On low degree polynomials in 2-round AES

Recent observations on polynomial structures of AES-like round functions are analysed in this note. We present computational evidence that input/output bits of AES-like 2-round transform up to $40$-bit, constructed with $8$-bit AES S-boxes, do not satisfy any relations of degree $3$. So it is very unlikely that actual AES 2-round transform admits any relations of degree $\leq 3$

Quantum Algorithms for Boolean Equation Solving and Quantum Algebraic Attack on Cryptosystems

Decision of whether a Boolean equation system has a solution is an NPC problem and finding a solution is NP hard. In this paper, we present a quantum algorithm to decide whether a Boolean equation system FS has a solution and compute one if FS does have solutions with any given success probability. The runtime complexity of the algorithm is polynomial in the size of FS and the condition number of FS. As a consequence, we give a polynomial-time quantum algorithm for solving Boolean equation systems if their condition numbers are small, say polynomial in the size of FS. We apply our quantum algorithm for solving Boolean equations to the cryptanalysis of several important cryptosystems: the stream cipher Trivum, the block cipher AES, the hash function SHA-3/Keccak, and the multivariate public key cryptosystems, and show that they are secure under quantum algebraic attack only if the condition numbers of the corresponding equation systems are large. This leads to a new criterion for designing cryptosystems that can against the attack of quantum computers: their corresponding equation systems must have large condition numbers

KLEIN: A New Family of Lightweight Block Ciphers

Resource-efficient cryptographic primitives become fundamental for realizing both security and efficiency in embedded systems like RFID tags and sensor nodes. Among those primitives, lightweight block cipher plays a major role as a building block for security protocols. In this paper, we describe a new family of lightweight block ciphers named KLEIN, which is designed for resource-constrained devices such as wireless sensors and RFID tags. Compared to the related proposals, KLEIN has advantage in the software performance on legacy sensor platforms, while in the same time its hardware implementation can also be compact

A Security Analysis of IoT Encryption: Side-channel Cube Attack on Simeck32/64

Simeck, a lightweight block cipher has been proposed to be one of the encryption that can be employed in the Internet of Things (IoT) applications. Therefore, this paper presents the security of the Simeck32/64 block cipher against side-channel cube attack. We exhibit our attack against Simeck32/64 using the Hamming weight leakage assumption to extract linearly independent equations in key bits. We have been able to find 32 linearly independent equations in 32 key variables by only considering the second bit from the LSB of the Hamming weight leakage of the internal state on the fourth round of the cipher. This enables our attack to improve previous attacks on Simeck32/64 within side-channel attack model with better time and data complexity of 2^35 and 2^11.29 respectively.Comment: 12 pages, 6 figures, 4 tables, International Journal of Computer Networks & Communication

Analysing Relations involving small number of Monomials in AES S- Box

In the present day, AES is one the most widely used and most secure Encryption Systems prevailing. So, naturally lots of research work is going on to mount a significant attack on AES. Many different forms of Linear and differential cryptanalysis have been performed on AES. Of late, an active area of research has been Algebraic Cryptanalysis of AES, where although fast progress is being made, there are still numerous scopes for research and improvement. One of the major reasons behind this being that algebraic cryptanalysis mainly depends on I/O relations of the AES S- Box (a major component of the AES). As, already known, that the key recovery algorithm of AES can be broken down as an MQ problem which is itself considered hard. Solving these equations depends on our ability reduce them into linear forms which are easily solvable under our current computational prowess. The lower the degree of these equations, the easier it is for us to linearlize hence the attack complexity reduces. The aim of this paper is to analyze the various relations involving small number of monomials of the AES S- Box and to answer the question whether it is actually possible to have such monomial equations for the S- Box if we restrict the degree of the monomials. In other words this paper aims to study such equations and see if they can be applicable for AES.Comment: 5 pages, 1 tabl

A New Algorithm for Solving Ring-LPN with a Reducible Polynomial

The LPN (Learning Parity with Noise) problem has recently proved to be of great importance in cryptology. A special and very useful case is the RING-LPN problem, which typically provides improved efficiency in the constructed cryptographic primitive. We present a new algorithm for solving the RING-LPN problem in the case when the polynomial used is reducible. It greatly outperforms previous algorithms for solving this problem. Using the algorithm, we can break the Lapin authentication protocol for the proposed instance using a reducible polynomial, in about 2^70 bit operations