Quantum resource estimates for computing elliptic curve discrete logarithms

We give precise quantum resource estimates for Shor's algorithm to compute discrete logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of a Toffoli gate network for controlled elliptic curve point addition, implemented within the framework of the quantum computing software tool suite LIQ$Ui|\rangle$. We determine circuit implementations for reversible modular arithmetic, including modular addition, multiplication and inversion, as well as reversible elliptic curve point addition. We conclude that elliptic curve discrete logarithms on an elliptic curve defined over an $n$-bit prime field can be computed on a quantum computer with at most $9n + 2\lceil\log_2(n)\rceil+10$ qubits using a quantum circuit of at most $448 n^3 \log_2(n) + 4090 n^3$ Toffoli gates. We are able to classically simulate the Toffoli networks corresponding to the controlled elliptic curve point addition as the core piece of Shor's algorithm for the NIST standard curves P-192, P-224, P-256, P-384 and P-521. Our approach allows gate-level comparisons to recent resource estimates for Shor's factoring algorithm. The results also support estimates given earlier by Proos and Zalka and indicate that, for current parameters at comparable classical security levels, the number of qubits required to tackle elliptic curves is less than for attacking RSA, suggesting that indeed ECC is an easier target than RSA.Comment: 24 pages, 2 tables, 11 figures. v2: typos fixed and reference added. ASIACRYPT 201

Mixed emotions to near-miss outcomes: a psychophysiological study with facial electromyography

Near-misses occur across many forms of gambling and are rated as unpleasant while simultaneously increasing the motivation to continue playing. On slot machines, the icon position relative to the payline moderates the effects of near-misses, with near-misses before the payline increasing motivation, and near-misses after the payline being rated as aversive. Near-misses are also known to increase physiological arousal compared to full-misses, but physiological measures to date have not been able to dissociate positive and negative emotional responses. The present study measured facial electromyography at the corrugator (brow) and zygomaticus (cheek) sites, as well as electrodermal activity (EDA), following gambling outcomes on a two-reel slot machine simulation in 77 novice gamblers. Behavioral data was collected using trial-by-trial ratings of motivation and valence. Wins were rated as more pleasant and increased motivation to continue playing, compared to non-win outcomes. Wins were also accompanied by increased EDA and zygomaticus activity. Near-misses after the payline were rated as more aversive than other non-wins, and this was accompanied by increased EDA and zygomaticus activity. Near-misses before the payline increased motivation to continue playing, and were accompanied by increased EDA. Thus, both subjective and physiological responses to near-misses differ for events falling either side of the payline. The ‘near-miss effect’ is not a unitary phenomenon. Facial EMG has differential sensitivity to positive and negative valence and may be a useful measure for future studies of gambling behavior

Nucleic acid-based fluorescent probes and their analytical potential

It is well known that nucleic acids play an essential role in living organisms because they store and transmit genetic information and use that information to direct the synthesis of proteins. However, less is known about the ability of nucleic acids to bind specific ligands and the application of oligonucleotides as molecular probes or biosensors. Oligonucleotide probes are single-stranded nucleic acid fragments that can be tailored to have high specificity and affinity for different targets including nucleic acids, proteins, small molecules, and ions. One can divide oligonucleotide-based probes into two main categories: hybridization probes that are based on the formation of complementary base-pairs, and aptamer probes that exploit selective recognition of nonnucleic acid analytes and may be compared with immunosensors. Design and construction of hybridization and aptamer probes are similar. Typically, oligonucleotide (DNA, RNA) with predefined base sequence and length is modified by covalent attachment of reporter groups (one or more fluorophores in fluorescence-based probes). The fluorescent labels act as transducers that transform biorecognition (hybridization, ligand binding) into a fluorescence signal. Fluorescent labels have several advantages, for example high sensitivity and multiple transduction approaches (fluorescence quenching or enhancement, fluorescence anisotropy, fluorescence lifetime, fluorescence resonance energy transfer (FRET), and excimer-monomer light switching). These multiple signaling options combined with the design flexibility of the recognition element (DNA, RNA, PNA, LNA) and various labeling strategies contribute to development of numerous selective and sensitive bioassays. This review covers fundamentals of the design and engineering of oligonucleotide probes, describes typical construction approaches, and discusses examples of probes used both in hybridization studies and in aptamer-based assays