Portrait of Craig Costello

Craig Costello



I am primarily interested in the cryptographic applications of algorithmic number theory and computational algebraic geometry; in particular, curve-, pairing-, and lattice-based cryptography.



Established: August 26, 2015

FourQlib is an efficient and portable math library that provides functions for computing essential elliptic curve operations on a new, high-performance curve called "FourQ". This curve targets the 128-bit security level and supports computations that are significantly faster than any other alternative; e.g., it is between four and five times faster than the NIST P-256 curve and between two and three times faster than Curve25519. The library is available for download at the link below.…

MSR Elliptic Curve Cryptography Library

Established: June 27, 2014

MSR ECCLib is an efficient cryptography library that provides functions for computing essential elliptic curve operations on a new set of high-security curves.  All computations on secret data exhibit regular, constant-time execution, providing protection against timing and cache attacks.  The library is available for download below. Library Features MSR ECCLib supports six high-security elliptic curves proposed in [2], which cover three security levels (128-, 192-, and 256-bit security) and two curve models. The curves have a…

Verifiable Computing

Established: August 24, 2011

Verifiable computation schemes enable a client to outsource the computation of a function F on various inputs to an untrusted worker, and then verify the correctness of the returned results. Critically, the outsourcing and verification procedures must be more efficient than performing the computation itself. In more detail, we introduce and formalize the notion of Verifiable Computation, which enables a computationally weak client to "outsource" the computation of an arbitrary function F on various dynamically-chosen…

Lattice-based Cryptography

Established: July 3, 2010

Lattices are geometric objects that have recently emerged as a powerful tool in cryptography. Lattice-based schemes have also proven to be remarkably resistant to sub-exponential and quantum attacks (in sharp contrast to their number-theoretic friends). Our goal is to use lattices to construct cryptographic primitives that are simultaneously highly efficient and highly functional. Our Techfest Poster on Lattice-based Cryptography

Number Theory and Arithmetic Geometry

Established: August 27, 2009

Research on number theory and arithmetic geometry Related Links Cryptography group Events Computer Security and Cryptography (April 12-16, 2010)








I previously was a post-doc in the Cryptography Research Group at MSR, a post-doc in the Department of Mathematics and Computer Science at Technische Universiteit Eindhoven in the Netherlands, a PhD student in the Information Security Institute at the Queensland University of Technology in Australia, twice an intern here at MSR, and a Fulbright Scholar visiting the Number Theory Group at the University of California, Irvine.