The Secret Value of Zero
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Upgrade when ready. It is defined as the Fiat-Shamir heuristic . It uses discrete logarithms to create a difficult puzzle for Eve, and an easy one for Peggy to prove, and for Victor to verify. First Peggy decides on her password pass , and generates a hash of it, and then converts this to an integer value x. Now Peggy wants to log on, so she send generates a new random number and sends Victor has value of t:. Victor thens sends her a challenge c and which is a random value that he has now used before. Note that the operations are conducted with mod p and it works because of the magic is logarithms:.
For a password reset, Peggy just contacts Victor and does some multi-factor authentication that she did when she registered her secret, and then registers a new secret. But now we have a problem. Well for this we introduce the inverse mod, and where we compute the inverse mod of r:.
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We just need something to find out a value of g to use, and we are now good to go:. And that is it. That is a world that puts Peggy at the centre, and pushes Victor to the edge. For passwords, we still live in the s, and we blindly build systems which give away a great deal of our most sensitive information. For Victor and Eve, that is fine, but, increasingly our world should be build for Peggy, and not Victor or Eve.
Go build a world for Peggy, and leave Eve with a massive electricity bill. For Victor, those who will change their ways, will benefit most from the new world that we are building. A new era begins …. The following is an oultine of this and related methods [ Slides ]:.
Peggy thus generates a random number v and Victor generates a random value c for a challenge [ paper ]: Parameters Peggy's Password : Peggy's Random v : Victor's Random challenge c : Prime Number: Determine. Peggy thus generates a random number v and Victor generates a random value c for a challenge [ paper ]: Parameters Peggy's Password : Peggy's Random v : Victor's Random challenge c : Prime Number: Determine We use a default prime number of In contrast, non-zero-sum describes a situation in which the interacting parties' aggregate gains and losses can be less than or more than zero.
A zero-sum game is also called a strictly competitive game while non-zero-sum games can be either competitive or non-competitive. Zero-sum games are most often solved with the minimax theorem which is closely related to linear programming duality ,  or with Nash equilibrium. Humans have a cognitive bias towards seeing situations as zero-sum, known as zero-sum bias. The zero-sum property if one gains, another loses means that any result of a zero-sum situation is Pareto optimal. Generally, any game where all strategies are Pareto optimal is called a conflict game. Zero-sum games are a specific example of constant sum games where the sum of each outcome is always zero.
Such games are distributive, not integrative; the pie cannot be enlarged by good negotiation. Situations where participants can all gain or suffer together are referred to as non-zero-sum. Thus, a country with an excess of bananas trading with another country for their excess of apples, where both benefit from the transaction, is in a non-zero-sum situation.
- Fiat–Shamir with a secret password.
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Other non-zero-sum games are games in which the sum of gains and losses by the players are sometimes more or less than what they began with. The idea of Pareto optimal payoff in a zero-sum game gives rise to a generalized relative selfish rationality standard, the punishing-the-opponent standard, where both players always seek to minimize the opponent's payoff at a favorable cost to himself rather to prefer more than less. The punishing-the-opponent standard can be used in both zero-sum games e.
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For two-player finite zero-sum games, the different game theoretic solution concepts of Nash equilibrium , minimax , and maximin all give the same solution. If the players are allowed to play a mixed strategy , the game always has an equilibrium. A game's payoff matrix is a convenient representation. Consider for example the two-player zero-sum game pictured at right or above. The order of play proceeds as follows: The first player red chooses in secret one of the two actions 1 or 2; the second player blue , unaware of the first player's choice, chooses in secret one of the three actions A, B or C.
Then, the choices are revealed and each player's points total is affected according to the payoff for those choices. Example: Red chooses action 2 and Blue chooses action B. When the payoff is allocated, Red gains 20 points and Blue loses 20 points. In this example game, both players know the payoff matrix and attempt to maximize the number of their points.
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Red could reason as follows: "With action 2, I could lose up to 20 points and can win only 20, and with action 1 I can lose only 10 but can win up to 30, so action 1 looks a lot better. If both players take these actions, Red will win 20 points. If Blue anticipates Red's reasoning and choice of action 1, Blue may choose action B, so as to win 10 points. If Red, in turn, anticipates this trick and goes for action 2, this wins Red 20 points. Instead of deciding on a definite action to take, the two players assign probabilities to their respective actions, and then use a random device which, according to these probabilities, chooses an action for them.
Each player computes the probabilities so as to minimize the maximum expected point-loss independent of the opponent's strategy.