Solving the LPN problem in cube-root time

In this paper it is shown that given a sufficient number of (noisy) random binary linear equations, the Learning from Parity with Noise (LPN) problem can be solved in essentially cube root time in the number of unknowns. The techniques used to recover the solution are known from fast correlation attacks on stream ciphers. As in fast correlation attacks, the performance of the algorithm depends on the number of equations given. It is shown that if this number exceeds a certain bound, and the bias of the noisy equations is polynomial in number of unknowns, the running time of the algorithm is reduced to almost cube root time compared to the brute force checking of all possible solutions. The mentioned bound is explicitly given and it is further shown that when this bound is exceeded, the complexity of the approach can even be further reduced

A Discrete Logarithm-based Approach to Compute Low-Weight Multiples of Binary Polynomials

Being able to compute efficiently a low-weight multiple of a given binary polynomial is often a key ingredient of correlation attacks to LFSR-based stream ciphers. The best known general purpose algorithm is based on the generalized birthday problem. We describe an alternative approach which is based on discrete logarithms and has much lower memory complexity requirements with a comparable time complexity.Comment: 12 page

Algebraic Attack on the Alternating Step(r,s)Generator

The Alternating Step(r,s) Generator, ASG(r,s), is a clock-controlled sequence generator which is recently proposed by A. Kanso. It consists of three registers of length l, m and n bits. The first register controls the clocking of the two others. The two other registers are clocked r times (or not clocked) (resp. s times or not clocked) depending on the clock-control bit in the first register. The special case r=s=1 is the original and well known Alternating Step Generator. Kanso claims there is no efficient attack against the ASG(r,s) since r and s are kept secret. In this paper, we present an Alternating Step Generator, ASG, model for the ASG(r,s) and also we present a new and efficient algebraic attack on ASG(r,s) using 3(m+n) bits of the output sequence to find the secret key with O((m^2+n^2)*2^{l+1}+ (2^{m-1})*m^3 + (2^{n-1})*n^3) computational complexity. We show that this system is no more secure than the original ASG, in contrast to the claim of the ASG(r,s)'s constructor.Comment: 5 pages, 2 figures, 2 tables, 2010 IEEE International Symposium on Information Theory (ISIT2010),June 13-18, 2010, Austin, Texa

A fast and light stream cipher for smartphones

We present a stream cipher based on a chaotic dynamical system. Using a chaotic trajectory sampled under certain rules in order to avoid any attempt to reconstruct the original one, we create a binary pseudo-random keystream that can only be exactly reproduced by someone that has fully knowledge of the communication system parameters formed by a transmitter and a receiver and sharing the same initial conditions. The plaintext is XORed with the keystream creating the ciphertext, the encrypted message. This keystream passes the NISTs randomness test and has been implemented in a videoconference App for smartphones, in order to show the fast and light nature of the proposed encryption system

Quantum Noise Randomized Ciphers

We review the notion of a classical random cipher and its advantages. We sharpen the usual description of random ciphers to a particular mathematical characterization suggested by the salient feature responsible for their increased security. We describe a concrete system known as AlphaEta and show that it is equivalent to a random cipher in which the required randomization is effected by coherent-state quantum noise. We describe the currently known security features of AlphaEta and similar systems, including lower bounds on the unicity distances against ciphertext-only and known-plaintext attacks. We show how AlphaEta used in conjunction with any standard stream cipher such as AES (Advanced Encryption Standard) provides an additional, qualitatively different layer of security from physical encryption against known-plaintext attacks on the key. We refute some claims in the literature that AlphaEta is equivalent to a non-random stream cipher.Comment: Accepted for publication in Phys. Rev. A; Discussion augmented and re-organized; Section 5 contains a detailed response to 'T. Nishioka, T. Hasegawa, H. Ishizuka, K. Imafuku, H. Imai: Phys. Lett. A 327 (2004) 28-32 /quant-ph/0310168' & 'T. Nishioka, T. Hasegawa, H. Ishizuka, K. Imafuku, H. Imai: Phys. Lett. A 346 (2005) 7

A Simple Attack on Some Clock-Controlled Generators

We present a new approach to edit distance attacks on certain clock-controlled generators, which applies basic concepts of Graph Theory to simplify the search trees of the original attacks in such a way that only the most promising branches are analyzed. In particular, the proposed improvement is based on cut sets defined on some graphs so that certain shortest paths provide the edit distances. The strongest aspects of the proposal are that the obtained results from the attack are absolutely deterministic, and that many inconsistent initial states of the target registers are recognized beforehand and avoided during search