Length-based cryptanalysis: The case of Thompson's Group

The length-based approach is a heuristic for solving randomly generated equations in groups which possess a reasonably behaved length function. We describe several improvements of the previously suggested length-based algorithms, that make them applicable to Thompson's group with significant success rates. In particular, this shows that the Shpilrain-Ushakov public key cryptosystem based on Thompson's group is insecure, and suggests that no practical public key cryptosystem based on this group can be secure.Comment: Final version, to appear in JM

Cryptanalysis of group-based key agreement protocols using subgroup distance functions

We introduce a new approach for cryptanalysis of key agreement protocols based on noncommutative groups. This approach uses functions that estimate the distance of a group element to a given subgroup. We test it against the Shpilrain-Ushakov protocol, which is based on Thompson's group F

Practical Attacks Against the Walnut Digital Signature Scheme

Recently, NIST started the process of standardizing quantum- resistant public-key cryptographic algorithms. WalnutDSA, the subject of this paper, is one of the 20 proposed signature schemes that are being considered for standardization. Walnut relies on a one-way function called E-Multiplication, which has a rich algebraic structure. This paper shows that this structure can be exploited to launch several practical attacks against the Walnut cryptosystem. The attacks work very well in practice; it is possible to forge signatures and compute equivalent secret keys for the 128-bit and 256-bit security parameters submitted to NIST in less than a second and in less than a minute respectively

The groupoidal analogue Theta~ to Joyal's category Theta is a test category

We introduce the groupoidal analogue \tilde\Theta to Joyal's cell category \Theta and we prove that \tilde\Theta is a strict test category in the sense of Grothendieck. This implies that presheaves on \tilde\Theta model homotopy types in a canonical way. We also prove that the canonical functor from \Theta to \tilde\Theta is aspherical, again in the sense of Grothendieck. This allows us to compare weak equivalences of presheaves on \tilde\Theta to weak equivalences of presheaves on \Theta. Our proofs apply to other categories analogous to \Theta.Comment: 41 pages, v2: references added, Remark 7.3 added, v3: metadata update

Post Quantum Cryptography from Mutant Prime Knots

By resorting to basic features of topological knot theory we propose a (classical) cryptographic protocol based on the `difficulty' of decomposing complex knots generated as connected sums of prime knots and their mutants. The scheme combines an asymmetric public key protocol with symmetric private ones and is intrinsecally secure against quantum eavesdropper attacks.Comment: 14 pages, 5 figure

A Practical Cryptanalysis of the Algebraic Eraser

Anshel, Anshel, Goldfeld and Lemieaux introduced the Colored Burau Key Agreement Protocol (CBKAP) as the concrete instantiation of their Algebraic Eraser scheme. This scheme, based on techniques from permutation groups, matrix groups and braid groups, is designed for lightweight environments such as RFID tags and other IoT applications. It is proposed as an underlying technology for ISO/IEC 29167-20. SecureRF, the company owning the trademark Algebraic Eraser, has presented the scheme to the IRTF with a view towards standardisation. We present a novel cryptanalysis of this scheme. For parameter sizes corresponding to claimed 128-bit security, our implementation recovers the shared key using less than 8 CPU hours, and less than 64MB of memory.Comment: 15 pages. Updated references, with brief comments added. Minor typos corrected. Final version, accepted for CRYPTO 201

