Short expressions of permutations as products and cryptanalysis of the Algebraic Eraser

On March 2004, Anshel, Anshel, Goldfeld, and Lemieux introduced the \emph{Algebraic Eraser} scheme for key agreement over an insecure channel, using a novel hybrid of infinite and finite noncommutative groups. They also introduced the \emph{Colored Burau Key Agreement Protocol (CBKAP)}, a concrete realization of this scheme. We present general, efficient heuristic algorithms, which extract the shared key out of the public information provided by CBKAP. These algorithms are, according to heuristic reasoning and according to massive experiments, successful for all sizes of the security parameters, assuming that the keys are chosen with standard distributions. Our methods come from probabilistic group theory (permutation group actions and expander graphs). In particular, we provide a simple algorithm for finding short expressions of permutations in $S_n$, as products of given random permutations. Heuristically, our algorithm gives expressions of length $O(n^2\log n)$, in time and space $O(n^3)$. Moreover, this is provable from \emph{the Minimal Cycle Conjecture}, a simply stated hypothesis concerning the uniform distribution on $S_n$. Experiments show that the constants in these estimations are small. This is the first practical algorithm for this problem for $n\ge 256$. Remark: \emph{Algebraic Eraser} is a trademark of SecureRF. The variant of CBKAP actually implemented by SecureRF uses proprietary distributions, and thus our results do not imply its vulnerability. See also arXiv:abs/12020598Comment: Final version, accepted to Advances in Applied Mathematics. Title slightly change

Defeating the Ben-Zvi, Blackburn, and Tsaban Attack on the Algebraic Eraser

The Algebraic Eraser Diffie-Hellman (AEDH) protocol was introduced in 2005 and published in 2006 by Anshel-Anshel-Goldfeld-Lemieux as a protocol suitable for use on platforms with constrained computational resources, such as FPGAs, ASICs, and wireless sensors. It is a group-theoretic cryptographic protocol that allows two users to construct a shared secret via a Diffie-Hellman-type scheme over an insecure channel. Building on the refuted 2012 permutation-based attack of Kalka-Teichner-Tsaban, in 2015 Ben-Zvi-Blackburn-Tsaban (BBT) presented a heuristic attack that attempts to recover the AEDH shared secret. In their paper BBT reference the AEDH protocol as presented to ISO for certification (ISO 29167-20) by SecureRF. The ISO draft contains two profiles using the Algebraic Eraser. One profile is unaffected by this attack; the second profile is subject to their attack provided the attack runs in real time. This is not the case in most practical deployments. The BBT attack is simply a targeted attack that does not attempt to break the method, system parameters, or recover any private keys. Rather, its limited focus is to recover the shared secret in a single transaction. In addition, the BBT attack is based on several conjectures that are assumed to hold when parameters are chosen according to standard distributions, which can be mitigated, if not avoided. This paper shows how to choose special distributions so that these conjectures do not hold making the BBT attack ineffective for braid groups with sufficiently many strands. Further, the BBT attack assumes that certain data is available to an attacker, but there are realistic deployment scenarios where this is not the case, making the attack fail completely. In summary, the BBT attack is flawed (with respect to the SecureRF ISO draft) and, at a minimum, over-reaches as to its applicability

Henri Temianka Correspondence; (brusilow)

This collection contains material pertaining to the life, career, and activities of Henri Temianka, violin virtuoso, conductor, music teacher, and author. Materials include correspondence, concert programs and flyers, music scores, photographs, and books.https://digitalcommons.chapman.edu/temianka_correspondence/1479/thumbnail.jp

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

Probabilistic Solutions of Equations in the Braid Group

Given a system of equations in a "random" finitely generated subgroup of the braid group, we show how to find a small ordered list of elements in the subgroup, which contains a solution to the equations with a significant probability. Moreover, with a significant probability, the solution will be the first in the list. This gives a probabilistic solution to: The conjugacy problem, the group membership problem, the shortest representation of an element, and other combinatorial group-theoretic problems in random subgroups of the braid group. We use a memory-based extension of the standard length-based approach, which in principle can be applied to any group admitting an efficient, reasonably behaving length function.Comment: Small update

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

The Influence of the Social Environment Context in Stress and Coping in Sport.

