Faster Pairings on Special Weierstrass Curves. - Craig Costello; Hüseyin Hisil; Colin Boyd; Juan Manuel González Nieto; Kenneth Koon-Ho Wong (IACR Cryptol. ePrint Arch., 2009)

Faster Pairing Computations on Curves with High-Degree Twists. - Craig Costello; Tanja Lange 001; Michael Naehrig (IACR Cryptol. ePrint Arch., 2009)

Avoiding Full Extension Field Arithmetic in Pairing Computations. - Craig Costello; Colin Boyd; Juan Manuel González Nieto; Kenneth Koon-Ho Wong (IACR Cryptol. ePrint Arch., 2010)

Delaying Mismatched Field Multiplications in Pairing Computations. - Craig Costello; Colin Boyd; Juan Manuel González Nieto; Kenneth Koon-Ho Wong (IACR Cryptol. ePrint Arch., 2010)

Fixed Argument Pairings. - Craig Costello; Douglas Stebila (IACR Cryptol. ePrint Arch., 2010)

Group Law Computations on Jacobians of Hyperelliptic Curves. - Craig Costello; Kristin E. Lauter (IACR Cryptol. ePrint Arch., 2011)

Attractive Subfamilies of BLS Curves for Implementing High-Security Pairings. - Craig Costello; Kristin E. Lauter; Michael Naehrig (IACR Cryptol. ePrint Arch., 2011)

Two is Greater than One. - Joppe W. Bos; Craig Costello; Hüseyin Hisil; Kristin E. Lauter (IACR Cryptol. ePrint Arch., 2012)

Particularly Friendly Members of Family Trees. - Craig Costello (IACR Cryptol. ePrint Arch., 2012)

High-Performance Scalar Multiplication using 8-Dimensional GLV/GLS Decomposition. - Joppe W. Bos; Craig Costello; Hüseyin Hisil; Kristin E. Lauter (IACR Cryptol. ePrint Arch., 2013)

Elliptic and Hyperelliptic Curves: a Practical Security Analysis. - Joppe W. Bos; Craig Costello; Andrea Miele (IACR Cryptol. ePrint Arch., 2013)

Exponentiating in Pairing Groups. - Joppe W. Bos; Craig Costello; Michael Naehrig (IACR Cryptol. ePrint Arch., 2013)

Faster Compact Diffie-Hellman: Endomorphisms on the x-line. - Craig Costello; Hüseyin Hisil; Benjamin Smith 003 (IACR Cryptol. ePrint Arch., 2013)

Post-quantum key exchange for the TLS protocol from the ring learning with errors problem. - Joppe W. Bos; Craig Costello; Michael Naehrig; Douglas Stebila (IACR Cryptol. ePrint Arch., 2014)

Geppetto: Versatile Verifiable Computation. - Craig Costello; Cédric Fournet; Jon Howell; Markulf Kohlweiss; Benjamin Kreuter; Michael Naehrig; Bryan Parno; Samee Zahur (IACR Cryptol. ePrint Arch., 2014)

Constructing abelian surfaces for cryptography via Rosenhain invariants. - Craig Costello; Alyson Deines-Schartz; Kristin E. Lauter; Tonghai Yang (LMS J. Comput. Math., 2014)

Subgroup security in pairing-based cryptography. - Paulo S. L. M. Barreto; Craig Costello; Rafael Misoczki; Michael Naehrig; C. C. F. Pereira Geovandro; Gustavo H. M. Zanon (IACR Cryptol. ePrint Arch., 2015)

Fast, uniform, and compact scalar multiplication for elliptic curves and genus 2 Jacobians with applications to signature schemes. - Ping Ngai Chung; Craig Costello; Benjamin Smith 003 (IACR Cryptol. ePrint Arch., 2015)

FourQ: four-dimensional decompositions on a Q-curve over the Mersenne prime. - Craig Costello; Patrick Longa (IACR Cryptol. ePrint Arch., 2015)

Complete addition formulas for prime order elliptic curves. - Joost Renes; Craig Costello; Lejla Batina (IACR Cryptol. ePrint Arch., 2015)

Frodo: Take off the ring! Practical, Quantum-Secure Key Exchange from LWE. - Joppe W. Bos; Craig Costello; Léo Ducas; Ilya Mironov; Michael Naehrig; Valeria Nikolaenko; Ananth Raghunathan; Douglas Stebila (IACR Cryptol. ePrint Arch., 2016)

Fast, uniform scalar multiplication for genus 2 Jacobians with fast Kummers. - Ping Ngai Chung; Craig Costello; Benjamin Smith 003 (IACR Cryptol. ePrint Arch., 2016)

