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This project involves research into the computational hardness of the search for short elements of the so-called Euclidean lattices. The hardness of this task is the measure of the security of one of the most promising family of cryptographic protocols that are conjectured to resist attacks from quantum computers. The transition toward such protocols is an immediate priority for the cryptography community. Indeed, quantum-safe primitives will need to be ready and deployed long before the construction of large scale quantum computers to account for the shelf life of encrypted data. The results from this research are disseminated to a large audience ranging from industrials willing to adopt quantum-safe primitives, university students, and K-12 students. This project supports a week-long cybersecurity camp for high school students who discover the fundamentals for security and cryptography through hands-on activities.
This project specifically focuses on the hardness of the search for short vectors in Euclidean lattices that are ideals of a number field. This special class of lattices, called ideal lattices, is very popular in lattice-based cryptography because it allows interesting optimizations including the use of significantly shorter keys. However, the restriction to a smaller class of lattices having more algebraic structure could also mean that the search for short elements is not as hard as in general lattices. Building on previous work of the investigator on the computation of invariants of number fields, this project investigates the algebraic methods allowing the search for short elements in ideal lattices.
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CAREER: Algebraic Methods for the Computation of Approximate Short Vectors in Ideal Lattices