Papers

• Craig Costello and Gaurish Korpal. On pairs of primes with small order reciprocity. Preprint.

• Maria Corte-Real Santos, Craig Costello, and Sam Frengley. Efficient algorithms for the detection of (N,N)-splittings and endomorphisms. Preprint.

• Craig Costello and Gaurish Korpal. Lollipops of pairing-friendly elliptic curves for composition of proof systems. Preprint.

• Maria Corte-Real Santos, Craig Costello, and Benjamin Smith. Efficient (3,3)-isogenies on fast Kummer surfaces. ANTS XVI. Full version.

• Maria Corte-Real Santos, Craig Costello, and Michael Naehrig. On cycles of pairing-friendly abelian varieties. CRYPTO 2024. Full version.

• Maria Corte-Real Santos, Craig Costello, and Sam Frengley. An algorithm for efficient detection of (N, N)-splittings and its application to the isogeny problem in dimension 2. PKC2024. Best Paper Award. Full version.

• Giacomo Bruno, Maria Corte-Real Santos, Craig Costello, Jonathan Komada Eriksen, Michael Meyer, Michael Naehrig, and Bruno Sterner. Cryptographic Smooth Neighbors. ASIACRYPT 2023. Full version.

• Maria Corte-Real Santos, Craig Costello and Jia Shi. Accelerating the Delfs-Galbraith algorithm with fast subfield root detection. CRYPTO 2022. Full version.

• Craig Costello. The Case for SIKE: A Decade of the Supersingular Isogeny Problem. The NIST 3rd Post-Quantum Cryptography Standardization Conference. White paper.

• Craig Costello, Michael Meyer and Michael Naehrig. Sieving for twin smooth integers with solutions to the Prouhet-Tarry-Escott problem. EUROCRYPT 2021. Full version.

• Craig Costello. B-SIDH: supersingular isogeny Diffie-Hellman using twisted torsion. ASIACRYPT 2020. Full version.

• Craig Costello and Benjamin Smith. The supersingular isogeny problem in genus 2 and beyond. PQCrypto 2020. Full version.

• Craig Costello, Patrick Longa, Michael Naehrig, Joost Renes and Fernando Virdia. Improved classical cryptanalysis of SIKE in practice. PKC 2020. Full version.

• Craig Costello. Supersingular isogeny key exchange for beginners. Invited paper at SAC 2019. Full version.

• Craig Costello. Computing supersingular isogenies on Kummer surfaces. ASIACRYPT 2018. Full version.

• Craig Costello and Huseyin Hisil. A simple and compact algorithm for SIDH with arbitrary degree isogenies. ASIACRYPT 2017. Full version.

• Craig Costello and Benjamin Smith. Montgomery curves and their arithmetic: the case of large characteristic fields. Special issue of Journal of Cryptographic Engineering in tribute to Peter L. Montgomery, 2017. Full version.

• Craig Costello, David Jao, Patrick Longa, Michael Naehrig, Joost Renes and David Urbanik. Efficient compression of SIDH public keys. EUROCRYPT 2017. Full version.

• Joppe Bos, Craig Costello, Léo Ducas, Ilya Mironov, Michael Naehrig, Valeria Nikolaenko, Ananth Raghunathan and Douglas Stebila. Frodo: Take off the ring! Practical, Quantum-Secure Key Exchange from LWE. ACM CCS 2016. Full version.

• Craig Costello, Patrick Longa and Michael Naehrig. Efficient algorithms for supersingular isogeny Diffie-Hellman. CRYPTO 2016. Full version.

• Joost Renes, Craig Costello and Lejla Batina. Complete addition formulas for prime order elliptic curves. EUROCRYPT 2016. Full version.

• Ping Ngai Chung, Craig Costello and Benjamin Smith. Fast, Uniform Scalar Multiplication for Genus 2 Jacobians with Fast Kummers. SAC 2016. Full version.

• Craig Costello and Patrick Longa. FourQ: four-dimensional decompositions on a Q-curve over the Mersenne prime. ASIACRYPT 2015. Full version.

• Paulo S. L. M. Barreto, Craig Costello, Rafael Misoczki, Michael Naehrig, Geovandro C. C. F. Pereira and Gustavo Zanon. Subgroup security in pairing-based cryptography. LATINCRYPT 2015. Full version.

• Craig Costello, Cedric Fournet, Jon Howell, Markulf Kohlweiss, Benjamin Kreuter, Michael Naehrig, Bryan Parno, and Samee Zahur. Gepetto: Versatile Verifiable Computation.  IEEE S&P2015. Full version.

• Joppe W. Bos, Craig Costello, Michael Naehrig, and Douglas Stebila. Post-quantum key exchange for the TLS protocol from the ring learning with errors problem. IEEE S&P2015. Full version.

• Joppe W. Bos, Craig Costello, Patrick Longa, and Michael Naehrig. Selecting Elliptic Curves for Cryptography: An Efficiency and Security Analysis. Journal of Cryptographic Engineering, 2015. Full version.

• Huseyin Hisil and Craig Costello. Jacobian Coordinates on Genus 2 Curves. ASIACRYPT 2014 and Journal of Cryptology. Full version.

• Craig Costello, Alyson Deines-Schartz, Kristin Lauter, and Tonghai Yang. Constructing Abelian Surfaces for Cryptography via Rosenhain Invariants. ANTS 2014. Full version.

• Craig Costello, Huseyin Hisil, and Benjamin Smith. Faster Compact Diffie-Hellman: Endomorphisms on the x-line. EUROCRYPT 2014. Full version.

• Joppe W. Bos, Craig Costello, and Andrea Miele. Elliptic and Hyperelliptic Curves: a Practical Security Analysis. PKC 2014. Full version.

• Joppe W. Bos, Craig Costello, and Michael Naehrig. Exponentiating in Pairing Groups. SAC 2013. Full version.

• Joppe W. Bos, Craig Costello, Huseyin Hisil and Kristin Lauter. High-Performance Scalar Multiplication using 8-Dimensional GLV/GLS Decomposition. CHES 2013. Full version.

• Joppe W. Bos, Craig Costello, Huseyin Hisil and Kristin Lauter. Fast Cryptography in Genus 2. EUROCRYPT 2013 and the Journal of Cryptology. Full version.

• Craig Costello. Fast formulas for computing cryptographic pairings. Ph.D. thesis.

• Craig Costello, Kristin Lauter, and Michael Naehrig. Attractive subfamilies of BLS Curves for Implementing High-Security Pairings. INDOCRYPT 2011. Full version.

• Craig Costello and Kristin Lauter. Group Law Computations on Jacobians of Hyperelliptic Curves. SAC 2011. Full version.

• Craig Costello and Douglas Stebila. Fixed Argument Pairings. LATINCRYPT 2010. Full version.

• Craig Costello, Colin Boyd, Juan Manuel Gonzalez Nieto, and Kenneth Koon-Ho Wong. Delaying mismatched field multiplications in pairing computations. WAIFI 2010. Full version.

• Craig Costello, Colin Boyd, Juanma Gonzalez-Nieto, and Kenneth Koon-Ho Wong. Avoiding full extension field arithmetic in pairing computations. AFRICACRYPT 2010. Full version.

• Craig Costello, Tanja Lange, and Michael Naehrig. Faster pairing computations on curves with high-degree twists. PKC 2010. Full version.

• Craig Costello, Huseyin Hisil, Colin Boyd, Juan Manuel Gonzalez Nieto, and Kenneth Koon-Ho Wong. Faster pairings on special Weierstrass curves. PAIRING 2009. Full version