoring in recent decades that do not have obvious analogs for ellipti…

In additional to the NFS algorithms, we also have the index calculus algorithms for DLP; see Joux this year.

Re: Why is elliptic curve cryptography not widely used, compared to RSA?

#26
The one main reason ECC was not adopted initially is also patents. Certicom held a majority of the patents on those and every time I tried to push for elliptic curves the first thing every one talked about was patents. So we mostly stayed away from it to avoid any issues later on. One other reason is Openssl did not implement support for them until recently (a few years ago), probably because of the patent confusion. It will pick up in a few years.

Re: Why is elliptic curve cryptography not widely used, compared to RSA?

#27
post #17

Not relevant to ECC, but if anyone here has spare time and any interest at all in crypto, please contribute to the linked site ( http://crypto.stackexchange.com )! In case anyone doesn't know, StackExchange is a network of Q&A websites, of which StackOverflow was the first. Sites go through a proposal process and, if enough people commit, a private and then public beta. The Cryptography StackExchange site is currentl…

Since you're clearly into this it would be useful if you could check the answer I gave elsewhere about RSA.

https://news.ycombinator.com/item?id=5853601

Feel free to email - probably better than cluttering up the threads here.

Re: Why is elliptic curve cryptography not widely used, compared to RSA?

#28
post #17

Not relevant to ECC, but if anyone here has spare time and any interest at all in crypto, please contribute to the linked site ( http://crypto.stackexchange.com )! In case anyone doesn't know, StackExchange is a network of Q&A websites, of which StackOverflow was the first. Sites go through a proposal process and, if enough people commit, a private and then public beta. The Cryptography StackExchange site is currentl…

To explain a potential adversary, how crypto works or how he becomes a valueable asset for any given intelligence service without any given payment may not even attract people like me.

Re: Why is elliptic curve cryptography not widely used, compared to RSA?

#29
I can't find a smartcard that does ECC. Anyone has one? PGPcard only does RSA (granted, up to 3072 bits -- but that makes for extra long signatures and messages).

GPG and SSH can do ECC for a long time now - where's the trustworthy hardware to help them?

Anyone know of something that can run e.g. on the YubiKey NEO?

Re: Why is elliptic curve cryptography not widely used, compared to RSA?

#30
post #13

I've often heard the claim that elliptic curve cryptography is not used much in practice compared to RSA. I don't doubt its true but I would like to have some evidence for it so I can also say it without being a parrot. I don't know anything about real world implementations of cryptography. How can I go about getting data that RSA is more widely used?

Well, probably the most widely used cryptography is SSL, specifically the kind used in HTTPS. The whole HTTPS ecosystem revolves around certificates authorities that sign your RSA key. So on that fact alone, I would say there's more RSA out there than ECC. SSH is also very widely used and it has traditionally used RSA keys, though it supports DSA keys, too and, more recently, ECDSA (the "EC" being elliptic curve). Sa…

SSL/X.509 and that whole ecosystem can use ECDSA based certificates and ECDH as key exchange, because it is explicitly designed to allow multiple variants of encryption algorithms.

There are relatively many widely deployed systems that use ECC because of resource constrains (short signatures, mainly). For example both Microsoft's product keys and FlexLM use something that is at least described in marketing materials as ECDSA.

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