Efficient hardware implementation of finite fields with applications to cryptography

DOI10.1007/s10440-006-9072-zzbMath1105.12003OpenAlexW4238750631MaRDI QIDQ850794

Tim Güneysu, Christof Paar, Sandeep S. Kumar, Jorge Guajardo, Jan Pelzl

Publication date: 6 November 2006

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-006-9072-z

zbMATH Keywords

cryptographyfield arithmeticbinary field arithmeticextension field arithmeticprime field arithmeticaddersmultiplication circuits

Mathematics Subject Classification ID

Related Items (3)

A new bit-serial multiplier over \(GF(pm)\) using irreducible trinomials ⋮ Complexity of computation in finite fields ⋮ A survey of some recent bit-parallel \(\mathrm{GF}(2^n)\) multipliers

Uses Software

• Xilinx

Cites Work

• A fast algorithm for computing multiplicative inverses in \(\text{GF}(2^ m)\) using normal bases
• Hyperelliptic cryptosystems
• Elliptic curve cryptosystems over small fields of odd characteristic
• Itoh-Tsujii inversion in standard basis and its application in cryptography and codes
• Modular Multiplication Without Trial Division
• A redundant representation of GF(qⁿ) for designing arithmetic circuits
• Efficient bit-serial multiplication and the discrete-time Wiener-Hopf equation over finite fields
• Bit Serial Multiplication in Finite Fields
• A Computer Algorithm for Calculating the Product AB Modulo M
• Elliptic Curve Cryptosystems
• New directions in cryptography
• Novel approaches to the design of VLSI RNS multipliers
• A method for obtaining digital signatures and public-key cryptosystems
• Residue Number Scaling and Other Operations Using ROM Arrays
• Irreducible trinomials over finite fields
• Fast combinatorial RNS processors for DSP applications
• The Montgomery inverse and its applications
• A low-complexity combinatorial RNS multiplier
• Progress in Cryptology - INDOCRYPT 2003
• On primitive trinomials (Mod 2)
• On primitive trinomials (mod 2), II
• On xn + x + 1 over GF(2)
• On the polynomial residue number system (digital signal processing)
• Efficient arithmetic in finite field extensions with application in elliptic curve cryptography.
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