On the Properties of Error Patterns in the Constant Lee Weight Channel

TL;DR

This paper investigates scalar multiplication effects on vectors in the Lee metric, highlighting implications for cryptography, and introduces methods for constructing and sampling vectors with constant Lee weight.

Contribution

It analyzes the scalar multiplication problem in the Lee metric and proposes an efficient method for generating and sampling vectors with constant Lee weight.

Findings

Scalar multiplication can alter Lee weight unpredictably.

A new method for constructing vectors with constant Lee weight.

An efficient uniform sampling technique for such vectors.

Abstract

The problem of scalar multiplication applied to vectors is considered in the Lee metric. Unlike in other metrics, the Lee weight of a vector may be increased or decreased by the product with a nonzero, nontrivial scalar. This problem is of particular interest for cryptographic applications, like for example Lee metric code-based cryptosystems, since an attacker may use scalar multiplication to reduce the Lee weight of the error vector and thus to reduce the complexity of the corresponding generic decoder. The scalar multiplication problem is analyzed in the asymptotic regime. Furthermore, the construction of a vector with constant Lee weight using integer partitions is analyzed and an efficient method for drawing vectors of constant Lee weight uniformly at random from the set of all such vectors is given.