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Describe the steps that Alice and Bob follow when they use

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 29E Chapter 4.6

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 29E

Describe the steps that Alice and Bob follow when they use the Diffie-Hellman key exchange protocol to generate a shared key. Assume that they use the prime p = 23 and take a = 5, which is a primitive root of 23, and that Alice selects k1 = 8 and Bob selects k2 = 5. (You may want to use some computational aid.)

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4/12 Social Psych Notes Behavior in Group Settings  Social/group effects on behavior and interpersonal effects  Group – group of people, naturally occur as 2-6 people o People prefer smaller groups when interaction is integral to the purpose of a group (i.e. accomplishing a task, enjoying each other socially)  Group participation will vary as a function of the number of people in the group  Perceived entativity – how does this change from individuals to a whole group collective (groupiness as a continuum) – group vs. not group – varying levels of groupiness  Gestalt Psychology: Donald Campbell (1958) – perceiving stimuli to be a single unit  Gestalt Principles of Groups o Proximity – the closer objects are in a visual field, the more likely we are to group them together o Similarity – if there is a commonality between people o Common Fate (interdependence) – everyone moving in the same direction  Minimal group paradigm – it really doesn’t take much to form groups because of our natural need to belong  Ex: give people the same color hat or shirt and they will begin to think they are a group somehow; give others a different color and this sense of groupiness increases o Give them something in common as well as competition  There is a natural inclination for people to perceive that other groups are violent or have hostile intent o Universities do this with sports rivalries o They make people in the same group like each other more and create a rivalry to make another group look bad Why be in a group  It helps to fulfill the need to belong  Uncertainty – identifying with a group can make the self more stable o Subjective uncertainty hypothesis: reaffirm self-relevant matters by asking what your group would do  Group culture – group members have to understand each other o Socially shared cognition  Empathy – the ability to perceive others’ emotional and physical states o Groups have high empathetic accuracy due to history of interaction  Norms – groups have their own rules for how to behave o This makes it easier to predict each other’s’ behavior  Transactive memory – group members delegate different domains of memory expertise to different individuals o Similar to division of labor – everyone has a job and remembers something specific; divide and conquer o Can be done without any verbal communication, but it increases if there is non-verbal communication  Diverse groups are often less stable – we are more attracted to those who are similar to us, groups require a level of homogeneity  BUT there is value to diversity – diverse groups perform better and are more flexible and creative – there is a wider range of skills and connections to others o Wide range of knowledge shared leads to better outcomes How Do Groups Influence Our Behavior  Social facilitation – Norman Triplet Study (beginning of semester) – when we are performing in from of a group, our performance will be enhanced o Cockroach social influence study o In the presence of coactors, performance increases  When the task is more difficult – roaches performed worse when others were present  Michaels (1982) – playing pool; experts vs. novice, number of shots made when people were there vs. not there o When alone experts were better than novices o With others experts were even better, novices were much worse  For what reason does the behavior of humans change in the presence of others – Arousal and the dominant response o Zajunc (1965) – the presence of others increases physiological arousal; this leads to the amplification of our dominant response to the situation (Ex: expert: making correct movements and decisions, novice: making incorrect movements and decisions) o When a task is simple, the task is learned the dominant response is to succeed  Social facilitation  increased arousal  dominant response  Social loafing – reducing one’s effort when in a group  In general, groups can get more done than individuals (because of specialization)  BUT groups result in the ability to free-ride (enjoy the benefits of the group without making an effort to contribute) o Sucker effect – wanting to avoid the risk of being the only member of the group contributing to the task or project  Rather than increase apprehension (acting in front of the group), performing WITH a group reduces arousal, which results in a lack of accountability for one’s own actions  When are groups loafless o When the task is meaningful and important o Working with friends rather than strangers (you don’t really care what strangers think of you) o If people have a collectivistic mindset or orientation o If personal efforts are identifiable Obedience and Conformity (note that this is in the influence chapter!)  