All-but-one Vector Commitments (AVCs) randomly opens all but one of the committed vector values. Typically AVCs are instantiated using Goldwasser-Goldreich-Micali (GGM) trees. Generating these trees comprises a significant computational cost for AVCs due to a large number of hash function calls. Correlated GGM (cGGM) trees have been proposed to halve the number of hash calls and Batched AVCs (BAVCs) using a single GGM tree were integrated in the FAEST signature scheme, which improves efficiency and reduces the signature sizes. This paper proposes BACON, a BAVC with aborts that leverages a single cGGM tree. BACON executes multiple instances of AVC in a single batch and enables an abort mechanism to probabilistically reduce the commitment size. We prove that BACON is secure under the ideal cipher model and the random oracle model. We also discuss the possible application of the proposed BACON and show the theoretical efficiency compared to state-of-the-art.

An involution is a permutation, such that its inverse is itself (i.e., cycle length ≤ 2). Due to this property, involutions have been used in many applications, including cryptography and coding theory. In this paper, we provide a systematic study of involutions that are defined over a finite field of characteristic 2. We characterize the involution property of several classes of polynomials and propose several constructions. Furthermore, we study the number of fixed points of involutions, which is a pertinent question related to permutations with short cycle. In this paper, we mostly have used combinatorial techniques.

In this paper we study involutions over a finite field of order 2n. We present some classes, several constructions of involutions and we study the set of their fixed points.

In this paper, we study permutation polynomials over the finite fields that have linear structures. We present some results on such a permutation which transforms a hyperplane to another hyperplane. We fully characterize the bilinear polynomial with linear structure. The most important result of this paper is to show the relation between a Maiorana-McFarland function with an affine derivative and a polynomial with a linear structure. Moreover, we highlight this result in the context of resilient functions which are based on Maiorana-McFarland construction.

We study permutations over the finite fields that have linear structures. Our main result is to show the relation between a Maiorana-McFarland function with an affine derivative and a polynomial with a linear structure.