Gokul Alex

"Learning with Errors" is a very intriguing term we come across when we study the fundamentals of lattice cryptography. It is a generalization of the Learning Parity with Noise (LPN) problem, which was originally formulated to describe how a machine might learn a secret linear function when the data is noisy or corrupted. The LPN assumption was first formally proposed as a hard problem for cryptography in 1993 by a team comprising Avirm Blum, Merrick Furst, Micheal Kerans, and Richard Lipton. LPN dealt w...

The National Institute of Standards and Technology (NIST), a globally prominent technology organization, views symmetric algorithms as quantum-resistant in principle, but with the caveat that their effective security is halved by Grover’s algorithm. It is interesting to note that the symmetric algorithms do not have a formal periodic structure that can be exploited by Shor’s algorithm. Thus, for a quantum computer, the category of symmetric algorithms functions like black boxes or random oracles. Advance...

While Hermann Minkowski laid the foundations for the geometric distribution of numbers in the early 19th century, he primarily dealt with fixed lattices. It was Carl Ludwig Siegel in 1945 who defined a random lattice, treating all the sets of possible lattices in a space. Siegel proved that there is a unique way to assign probabilities to the space of all possible lattices. Thus, lattice problems like the average length of the shortest vector in a general lattice became measurable. However, it took anoth...