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On the Existence of Non-Linear Invariants and Algebraic Polynomial Constructive Approach to Backdoors in Block Ciphers
block ciphers Boolean functions Algebraic Normal Form
2018/11/19
In this paper we study cryptanalysis with non-linear polynomials cf. Eurocrypt’95 (adapted to Feistel ciphers at Crypto 2004). Previously researchers had serious difficulties in making such attacks wo...
Block Cipher Invariants as Eigenvectors of Correlation Matrices
invariant subspace attack nonlinear invariant attack linear cryptanalysis
2018/8/21
A new approach to invariant subspaces and nonlinear invariants is developed. This results in both theoretical insights and practical attacks on block ciphers. It is shown that, with minor modification...
Constructing Abelian Surfaces for Cryptography via Rosenhain Invariants
hyperelliptc curves complex multiplication Rosenhain invariants
2016/1/9
This paper presents an algorithm to construct cryptographically strong genus 2 curves and their
Kummer surfaces via Rosenhain invariants and related Kummer parameters. The most common
version of the...
On the Classification of Differential Invariants for Multivariate Post-Quantum Cryptosystems"
Matsumoto-Imai multivariate public key cryptography differential symmetry
2013/4/18
Multivariate Public Key Cryptography(MPKC) has become one of a few options for security in the quantum model of computing. Though a few multivariate systems have resisted years of effort from the cryp...
Computing genus 2 curves from invariants on the Hilbert moduli space
public-key cryptography Hyperelliptic curve cryptography
2010/7/13
We give a new method for generating genus 2 curves over a finite field with a given number of points on the Jacobian of the curve. We define two new invariants for genus 2 curves as values of modular ...
We adapt the CRT approach to computing Hilbert class polynomials
to handle a wide range of class invariants. For suitable discriminants D, this
improves its performance by a large constant factor, m...