Lazarus (1999) model of stress and coping is based on the reciprocal interaction between the person and the environment. The aim of this study therefore was to examine whether the social environment (significant others) are of influence on the stress and coping of team athletes. The study consisted of two separate studies in which a total of 12 team athletes participated. First, six field hockey players (two males, four females) aged 18-29 years (M = 23.0 years) participated in a diary study. Second, six team athletes of different sports (two males, four females) aged 24-29 years (M = 25.8 years) were interviewed. The results showed that in particular teammates are important for the appraisal of stress and coping in team sports. For over half (i.e., 51.5%) of the reported stressors in the diary study the participants felt that others were of influence on their coping. Team athletes experienced the highest stress intensity during competition, or when they appraised the situation as a threat. When others were of influence the team athletes were most likely to appraise the situation as a challenge and use problem- or emotion-focused coping strategies. These finding might provide a new portal for intervention to enhance coping with stress in sport and enhance performance and satisfaction

Sovereignty and Interdependence in EU Military Procurement Regulation

In his dissertation, Nathan Meershoek evaluates the effectiveness and appropriateness of Directive 2009/81/EC, which aims to strengthen the military 'strategic autonomy' of the European Union by liberalizing European defence industries. This liberalization is based on public procurement obligations for the Member States within the legal framework of the internal market. The first part of the dissertation builds on international relations theories to evaluate the extent to which geopolitical power structures constrain EU integration and regulation of military procurement. This is relevant because exception to the Directive can be justified by national security interests. Due to the significant differences in the military interests of the Member States, it is concluded that the economic interdependence approach - inherent in the chosen legal basis within the EU's internal market competence - is unsuitable as a basis for regulating military procurement. In military procurement the military-strategic interests of the Member States are decisive, so decisions are mainly aimed at strengthening independence (or, in other words, sovereignty) and/or military interdependence. Successful European integration in this area within the economically oriented system of the single market is therefore unlikely. In light of this conclusion, the second part of the dissertation answers the question whether the Directive was adopted on the correct legal basis in the EU Treaties. After considering the role of sovereignty in the division of competences between the EU and its Member States in the field of military security, the legal characteristics of the security exceptions in the EU Treaties and the substance of the Directive, it is finally concluded that the Directive was adopted on the wrong legal basis in the EU Treaties. Based on the previous conclusions, the final part of the thesis provides guidance for a better regulation; first of all, by placing the regulation primarily within the intergovernmental EU Defence Policy. Based on five general principles - aimed at better facilitating sovereignty and interdependence - recommendations are given on how the regulation could be improved

Immigrant and Refugee COVID-19 Vaccination Attitudes in South Philadelphia

Immigrants and refugees have been disproportionately affected by the COVID-19 pandemic; therefore, it is important to determine the specific factors that are promoting vaccination in the immigrant and refugee populations to develop equitable health services. This study surveys the attitudes toward COVID-19 vaccination and vaccine mandates in the Southeast Asian and Hispanic immigrant and refugee populations in South Philadelphia. A questionnaire was administered to all patients receiving the COVID-19 vaccine during six clinic days from November 15th-31st 2021. Investigators asked participants about their intention behind vaccination, barriers to access, work requirements regarding COVID-19 vaccination, and attitudes toward vaccine mandates. For people receiving their booster vaccine, the most cited reasons for getting vaccinated were protecting their health (75.4%) and travel (11.0%), whereas most people receiving their first or second vaccine were most motivated by vaccine mandates at work (34.6%) and health (30.8%). Staying healthy or “health” was the most common reason for getting vaccinated among people receiving their booster vaccine (74.8%) which was significantly higher than the proportion of people getting their first or second vaccine (30.7%) (p<0.05). As people continue to get vaccinated, determining motivating factors can help promote appropriate messaging. The results of the study suggest that, in a clinical setting geared towards Southeast Asian and Hispanic immigrants and refugees, those getting their first and second dose were motivated by work mandates more than health at the time of the study, whereas those adults receiving their booster are most motivated by health and safely traveling. As we continue to aim for mass vaccination, vaccine mandates appear to be an effective method of motivating people to get their first and second dose