A team from Inria in Nancy and the Lorraine Research Laboratory and its applications (Loria – Inria, CNRS), associated with the universities of Limoges and San Diego (California), simultaneously beat two digital records. Both of these prowess experience the robustness of computer security systems as common as credit card payments or online communications. These researchers have demonstrated to what level the safety chains of such systems could hold, as they explained on Monday 2 December at the conference Elliptic curve cryptography in Bochum (Germany). These levels are measured by the size of the numbers, called keys, used in security protocols. Their answer is that the use of any number less than 240 digits (or 795 bits) is dangerous. That is, the encryption it allows could be broken and the messages decrypted.
Previous records for this type of exercise were 2009 and 2016 for 768-bit numbers. These few bits of discrepancy may seem small, but the experts felt that the "breaking" should be two and a half times more difficult.
The software used is now open source
It took 35 million computing hours (or 4,000 years for a PC with a single core) and three computing centers to overcome both records. The project was launched more than a year ago and consisted in improving the previous algorithm. Moreover, at equivalent machine power, researchers took 25% less time for this record than for the previous one. The software used is now open source, "There too a first", says Emmanuel Thomé, head of the team at Loria.
Two mathematical operations
Both records are related to two mathematical operations. The first is to look for the two prime numbers whose product gives the key of 795 bits. These numbers are then used to encrypt communications or messages. The second, called the discrete logarithm problem, involves power calculations and is usually used to protect the first step of a security protocol. Both are mathematical functions that are all the more difficult to reverse because the numbers involved are large.
The security of current computer exchanges is however not threatened since the keys used, or in any case recommended, are much larger, of the order of 2048 bits. "One of the benefits of this demonstration is to have shown that the two calculations are almost as difficult as the other, whereas the community thought that the problem of the discrete logarithm was harder", notes Emmanuel Thomé, who still identified a connected object with a key of 768 bits only.