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Math Advance Suggest RSA Encryption Could Fall Within 5 Years
holy_calamity writes "The two encryption systems used to secure the most important connections and digital files could become useless within years, reports MIT Technology Review, due to progress towards solving the discrete logarithm problem. Both RSA and Diffie-Hellman encryption rely on there being no efficient algorithm for that problem, but French math professor Antoine Joux has published two papers in the last six months that suggest one could soon be found. Security researchers that noticed Joux's work recommend companies large and small begin planning to move to elliptic curve cryptography, something the NSA has said is best practice for years. Unfortunately, key patents for implementing elliptic curve cryptography are controlled by BlackBerry."
Wow, that is so wrong.
RSA is an asymmetric (aka publick key) cipher - because it requires two keys - one to encrypt, one to decrypt. AES, DES, 3DES are symmetric ciphers because you use the same key to encrypt and decrypt.
RSA and EC (elliptic curve) encryption is useful if you want to send data to someone without the hassles of secretly sharing the key ahead of time - e.g., I can encrypt a message using the public key and only the private key can decrypt it. Or I can use my private key to encrypt a message, and the public key can be used to decrypt it (the latter is often used to sign stuff, except the message is typically a hash instead of the original message).
The reason you use AES, DES, 3DES is because public key encryption is hideously slow. In the case of RSA, you're exponentiating one horrendously large number with other horrendously large numbers. (If your message is long, that horrendously large number Is big).
That's why what every public key encryption thing does is it encrypts the message with a fast symmetric cipher like AES, then encrypts the key (much shorter) with RSA or EC. If I want to send you a document, I encrypt it with AES, then use your public key to encrypt the AES key I used.
It's also why signing uses a hash - it's easier to encrypt the hash than the message. And verification just means recomputing the hash, and then decrypting the encrypted hash with the public key, producing the original hash to which can be compared to the just computed one.
The breakthrough in math would be a way to factor a large number quickly - which is what RSA relies on for security - it's easy to multiply two big numbers, but it's very time consuming to factor it.
I didn't say that you said that AES could replace RSA: I said that your AES/DES analogy didn't support your statement that RSA is or should be deprecated. That may sound like I'm nitpicking here, but I'm really not: it's pretty fundamental to my point. And the reason is this:
This absolutely need not be true. RSA for instance is based in part around a hardness assumption: that given a very large number n which is the product of p and q, it is far harder to find p and q from n then it is to find n from p and q. Assume for the sake of argument that this is the only hardness assumption RSA depends on. (If the summary isn't misleading it apparently also depends on the hardness of discrete log, but I don't know how.)
If the hardness assumption holds, then RSA as such will never be insecure. Why? Suppose you say "here is a computer capable of factoring a number n with b bits." I'll say "OK, fine; I'll use 100*b bits (or something)"; because multiplying is so much easier than factoring, your computer will still be able to carry out that task but it won't be able to crack my key.
In other words, if the hardness assumption holds, RSA doesn't have a specific difficulty: it can scale with computational power. That's why you see people using 2048-bit keys now instead of 512-bit keys a couple of decades ago.
The only things that the age of the algorithm has to say about the security of it is (1) if the difficulty cannot scale with computational power (true of DES, not true of RSA) and (2) being out longer gives people more time to find flaws in its assumptions.
But here's the thing: #2 isn't necessarily bad or speak against the algorithm. It is conceivable that the assumptions just fundamentally hold. If they do, being out longer will not impact the security at all. If anything, being out longer with no one discovering anything should give a higher assurance that an algorithm is secure than a newer one would.
I don't think I've ever heard a blanket statement about RSA being insecure -- only things like certain key sizes or certain implementations or PRNGs being insecure. (Wikipedia also lists a couple of side-channel and plain-text attacks, but those are also arguably quality-of-implementation issues, and similar attacks exist for EC systems.) The intro to the Wikipedia article says nothing about RSA being insecure. "Deprecated" and "discouraged" both fail to appear on the page.
The strongest statement against RSA I've heard is just that EC is better.
Except that the DES vs AES case is not even close to being the same case, as Adam Van Ymeren said in response to you, and then I elaborated on elsewhere and above.
The reason it's not even close is that DES does not scale with computational power, because it has a fixed key size.