Amoeba basis of zero-dimensional varieties

On Gröbner Basis Detection for Zero-dimensional Ideals

The Gröbner basis detection (GBD) is defined as follows: Given a set of polynomials, decide whether there exists -and if “yes” finda term order such that the set of polynomials is a Gröbner basis. This problem was shown to be NP-hard by Sturmfels and Wiegelmann. We show that GBD when studied in the context of zero dimensional ideals is also NP-hard. An algorithm to solve GBD for zero dimensiona...

A Zero-Dimensional Gröbner Basis for AES-128

We demonstrate an efficient method for computing a Gröbner basis of a zero-dimensional ideal describing the key-recovery problem from a single plaintext/ciphertext pair for the full AES-128. This Gröbner basis is relative to a degree-lexicographical order. We investigate whether the existence of this Gröbner basis has any security implications for the AES.

Cryptography on Trace-Zero Varieties

Zero-dimensional proximities and zero-dimensional compactifications

Article history: Received 4 August 2008 Received in revised form 12 December 2008 Accepted 13 December 2008 MSC: 54E05 54D35 54G05

Pairing with Supersingular Trace Zero Varieties Revisited

A Trace Zero Variety is a specific subgroup of the group of the divisor classes on a hyperelliptic curve C/Fq, which are rational over a small degree extension Fqr of the definition field. Trace Zero Varieties (TZV) are interesting for cryptographic applications since they enjoy properties that can be exploited to achieve fast arithmetic and group construction. Furthermore, supersingular TZV al...