On polynomial modular number systems over \(\mathbb{Z}/p\mathbb{Z}\)

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Lattices and convex bodies (number-theoretic aspects) (11H06) Polynomials over finite fields (11T06) Algorithms in computer science (68W99)

Cites Work

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LLL for ideal lattices: re-evaluation of the security of Gentry-Halevi's FHE scheme
Korkin-Zolotarev bases and successive minima of a lattice and its reciprocal lattice
On Lovász' lattice reduction and the nearest lattice point problem
Factoring polynomials with rational coefficients
Sur quelques cas d'irréductibilité des polynomes à coefficients rationnels.
Saber: module-LWR based key exchange, CPA-secure encryption and CCA-secure KEM
An alternative approach for SIDH arithmetic
An introduction to the geometry of numbers.
Mathematics of Public Key Cryptography
Algorithms for the Shortest and Closest Lattice Vector Problems
Efficient Multiplication over Extension Fields
On the Irreducibility of Certain Trinomials and Quadrinomials.
Modular Multiplication Without Trial Division
Efficient Modular Arithmetic in Adapted Modular Number System Using Lagrange Representation
Improved Analysis of Kannan’s Shortest Lattice Vector Algorithm
Finite Field Multiplication Combining AMNS and DFT Approach for Pairing Cryptography
Elliptic Curve Cryptosystems
A New Algorithm for Factoring Polynomials Over Finite Fields
A method for obtaining digital signatures and public-key cryptosystems
Block Reduced Lattice Bases and Successive Minima
Fast Cryptography in Genus 2
The factorization of certain quadrinominals.
Cryptographic Hardware and Embedded Systems - CHES 2004
Schönemann–Eisenstein–Dumas-Type Irreducibility Conditions that Use Arbitrarily Many Prime Numbers
On quadratic forms.
Faster integer multiplication using short lattice vectors

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