Effects of synchronous music on treadmill running among elite triathletes

This is the post-print version of the final paper published in Journal of Science and Medicine in Sport. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2011 Elsevier B.V.Objectives: Music can provide ergogenic, psychological, and psychophysical benefits during physical activity, especially when movements are performed synchronously with music. The present study developed the train of research on synchronous music and extended it to elite athletes. Design: Repeated-measures laboratory experiment. Method: Elite triathletes (n = 11) ran in time to self-selected motivational music, a neutral equivalent and a no-music control during submaximal and exhaustive treadmill running. Measured variables were time-to-exhaustion, mood responses, feeling states, RPE, blood lactate concentration, oxygen consumption and running economy. Results: Time-to-exhaustion was 18.1% and 19.7% longer, respectively, when running in time to motivational and neutral music, compared to no music. Mood responses and feeling states were more positive with motivational music compared to either neutral music or no music. RPE was lowest for neutral music and highest for the no-music control. Blood lactate concentrations were lowest for motivational music. Oxygen consumption was lower with music by 1.0%–2.7%. Both music conditions were associated with better running economy than the no-music control. Conclusions: Although neutral music did not produce the same level of psychological benefits as motivational music, it proved equally beneficial in terms of time-to-exhaustion and oxygen consumption. In functional terms, the motivational qualities of music may be less important than the prominence of its beat and the degree to which participants are able to synchronise their movements to its tempo. Music provided ergogenic, psychological and physiological benefits in a laboratory study and its judicious use during triathlon training should be considered.QAS Centre of Excellence for Applied Sport Science Researc

Personality differences amongst drag racers and archers: implications for sport injury rehabilitation

Personality trait of an athlete is a significant factor in sports injury rehabilitation. The aim of the present study is to investigate whether there are differences in personality traits between male and female, professional and amateur athletes from sports representing two ends of extreme to traditional namely; drag racing and archery. Overall 189 male and female, professional and amateur drag racers (n=144) and archers (n=45) took part in this study. Participants completed the personality traits of extroversion and neuroticism as measured by Eysenck’s classic Personality Inventory dimensions and thrill and adventure seeking (TAS), experience seeking (ES), disinhibition (DIS), boredom susceptibility (BS), and sensation seeking (SS) as measured by Zuckerman’s Sensation Seeking Scale. The results showed that professionals scored significantly lower on neuroticism compared to amateurs. Drag racers scored significantly higher on TAS, DIS, and SS compared to archers and there were gender differences amongst archers on TAS and SS with males scoring higher than females. Such differences in personality factors and the readiness to take risks, lack of caution, and adventurous spirit can influence the risk of injury in athletes and indeed may influence the outcome of rehabilitation. Practitioners would need to recognise difference in personality traits associated with the type of sport and the choice of interventions strategies

Revisiting the exercise heart rate-music tempo preference relationship

In the present study, we investigated a hypothesized quartic relationship (meaning three inflection points) between exercise heart rate (HR) and preferred music tempo. Initial theoretical predictions suggested a positive linear relationship (Iwanaga, 1995a, 1995b); however, recent experimental work has shown that as exercise HR increases, step changes and plateaus that punctuate the profile of music tempo preference may occur (Karageorghis, Jones, & Stuart, 2008). Tempi bands consisted of slow (95–100 bpm), medium (115–120 bpm), fast (135–140 bpm), and very fast (155–160 bpm) music. Twenty-eight active undergraduate students cycled at exercise intensities representing 40, 50, 60, 70, 80, and 90% of their maximal HR reserve while their music preference was assessed using a 10-point scale. The Exercise Intensity x Music Tempo interaction was significant, F(6.16, 160.05) = 7.08, p < .001, ηp 2 =.21, as was the test for both cubic and quartic trajectories in the exercise HR–preferred-music-tempo relationship (p < .001). Whereas slow tempo music was not preferred at any exercise intensity, preference for fast tempo increased, relative to medium and very fast tempo music, as exercise intensity increased. The implications for the prescription of music in exercise and physical activity contexts are discussed

Quantum Knitting

We analyze the connections between the mathematical theory of knots and quantum physics by addressing a number of algorithmic questions related to both knots and braid groups. Knots can be distinguished by means of `knot invariants', among which the Jones polynomial plays a prominent role, since it can be associated with observables in topological quantum field theory. Although the problem of computing the Jones polynomial is intractable in the framework of classical complexity theory, it has been recently recognized that a quantum computer is capable of approximating it in an efficient way. The quantum algorithms discussed here represent a breakthrough for quantum computation, since approximating the Jones polynomial is actually a `universal problem', namely the hardest problem that a quantum computer can efficiently handle.Comment: 29 pages, 5 figures; to appear in Laser Journa