Obedience – acting in accord with a direct order from someone who is in a perceived position of power – direct social influence  Some obedience is necessary – obeying traffic laws  Blind obedience can be bad – i.e. Nazi Germany, led to Milgrim’s work  Milgrim’s Study on Obedience – participants told this is a study on punishment and learning o 1 person is the teacher, other is the learner (learner is actually a confederate) o Teacher asks questions and shocks the learner for each error; each incorrect response increases the voltage by 15 volt increments o Learner starts by vocalizing that they have heart problems o If participants questioned the shocks, they were told that it was very important and asked to continue, but they could refuse and quit and any time o Even when the learner was thought to be dead or unconscious, 60% of participants still continued o They manipulated: types of schools for study location, researcher appearance (old/young, lab coat/no lab coat)  Conformity – a change in behavior or beliefs as a result of real or imagined social pressure; acting differently than you would when alone; 2 types: compliance and acceptance  Compliance: publicly acting in accord with social pressure while privately disagreeing o say yes, but believe no  Acceptance: acting and believing in accord with social pressure o say yes, and believe yes  Informational Social Influence: evidence about reality that we get from others o Ex: saying “Warrrrrrrrrr Eagle! Hey!” at kickoffs o Usually watching instead of asking others o Leads to acceptance; what the group is doing is correct  Classic Study – Sherif: Autokinetic Effect – shine a dot of light in a dark room o Have participants estimate movement (it’s not actually moving) alone, then with others o Over several days, participants will change their estimates according to other’s  Affected by: o Whether or not situation is ambiguous or new o Do other people appear to be experts  Normative Social Influence: Behavior is shaped by a desire to fulfill others’ expectations – often to gain approval o Leads to compliances  Classic Study – Asch: Line Study o Participants are first alone, then in a group (of confederates) o Asked to judge which of 3 lines matches the test line o Confederates all give the wrong answer o Level of conformity = the # of errors the participant agrees with  Conformity gets a bad name, but it’s actually really prosocial Group Decision Making – Do groups make good decisions  Two heads are better than 1 vs. too many cooks in the kitchen  Brainstorming – creative thinking in groups; Does it work  Paulus et al. 1993, Stroche et al. 1992 – groups who brainstorm like the tasks more, evaluate their work more favorably; individuals say that groups probably perform better o But NOT really (Mullen et al. 1991) – individuals came up with more and better ideas than groups  Groups are less creative, but what about when a group just needs to make a decision – the risky shift and group polarization  Risky shift – when groups make decisions they tend to make especially extreme decisions – more extreme than individual group members initial opinion  Group polarization – groups go to either extremes (risky or cautious) o It isn’t restrict to risky vs. cautious decisions o Decisions become extreme toward one or the other  Imagine you were indecisive about going to grad school: o Fellow students: maybe go  YES go! (after group discussion) o Family members: maybe no  NO go (after group discussion)  Why does this happen  Groups often fail to engage in normal problem solving processes o Process Loss: when group decision making inhibits good problem solving o Ex: unshared information, deindividuation/depersonalization  One of the most important considerations for making good decisions is considering all relevant information o Individuals – seek out all information o Groups – see out and share all info, BUT not all information is shared  Anderson and Baker Study – groups of 7 were given the task of hiring a new employee (Mr. Anderson or Mr. Baker) o There were 7 reasons to hire Mr. A, 4 reasons to hire Mr. B, and all reasons were prejudged to be of equal importance o Mr. A is clearly the answer, but groups choose Mr. B o Distribution of information to the participants occurred before the group met; BUT each participant was given all 4 reasons for Mr. B and 1 each for Mr. A  so they came in already favoring Mr. B, didn’t share information, and chose incorrectly  Common Knowledge Effect – the assumption that others know something because you know it  Other factors can lead to good decision making o Self-awareness – conscious self-reflection, knowledge that you are being evaluated o Accountability – knowledge that you will be held responsible for your decisions  Deindividuation – loss of self-awareness that occurs when we lack identifiability o Not identifiable = not accountable; this often results in antisocial behaviors (cheating, stealing, aggression) o Ex: KKK members are not identifiable, this makes them more likely to do bad things  Being in a group makes you less identifiable, even if you are unmasked

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Chapter 4.6, Problem 29E is Solved
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Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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