Slashdot Mirror
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."
Your first sentence sounds weird to me, and it isn't supported by your second. AES can't be a suitable replacement for RSA because AES is a secret-key system and RSA is a public-key one.
I'm not a crypto person, but RSA and elliptic-curve systems are the only two public-key systems I can think of. (There are others that allow secure exchange of a secret key, but that's different.)
Based on my limited understanding, proving P = NP would not necessarily and automatically provide a manner of constructing reductions. It might. But there are proofs in computation theory that demonstrate limit complexities but do not provide the algorithms that might implement them, nor do they (currently, visibly) provide any indication of how that algorithm may be arrived at.
Besides, proving P = NP would have a vast number of consequences that would echo across mathematics and the more fundamental sciences. To harp upon the security implications is as short-sighted as fretting that all-out thermonuclear war would negatively affect the postal delivery service.
"Place me in the company of those who seek Truth, but deliver me from those who believe to have found it."
The story is talking about the possibility of a mathematical breakthrough that would make solving the discrete logarithm problem (and possibly the integer factorisation problem) much, much easier. RSA relies on it being much easier to raise something to an integer power than to find a discrete logarithm (inverse operations). If you figure out how to make the two operations of similar difficulty then any encryption scheme based on them is hopelessly broken for any key size.
You misunderstand the difference between throwing hardware at a problem and coming up with a more efficient algorithm.
RSA doesn't specify a key length. I can use a key that's 64 bits long (used originally but insecure today) or 1 megabit long (secure against known classical algorithms for the age of the universe no matter how much hardware you throw at it). As hardware gets better I can encrypt things using longer keys, in the same amount of time. It takes you MUCH MORE time to decrypt that, even with the better hardware. So long as you keep increasing key length as hardware gets faster, the encryption actually gets BETTER with better hardware.
The article is talking about a breakthrough in mathematics that could make solving discrete algorithms much faster. If it made it anywhere near as fast as exponentiation then it wouldn't take me much longer to decrypt your message than it took you to encrypt it, regardless of key length.
DES is insecure because it uses fixed length keys, that became practical to brute force. RSA doesn't have that problem. The situations are entirely different, and the potential breaking of RSA is much more interesting, and much more of an accomplishment.