Research

From arithmetic to systems.

I am interested in what happens when cryptographic structure meets implementation constraints: instruction sets, memory, side channels, wire formats, protocols, and deployment.

Post-quantum cryptographySQIsignIsogeniesFinite-field arithmeticDiscrete logarithmsCryptanalysisProtocol deployment
Francisco Rodríguez-Henríquez beside a Never Stop Reading sign

Post-quantum cryptography

My current work is strongly connected to the design, analysis, and implementation of post-quantum public-key primitives, particularly compact signatures and isogeny-based techniques.

SQIsign is a central example. Its exceptionally small public keys and signatures create an unusual design point: communication is extremely compact, while implementation cost and protocol integration remain important engineering questions. I am interested both in the underlying arithmetic and in what those tradeoffs mean once the scheme enters a larger system.

More broadly, I work on efficient post-quantum implementations, migration strategies, and the practical consequences of choosing one primitive over another rather than treating primitive benchmarks as the complete system story.

High-performance cryptography

Efficient cryptography is often an arithmetic problem disguised as a protocol problem.

My work has long focused on finite-field arithmetic, elliptic curves, pairings, and architecture-aware implementation. Recent projects include optimized SQIsign verification on Intel and Cortex-M4 and automatic generation of fast finite-field arithmetic for embedded processors.

The implementation perspective includes algorithmic restructuring, vectorization, constant-time behavior, memory use, instruction-set specialization, and the boundary between portable code and architecture-specific acceleration.

Cryptanalysis

We can also use cryptanalysis to understand systems that were never designed as cryptographic objects.

Recent collaborations have explored cryptanalytic extraction of neural-network parameters, including the hard-label setting. Earlier work includes discrete-logarithm computation, implementation attacks, and side-channel protections for isogeny-based cryptography.

Record computation. In 2016, with Gora Adj, Isaac Canales-Martínez, Nareli Cruz-Cortés, Alfred Menezes, Thomaz Oliveira, and Luis Rivera-Zamarripa, I participated in the computation of discrete logarithms in GF(36·509), a 4,841-bit finite field. Read more →

Cryptography in real systems

A primitive may perform beautifully in isolation, but once a protocol adds framing, transport, caching, and operational constraints, the system can tell a very different story.

These interactions form a central part of my current research. I study post-quantum authentication, PKI, protocol migration, and how key and signature sizes propagate through real systems. Instead of asking only which primitive benchmarks faster, I ask how the surrounding protocol changes the tradeoffs among competing designs.

Throughout this work, I try to distinguish the costs and benefits inherent in the cryptographic primitive from those introduced by the surrounding protocol. Making that distinction helps reveal when a faster algorithm actually leads to a better system.

The longer arc

Over the years my work has also covered elliptic-curve arithmetic, pairing-based cryptography, hardware acceleration, reconfigurable architectures, finite-field algorithms, discrete logarithms, and implementation security. The common thread is efficient public-key cryptography grounded in explicit arithmetic and measured implementation.