On the Feistel Counterpart of the Boomerang Connectivity Table: Introduction and Analysis of the FBCT 📺
At Eurocrypt 2018, Cid et al. introduced the Boomerang Connectivity Table (BCT), a tool to compute the probability of the middle round of a boomerang distinguisher from the description of the cipher’s Sbox(es). Their new table and the following works led to a refined understanding of boomerangs, and resulted in a series of improved attacks. Still, these works only addressed the case of Substitution Permutation Networks, and completely left out the case of ciphers following a Feistel construction. In this article, we address this lack by introducing the FBCT, the Feistel counterpart of the BCT. We show that the coefficient at row Δi, ∇o corresponds to the number of times the second order derivative at points Δi, ∇o) cancels out. We explore the properties of the FBCT and compare it to what is known on the BCT. Taking matters further, we show how to compute the probability of a boomerang switch over multiple rounds with a generic formula.
X-FCSR: a new software oriented stream cipher based upon FCSRs
Feedback with Carry Shift Registers (FCSRs) are a promising alternative to LFSRs in the design of stream cipher. The previous constructions based on FCSRs were dedicated to hardware applications. In this paper, we will describe X-FCSR a family of software oriented stream cipher using FCSRs. The core of the system is composed of two 256-bits FCSRs. We propose two versions: X-FCSR-128 and X-FCSR-256 which output respectively 128 and 256 bits at each iteration. We study the resistance of our design against several cryptanalyses. In this way, we achieve a high throughput and secure stream ciphers suitable for software applications (6.3 cycles/byte).