Pruned Bit-Reversal Permutations: Mathematical Characterization, Fast Algorithms and Architectures

A mathematical characterization of serially-pruned permutations (SPPs) employed in variable-length permuters and their associated fast pruning algorithms and architectures are proposed. Permuters are used in many signal processing systems for shuffling data and in communication systems as an adjunct to coding for error correction. Typically only a small set of discrete permuter lengths are supported. Serial pruning is a simple technique to alter the length of a permutation to support a wider range of lengths, but results in a serial processing bottleneck. In this paper, parallelizing SPPs is formulated in terms of recursively computing sums involving integer floor and related functions using integer operations, in a fashion analogous to evaluating Dedekind sums. A mathematical treatment for bit-reversal permutations (BRPs) is presented, and closed-form expressions for BRP statistics are derived. It is shown that BRP sequences have weak correlation properties. A new statistic called permutation inliers that characterizes the pruning gap of pruned interleavers is proposed. Using this statistic, a recursive algorithm that computes the minimum inliers count of a pruned BR interleaver (PBRI) in logarithmic time complexity is presented. This algorithm enables parallelizing a serial PBRI algorithm by any desired parallelism factor by computing the pruning gap in lookahead rather than a serial fashion, resulting in significant reduction in interleaving latency and memory overhead. Extensions to 2-D block and stream interleavers, as well as applications to pruned fast Fourier transforms and LTE turbo interleavers, are also presented. Moreover, hardware-efficient architectures for the proposed algorithms are developed. Simulation results demonstrate 3 to 4 orders of magnitude improvement in interleaving time compared to existing approaches.Comment: 31 page

Extending Differential Fault Analysis to Dynamic S-Box Advanced Encryption Standard Implementations

Advanced Encryption Standard (AES) is a worldwide cryptographic standard for symmetric key cryptography. Many attacks try to exploit inherent weaknesses in the algorithm or use side channels to reduce entropy. At the same time, researchers strive to enhance AES and mitigate these growing threats. This paper researches the extension of existing Differential Fault Analysis (DFA) attacks, a family of side channel attacks, on standard AES to Dynamic S-box AES research implementations. Theoretical analysis reveals an expected average keyspace reduction of 2-88:9323 after one faulty ciphertext using DFA on the State of Rotational S-box AES-128 implementations. Experimental results revealed an average 2-88:8307 keyspace reduction and confirmed full key recovery is possible

Implementing 128-bit Secure MPKC Signatures

Multivariate Public Key Cryptosystems (MPKCs) are often touted as future-proofing against Quantum Computers. In 2009, it was shown that hardware advances do not favor just ``traditional\u27\u27 alternatives such as ECC and RSA, but also makes MPKCs faster and keeps them competitive at 80-bit security when properly implemented. These techniques became outdated due to emergence of new instruction sets and higher requirements on security. In this paper, we review how MPKC signatures changes from 2009 including new parameters (from a newer security level at 128-bit), crypto-safe implementations, and the impact of new AVX2and AESNI instructions. We also present new techniques on evaluating multivariate polynomials, multiplications of large finite fields by additive Fast Fourier Transforms, and constant time linear solvers

A Comprehensive Account of Sound Sequence Imitation in the Songbird

The amazing imitation capabilities of songbirds show that they can memorize sensory sequences and transform them into motor activities which in turn generate the original sound sequences. This suggests that the bird's brain can learn 1.) to reliably reproduce spatio-temporal sensory representations and 2.) to transform them into corresponding spatio-temporal motor activations by using an inverse mapping. Neither the synaptic mechanisms nor the network architecture enabling these two fundamental aspects of imitation learning are known. We propose an architecture of coupled neuronal modules that mimick areas in the song bird and show that a unique synaptic plasticity mechanism can serve to learn both, sensory sequences in a recurrent neuronal network, as well as an inverse model that transforms the sensory memories into the corresponding motor activations. The proposed membrane potential dependent learning rule together with the architecture that includes basic features of the bird's brain represents the first comprehensive account of bird imitation learning based on spiking neurons

Exponential S-Boxes: a Link Between the S-Boxes of BelT and Kuznyechik/Streebog

The block cipher Kuznyechik and the hash function Streebog were recently standardized by the Russian Federation. These primitives use a common 8-bit S-Box, denote

Exponential S-Boxes: a Link Between the S-Boxes of BelT and Kuznyechik/Streebog

The block cipher Kuznyechik and the hash function Streebog were recently standardized by the Russian Federation. These primitives use a common 8-bit S-Box, denoted , which is given only as a look-up table. The rationale behind its design is, for all practical purposes, kept secret by its authors. In a paper presented at Eurocrypt 2016, Biryukov et al. reverse-engineered this S-Box and recovered an unusual Feistel-like structure relying on finite field multiplications. In this paper, we provide a new decomposition of this S-Box and describe how we obtained it. The first step was the analysis of the 8-bit S-Box of the current standard block cipher of Belarus, BelT. This S-Box is a variant of a so-called exponential substitution, a concept we generalize into pseudo-exponential substitution. We derive distinguishers for such permutations based on properties of their linear approximation tables and notice that shares some of them. We then show that indeed has a decomposition based on a pseudo-exponential substitution. More precisely, we obtain a simpler structure based on an 8-bit finite field exponentiation, one 4-bit S-Box, a linear layer and a few modular arithmetic operations. We also make several observations which may help cryptanalysts attempting to reverse-engineer other S-Boxes. For example, the visual pattern used in the previous work as a starting point to decompose is mathematically formalized and the use of differential patterns involving operations other than exclusive-or is explored