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Craig Costello. B-SIDH: supersingular isogeny Diffie-Hellman using twisted torsion. Preprint 2019.

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

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

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

Craig Costello. Computing supersingular isogenies on Kummer surfaces. ASIACRYPT 2018.

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

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.

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

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.

Craig Costello, Patrick Longa and Michael Naehrig. Efficient algorithms for supersingular isogeny Diffie-Hellman. CRYPTO 2016. (Code).

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

Ping Ngai Chung, Craig Costello and Benjamin Smith. Fast, uniform, and compact scalar multiplication for elliptic curves and genus 2 Jacobians with applications to signature schemes. SAC 2016.

Craig Costello and Patrick Longa. FourQ: four-dimensional decompositions on a Q-curve over the Mersenne prime. ASIACRYPT 2015. (Code)

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. 

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

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. (Code)

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. (Code)

Huseyin Hisil and Craig Costello. Jacobian Coordinates on Genus 2 Curves. ASIACRYPT 2014 and Journal of Cryptology. (Code, more code)

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

Craig Costello, Huseyin Hisil, and Benjamin Smith. Faster Compact Diffie-Hellman: Endomorphisms on the x-line. EUROCRYPT 2014. (Code, more code)

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

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

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

Joppe W. Bos, Craig Costello, Huseyin Hisil and Kristin Lauter. Fast Cryptography in Genus 2. EUROCRYPT 2014 and the Journal of Cryptology. (Code, more code)

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.

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

Craig Costello and Douglas Stebila. Fixed Argument Pairings. LATINCRYPT 2010.

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

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

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

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