Frauke Bleher
University of Iowa, IA·Mathematics & Statistics
Quantum computers could one day break many of the encryption methods that protect online banking and other digital communication. Lattice-based cryptography is a leading family of encryption schemes designed to resist such attacks.
- Fields
Mathematics & Statistics
Computer Science
- Topics
number theory
lattice-based cryptography
post-quantum cryptography
- Grants
- 1 known grant, through Jun 2028
What they work on
- Improve explicit constructions of infinite families of number fields with small root discriminants, using Galois cohomology, explicit Chebotarev theorems and p-adic and modular-form methods related to Hilbert's 12th problem.
- Determine the computational complexity of constructing number fields with small root discriminants and of performing arithmetic in their rings of integers.
- Develop fast Fourier methods for the arithmetic operations needed in lattice-based cryptography over these dense lattices.
- Build efficient cryptographic protocols from these rings, including collision-resistant hash functions, homomorphic commitments, zero-knowledge proofs and digital signatures.
More about the research
A lattice is a regular grid of points in many dimensions. This collaborative project uses recent advances in number theory to make lattice-based cryptography more efficient. It builds lattices that support both addition and multiplication and that pack their points more densely than the lattices now typically used.
Why it matters
Secure communication, such as the transfer of financial data, will need encryption that survives quantum computers. Denser, faster lattices built from number fields with small root discriminants could make quantum-resistant tools more efficient. These tools include hash functions, digital signatures and zero-knowledge proofs.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Jason LeGrow
Virginia Polytechnic Institute and State University, VA·Computer Science
Construct post-quantum blind signatures, threshold signatures and multisignatures based on lattices, error-correcting codes and group actions such as isogenies, maps between elliptic curves.
Jean-Francois Biasse
University of South Florida, FL·Mathematics & Statistics
Investigate hard algebraic and number-theoretic problems, including finding short vectors in Euclidean lattices, isogenies between curves, and inverting group actions, as foundations for next-generation cryptosystems.
Omkant Pandey
Stony Brook University, NY·Computer Science·Early-career
Construct secure multi-party computation protocols that remain secure when many sessions run concurrently and the adversary is a quantum computer, closing open questions in post-quantum secure computation.
The school
University of Iowa: 32 labs on PI Pages, $703M a year on research, 418 research doctorates a year.
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