Efficient compression of SIDH public keys. - Craig Costello; David Jao; Patrick Longa; Michael Naehrig; Joost Renes; David Urbanik (IACR Cryptol. ePrint Arch., 2016)

Efficient algorithms for supersingular isogeny Diffie-Hellman. - Craig Costello; Patrick Longa; Michael Naehrig (IACR Cryptol. ePrint Arch., 2016)

Selecting elliptic curves for cryptography: an efficiency and security analysis. - Joppe W. Bos; Craig Costello; Patrick Longa; Michael Naehrig (J. Cryptogr. Eng., 2016)

Fast Cryptography in Genus 2. - Joppe W. Bos; Craig Costello; Hüseyin Hisil; Kristin E. Lauter (J. Cryptol., 2016)

Montgomery curves and their arithmetic. - Craig Costello; Benjamin Smith 003 (CoRR, 2017)

A simple and compact algorithm for SIDH with arbitrary degree isogenies. - Craig Costello; Hüseyin Hisil (IACR Cryptol. ePrint Arch., 2017)

Jacobian Coordinates on Genus 2 Curves. - Hüseyin Hisil; Craig Costello (J. Cryptol., 2017)

Computing supersingular isogenies on Kummer surfaces. - Craig Costello (IACR Cryptol. ePrint Arch., 2018)

Montgomery curves and their arithmetic - The case of large characteristic fields. - Craig Costello; Benjamin Smith 003 (J. Cryptogr. Eng., 2018)

The supersingular isogeny problem in genus 2 and beyond. - Craig Costello; Benjamin Smith 003 (IACR Cryptol. ePrint Arch., 2019)

B-SIDH: supersingular isogeny Diffie-Hellman using twisted torsion. - Craig Costello (IACR Cryptol. ePrint Arch., 2019)

Supersingular isogeny key exchange for beginners. - Craig Costello (IACR Cryptol. ePrint Arch., 2019)

Improved Classical Cryptanalysis of the Computational Supersingular Isogeny Problem. - Craig Costello; Patrick Longa; Michael Naehrig; Joost Renes; Fernando Virdia (IACR Cryptol. ePrint Arch., 2019)

Improved Classical Cryptanalysis of SIKE in Practice. - Craig Costello; Patrick Longa; Michael Naehrig; Joost Renes; Fernando Virdia (Public Key Cryptography (2), 2020)

Sieving for twin smooth integers with solutions to the Prouhet-Tarry-Escott problem. - Craig Costello; Michael Meyer 001; Michael Naehrig (IACR Cryptol. ePrint Arch., 2020)

The Case for SIKE: A Decade of the Supersingular Isogeny Problem. - Craig Costello (IACR Cryptol. ePrint Arch., 2021)

SuperSolver: accelerating the Delfs-Galbraith algorithm with fast subfield root detection. - Maria Corte-Real Santos; Craig Costello; Jia Shi (IACR Cryptol. ePrint Arch., 2021)

Accelerating the Delfs-Galbraith Algorithm with Fast Subfield Root Detection. - Maria Corte-Real Santos; Craig Costello; Jia Shi (CRYPTO (3), 2022)

Cryptographic Smooth Neighbors. - Giacomo Bruno; Maria Corte-Real Santos; Craig Costello; Jonathan Komada Eriksen; Michael Naehrig; Michael Meyer 001; Bruno Sterner (IACR Cryptol. ePrint Arch., 2022)

An algorithm for efficient detection of (N, N)-splittings and its application to the isogeny problem in dimension 2. - Maria Corte-Real Santos; Craig Costello; Sam Frengley (IACR Cryptol. ePrint Arch., 2022)

Efficient (3, 3)-isogenies on fast Kummer surfaces. - Maria Corte-Real Santos; Craig Costello; Benjamin Smith 003 (CoRR, 2024)

Lollipops of pairing-friendly elliptic curves for composition of proof systems. - Craig Costello; Gaurish Korpal (IACR Cryptol. ePrint Arch., 2024)

On cycles of pairing-friendly abelian varieties. - Maria Corte-Real Santos; Craig Costello; Michael Naehrig (IACR Cryptol. ePrint Arch., 2024)

Efficient (3,3)-isogenies on fast Kummer surfaces. - Maria Corte-Real Santos; Craig Costello; Benjamin Smith 003 (IACR Cryptol. ePrint Arch., 2024)

On pairs of primes with small order reciprocity. - Craig Costello; Gaurish Korpal (IACR Cryptol. ePrint Arch., 2025)

Efficient algorithms for the detection of (N,N)-splittings and endomorphisms. - Maria Corte-Real Santos; Craig Costello; Sam Frengley (IACR Cryptol. ePrint Arch., 2025)