Earlier quoted context omitted.
How do you securely share the AES key?
AES is really great compared to RSA, so I put my AES key on my website instead of my RSA public key. It's made it very easy for people to contact me securely.
AES is symmetric...
Bruce Schneier has changed his PGP key to 4096 bits
101–110 of 144 posts
Re: Bruce Schneier has changed his PGP key to 4096 bits
#102Earlier quoted context omitted.
AES is really great compared to RSA, so I put my AES key on my website instead of my RSA public key. It's made it very easy for people to contact me securely.
AES is symmetric...
Yeah, that makes it really convenient for me if I have to decrypt an important message from a public computer.
Re: Bruce Schneier has changed his PGP key to 4096 bits
#103There is nothing suspicious with that. He has worked previously in mostly corporate and private context, so 2048 is just fine. Now he works with people and data NSA wants their hands on and he wants the data to be secure also in the future. It's just reasonable to move to 4096 key sizes. http://www.pgp.net/pgpnet/pgp-faq/pgp-faq-keys.html#key-size >Dr Lenstra and Dr Verheul offer their recommendations for keylengths.…
Your secrets are not safe against multinational corporations with 1024 bit keys. The likely cost of the capability to break a 1024 bit key is probably (for a private entity) in the low tens of millions. You wouldn't even be safe from the operators of HN with that margin of security.
Now you've got me imagining what kind of data / communications would be deemed valuable enough to someone to make that kind of monetary expenditure worthwhile.
Re: Bruce Schneier has changed his PGP key to 4096 bits
#104Earlier quoted context omitted.
There's no need for a quantum computer. Everyone should be using at least 4096bit RSA. 1024bit RSA keys can be factored with conventional non-specialized hardware (read: CPU's, not even GPU's) with GNFS. IMHO, 2048bit RSA keys can be factored by custom hardware that the NSA has developed. I posted my reasoning for this hypothesis in other hackernews threads. A very quick/terse run down of the main key points - 1) NSA…
The (public) factorization record with GNFS is 768 bits, in an effort that took about 2000 CPU years. 1024 bits is about 1000x harder, so probably within reach with government resources. 2048 bits is 10^12 times harder, which surely is out of reach for the time being time unless the NSA has a better algorithm.
Lenstra et al performed the factorization you cite, again on CPUs. Lenstra said in 2007 that he expected with in 5 years to be able to do 1024bit number - again with CPUs. 2048bit is no where near 10^12 harder if you use GPUs with larger word/op/register sizes. That's especially so with FGPAs/custom hardware with custom sized words/registers/ops. With FGPAs and custom hardware you can also locate things physically in places to give a speed advantage. I really don't think you'd need a replacement for GNFS to do a 2048bit number.
This isn't directed at you, but I wish people would stop talking about how strong crypto is if they haven't written software to break it, don't understand the mathematics, and don't understand hardware design. I just facepalm and shake my head when people post publicly that you'd have to boil the oceans to factor a 1024bit number (break a 1024bit RSA openPGP key).
Re: Bruce Schneier has changed his PGP key to 4096 bits
#105Re: Bruce Schneier has changed his PGP key to 4096 bits
#106Earlier quoted context omitted.
How do you securely share the AES key?
AES is really great compared to RSA, so I put my AES key on my website instead of my RSA public key. It's made it very easy for people to contact me securely.
One of the saddest things about Snowden/Manning/NSA/etc. is that sarcasm and irony are no longer really safe to use in anything even vaguely related. Must really hurt The Onion.
Re: Bruce Schneier has changed his PGP key to 4096 bits
#107Earlier quoted context omitted.
>perhaps we need a geolocation aware social network a la Square but just for notifying you of other nearby PGP users... To what end though? What do you share in common with them other than the fact that you're both probably interested in cryptography? Just because you can easily communicate back and forth with encrypted messages doesn't mean you'll actually have much to talk about.
I want people to sign my public key. I don't care who they are but the more people do the more people can trust that it really is my key. Imagine if your phone told you that you are at the same coffee shop as someone who is also a registered PGP user and has not yet signed your key. That would be pretty easy, right?
I want something that makes signatures of defined meaning.
Like, signatures on my key for "controls the hn:rdl account", "controls rdl@mit.edu email address" etc. With dates, so I can accumulate multiple signatures over time.
I'd trust a key from someone with 14 years of "controlled ... email address" signatures on it more than someone showing me a plastic ID card in a bar.
Re: Bruce Schneier has changed his PGP key to 4096 bits
#108I know the fundamental idea behind PGP and related technologies. My question is, if bumping his key from 2048 to 4096 bits will keep him safe until around the year 2020 (as stated by a previous reader, and from keylength.com), why not just use a 8192 bit key, or 16384 bit key and be safe for virtually your lifetime? Does the computing cost to encrypt/decrypt make this impractical?
Time complexity of RSA operations is somewhere between O(n^2) and O(n^3) with n being number of bits of modulus, so using longer keys than necessary gets impractical really fast.
But doesn't PGP/GPG use the pub/priv key only to encrypt/decrypt a _symmetric_ key for the encryption/decryption of the actual data?
Re: Bruce Schneier has changed his PGP key to 4096 bits
#109Earlier quoted context omitted.
AES is really great compared to RSA, so I put my AES key on my website instead of my RSA public key. It's made it very easy for people to contact me securely.
AES is symmetric...
exactly... I am just as confused as you are. What's the point of using AES if you are putting its key out on the open? O_O that's like using a very sophisticated lock on your front door and put up a sign saying "The key is under the Mat"
Re: Bruce Schneier has changed his PGP key to 4096 bits
#110I know the fundamental idea behind PGP and related technologies. My question is, if bumping his key from 2048 to 4096 bits will keep him safe until around the year 2020 (as stated by a previous reader, and from keylength.com), why not just use a 8192 bit key, or 16384 bit key and be safe for virtually your lifetime? Does the computing cost to encrypt/decrypt make this impractical?
Time complexity of RSA operations is somewhere between O(n^2) and O(n^3) with n being number of bits of modulus, so using longer keys than necessary gets impractical really fast.
It should be O(n^2). Doubling the length of the key will incur a four-fold time requirement for any single RSA operation. (I verified this a few years ago when writing an article about practical cryptosystems.)
The reason is actually quite simple. As far as I understand, the bignum libraries store the large numbers as an array of "limbs". Doing a bignum operation requires the library to iterate through the array, one limb and a time. The operations required for a single RSA calculation are effectively "run every limb in array A against every limb in array B". So you have a nested for-loop for N elements without possibility for early termination.
As for the numbers from the article: my old 400MHz box spent 20ms signing or encrypting a block of data with 1024-bit RSA key. The same operations took 80ms with a 2048-bit key.