Lattice Based Cryptography

Cryptography based on the hardness of lattice problems is seen as a very promising replacement of traditional cryptography after the eventual coming of quantum computers. This method uses the difficulty of lattice problems over the module lattices used in earlier encryption standards. Indeed, if you look at the entrants to the “post-quantum” international competition run by the US National Institute for Standards in Technology, which is focused on standardizing new post-quantum secure cryptography, you will notice that the largest family of submissions consist of lattice-based schemes including the few cited above. The delithium is one of these digital signatures that bypasses the use of complex mathematical equation. Basically, any regular space grid of points stretching out to infinity is a lattice and they are well understood and widely studied by mathematicians going back at least as far as the early 1800s. This encryption uses large lattices to calculate vectors positions which immensely increases the amount of operating space required to run the algorithm. Although highly secure, and relatively quick compared XMSS algorithm. The Delithium requires high processing power and cannot be used on smaller devices which limits its scalability.

 Lattice problems are proving to be incredibly versatile in terms of the types of cryptographic schemes they allow us to build. In fact, not only are we able to replace essentially all our currently endangered schemes, but lattice problems even allow for entirely new classes of quantum proof cryptographic. Another lattice-based encryption candidate submitted to the NSIT is the Falcon encryption which tackled the scalability and resource consumption problem encountered by the Delithium algorithm. The Falcon encryption is based on NTRU lattice problems which smaller lattices with more limited vector points. This allows for a more compact encryption that requires significantly lower processing power to run on. A lighter encryption uses less RAM (30KB) and is compatible with small, memory limited devices. At the detriment of smaller keys, this encryption resolves the scalability limitation usually posed by quantum proof cryptography.