Everything about Finite field arithmetic

🧭 Start here: a 6-step reading path

1. Read the overview: Finite field arithmeticA 5-minute orientation
2. Skim a recent paper: VLSI Architecture of S-Box With High Area Efficiency Based on Composite Field ArithmeticInfluential work since 2022
3. Pick up a classic book: The School Track MeetThe most-reprinted book on the subject
4. Read the landmark paper: Efficient semisystolic architectures for finite-field arithmeticCited 111 times
5. Go sideways: Finite fieldA closely related topic
6. Go sideways: Rijndael S-boxA closely related topic

🏆 Landmark papers (most cited)

• Efficient semisystolic architectures for finite-field arithmetic

  S.K. Jain, L. Song, K.K. Parhi · 1998 · IEEE Transactions on Very Large Scale Integration (VLSI) Systems · 111 citations

• The Arithmetic of Polynomials in a Galois Field

  Leonard Carlitz · 1932 · American Journal of Mathematics · 59 citations

• ISA Extensions for Finite Field Arithmetic

  Erdem Alkim, Hülya Evkan, Norman Lahr · 2020 · IACR Transactions on Cryptographic Hardware and Embedded Systems · 52 citations

• Field programmable gate arrays and floating point arithmetic

  B. Fagin, C. Renard · 1994 · IEEE Transactions on Very Large Scale Integration (VLSI) Systems · 43 citations

• Finite Field Arithmetic for Cryptography

  Erkay Savas, Cetin Koc · 2010 · IEEE Circuits and Systems Magazine · 39 citations

• Arithmetic of function field units

  Bruno Anglès, Floric Tavares Ribeiro · 2016 · Mathematische Annalen · 21 citations

• Finite field models in arithmetic combinatorics – ten years on

  J. Wolf · 2015 · Finite Fields and Their Applications · 20 citations

• Stable arithmetic regularity in the finite field model

  C. Terry, J. Wolf · 2018 · Bulletin of the London Mathematical Society · 18 citations

🆕 Influential since 2022

• VLSI Architecture of S-Box With High Area Efficiency Based on Composite Field Arithmetic

  You-Tun Teng, Wen-Long Chin, Deng-Kai Chang · 2022 · IEEE Access · 26 citations

• An Optimized M-Term Karatsuba-Like Binary Polynomial Multiplier for Finite Field Arithmetic

  Madhan Thirumoorthi, Moslem Heidarpur, Mitra Mirhassani · 2022 · IEEE Transactions on Very Large Scale Integration (VLSI) Systems · 25 citations

• Flexible and area-efficient Galois field Arithmetic Logic Unit for soft-core processors

  Yao-Ming Kuo, Francisco Garcia-Herrero, Oscar Ruano · 2022 · Computers and Electrical Engineering · 8 citations

• On the Arithmetic Fundamental Lemma conjecture over a general $p$-adic field

  A. Mihatsch, W. Zhang · 2023 · Journal of the European Mathematical Society · 6 citations

• Accelerating Finite Field Arithmetic for Homomorphic Encryption on GPUs

  Neal Livesay, Gilbert Jonatan, Evelio Mora · 2023 · IEEE Micro · 5 citations

📚 Books worth reading

• The School Track MeetAlex Zander · 2013
• Representation theory of finite groups and associative algebrasCharles W. Curtis · 1962
• Stay in lineTeddy Slater, Gioia Fiammenghi · 1996
• 📕Perfectoid SpacesDebargha Banerjee, Kiran S. Kedlaya · 2019
• Arithmetic and Geometry Around Galois TheoryPierre Dèbes · 2012
• Algebraic geometry codesM. A. Tsfasman, Michael Tsfasman · 2007
• Collected Works of John TateBarry Mazur, Jean-Pierre Serre · 2016
• 📕Arithmétique des courbes elliptiques et théorie d'IwasawaBernadette Perrin-Riou · 1983

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics

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