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Some Exercise Answers to A Computational Introduction to Number Theory and Algebra by Victor Shoup (2nd Ed)

1 minute read

Published:

I’m currently learning the basics of number theory and algebra through “A Computational Introduction to Number Theory and Algebra by Victor Shoup”, recommended by my supervisor, Ron Steinfeld. To support others learning independently like myself, I’ll be sharing some of my solutions to the exercises from this book. I hope this will spark discussions and mutual learning. If you spot any inaccuracies or have suggestions, please feel free to reach out at Xinyu.Zhang1@monash.edu. (I’ll continue updating this blog whenever I find some free time, so check back for new insights!)

portfolio

publications

Revocable and linkable ring signature

Published in International Conference on Information Security and Cryptology (Inscrypt 2019), 2019

Keywords: Ring signature, Ring confidential transaction, Revocability, Linkability

Recommended citation: Zhang, Xinyu, Joseph K. Liu, Ron Steinfeld, Veronika Kuchta, and Jiangshan Yu. "Revocable and linkable ring signature." In Information Security and Cryptology: 15th International Conference, Inscrypt 2019, Nanjing, China, December 6–8, 2019, Revised Selected Papers 15, pp. 3-27. Springer International Publishing, 2020.
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DualRing-PRF: Post-Quantum (Linkable) Ring Signatures from Legendre and Power Residue PRFs

Published in The 29th Australasian Conference on Information Security and Privacy (ACISP 2024), 2024

Keywords: Ring Signature; Linkability; Post-Quantum; Symmetric Key Primitives

Recommended citation: Zhang, Xinyu, Ron Steinfeld, Joseph K. Liu, Muhammed F. Esgin, Dongxi Liu, and Sushmita Ruj. "DualRing-PRF: Post-quantum (Linkable) Ring Signatures from Legendre and Power Residue PRFs." In Australasian Conference on Information Security and Privacy, pp. 124-143. Singapore: Springer Nature Singapore, 2024.
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Loquat: A SNARK-Friendly Post-Quantum Signature based on the Legendre PRF with Applications in Ring and Aggregate Signatures

Published in Annual International Cryptology Conference (Crypto), 2024

Keywords: Post-Quantum Signature, Legendre PRF, SNARK, Aggregate Signature, ID-Based Ring Signature

Recommended citation: Zhang, Xinyu, Ron Steinfeld, Muhammed F. Esgin, Joseph K. Liu, Dongxi Liu, and Sushmita Ruj. "Loquat: A SNARK-Friendly Post-quantum Signature Based on the Legendre PRF with Applications in Ring and Aggregate Signatures." In Annual International Cryptology Conference, pp. 3-38. Cham: Springer Nature Switzerland, 2024.
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talks

Post-Quantum Signatures from Symmetric Key Primitives

Published:

The talk introduced various symmetric key primitives-based post-quantum signatures, including hash-based one time signatures, XMSS, SPHINCS+, Picnic, and our work Loquat which was published in Crypto 2024.

teaching

FIT5163 Information and Computer Security

Master course, Monash University, Faculty of Information Technology, 2026

This course is a cryptography foundation unit, students will learn symmetric key cryptography, asymmetric key cryptography such as RSA, DH key exchange, IBE, Schnorr’s signature, ring signature, lightweight cryptosystem, database security etc.

FIT1047 Introduction to Computer Systems, Networks and Security

Undergraduate Course, Monash University, Faculty of Information Technology, 2026

This is a foundation unit for computer science. The unit will cover logic circuit construction, circuit optimization, assembly languages, computer network, and information security.