In mathematics, what object commonly seen in video games with secret getaways is used to describe a function that is easy to compute in one direction but very hard to compute the opposite way?
"also a permutation—that is, a one-way function that is bijective. One-way permutations are an important cryptographic primitive, and it is not known if their existence is implied by the existence of one-way functions. A trapdoor one-way function or trapdoor permutation is a special kind of one-way function. Such a function is hard to invert unless some secret information, called the ""trapdoor"", is known. A collision-free hash function ""f"" is a one-way function that is also ""collision-resistant""; that is, no randomized polynomial time algorithm can find a collision—distinct values ""x"", ""y"" such that ""f""(""x"") = ""f""(""y"")—with non-negligible probability. If ""f"" is"
"One-way function In computer science, a one-way function is a function that is easy to compute on every input, but hard to invert given the image of a random input. Here, ""easy"" and ""hard"" are to be understood in the sense of computational complexity theory, specifically the theory of polynomial time problems. Not being one-to-one is not considered sufficient of a function for it to be called one-way (see Theoretical definition, below). The existence of such one-way functions is still an open conjecture. In fact, their existence would prove that the complexity classes P and NP are not equal, thus"
"known as the ""universal one-way function"". The problem of finding a one way function is thus reduced to proving that one such function exists. One-way function In computer science, a one-way function is a function that is easy to compute on every input, but hard to invert given the image of a random input. Here, ""easy"" and ""hard"" are to be understood in the sense of computational complexity theory, specifically the theory of polynomial time problems. Not being one-to-one is not considered sufficient of a function for it to be called one-way (see Theoretical definition, below). The existence of such"
"to be sharp and perceptive when interacting with found objects, which must often be used in ways contradictory to their purpose. The site criticised the challenge in locating certain items, and learning of the existence of others. Citing examples such as a coin on the beach, a hairpin on the sofa or a hook on the anchor, ""Secret Service"" noted that these items are the size of a single pizel and not visible on the screen, necessitating the player to find them by pixel hunting with their mouse, ""creating unnecessary downtime"". Due to this inhibitive difficulty, the magazine suggests that"
"for their effectiveness on a class of problems in mathematics called one-way functions, which require relatively little computational power to execute, but vast amounts of power to reverse, if reversal is possible at all. A classic example of a one-way function is multiplication of very large prime numbers. It's fairly quick to multiply two large primes, but very difficult to find the factors of the product of two large primes. Because of the mathematics of one-way functions, most possible keys are bad choices as cryptographic keys; only a small fraction of the possible keys of a given length are suitable,"
"Wraparound (video games) Wraparound, in video games, is a gameplay variation on the single-screen in which space is finite but unbounded; objects leaving one side of the screen immediately reappear on the opposite side, maintaining speed and trajectory. This is referred to as ""wraparound"", since the top and bottom of the screen wrap around to meet, as do the left and right sides (in mathematics, this is known as a Euclidean 2-torus). Some games wrap around in some directions but not others, such as games of the ""Civilization"" series that wrap around left to right, or east and west but"
"a given axis and angle, one can easily construct the corresponding quaternion, and conversely, for a given quaternion one can easily read off the axis and the angle. Both of these are much harder with matrices or Euler angles. In video games and other applications, one is often interested in “smooth rotations”, meaning that the scene should slowly rotate and not in a single step. This can be accomplished by choosing a curve such as the spherical linear interpolation in the quaternions, with one endpoint being the identity transformation 1 (or some other initial rotation) and the other being the"
"resolving the foremost unsolved question of theoretical computer science. The converse is not known to be true, i.e. the existence of a proof that P and NP are not equal would not directly imply the existence of one-way functions. In applied contexts, the terms ""easy"" and ""hard"" are usually interpreted relative to some specific computing entity; typically ""cheap enough for the legitimate users"" and ""prohibitively expensive for any malicious agents"". One-way functions, in this sense, are fundamental tools for cryptography, personal identification, authentication, and other data security applications. While the existence of one-way functions in this sense is also an"
"for the players, and vice versa. The ""value"" of a game is the maximum winning probability for the players over all strategies. The unique games conjecture states that for every sufficiently small pair of constants ε, δ > 0, there exists a constant ""k"" such that the following promise problem (""L"", ""L"") is NP-hard: where ""G"" is a unique game whose answers come from a set of size ""k"". Alternatively, the unique games conjecture postulates the existence of a certain type of probabilistically checkable proof for problems in NP. A unique game can be viewed as a special kind of"
"shown, and another more challenging one in which each number begins hidden and only appears when it's in its proper position. In this submarine-hunting game, the player must identify the locations of a random number of submarines hidden within the playing area. The player moves his ship north, south, east or west, and the areas over which the ship travels light up green. If a submarine is within the area through which the ship has moved, it will appear as a black silhouette; moving directly over a submarine marks it as found. To help direct the search, the player can"
"be viewed in artificial 3D, often resulting in features that escaped notice becoming apparent to the viewer as the brain provides dimensional interpretation to what was heretofore a two-dimensional image. Finding Hidden Objects -- The Van Hare Effect provides viewers with a fast and easy way to find hidden objects, such as in ""hidden object games"", where two images are presented side-by-side and the viewer is challenged to find the missing items or changes from one image to the next. By employing cross-eyed viewing and the Van Hare Effect, the changes are instantly evident, either appearing as throbbing differences or"
"aspects of such analysis. A mathematical game that is well known in European culture is tic-tac-toe (noughts-and-crosses). This is a geometrical game played on a 3-by-3 square; the goal is to form a straight line of three of the same symbol. There are many broadly similar games from all parts of England, to name only one country where they are found. Another kind of geometrical game involves objects that move or jump over each other within a specific shape (a ""board""). There may be captures. The goal may be to eliminate the opponent's pieces, or simply to form a certain"
"Horizon effect The horizon effect, also known as the horizon problem, is a problem in artificial intelligence where, in many games, the number of possible states or positions is immense and computers can only feasibly search a small portion of it, typically a few plies down the game tree. Thus, for a computer searching only five plies, there is a possibility that it will make a detrimental move, but the effect is not visible because the computer does not search to the depth of the error (""i.e."" beyond its ""horizon""). When evaluating a large game tree using techniques such as"
"ancient castle school of Hogwarts (where much of the action takes place) contains numerous secret and magical passages hidden behind paintings, statuary, and furniture. In role-playing games, secret passages, like traps, can be found in all sorts of buildings, especially in dungeons and castles in high fantasy role-playing games. The mansion in the board game ""Cluedo"" (""Clue"") has two secret passages that players can use to move to an opposite corner of the board. Computer and video games often feature hidden areas, sometimes as an important part of the game and other times as an Easter egg. Such areas can"
"seems to be very difficult to determine the value of an unsatisfiable game, even approximately. The unique games conjecture formalises this difficulty. More formally, the (""c"", ""s"")-gap label-cover problem with unique constraints is the following promise problem (""L"", ""L""): where ""G"" is an instance of the label cover problem with unique constraints. The unique games conjecture states that for every sufficiently small pair of constants ε, δ > 0, there exists a constant ""k"" such that the (1 - δ, ε)-gap label-cover problem with unique constraints over alphabet of size ""k"" is NP-hard. Instead of graphs, the label cover problem"
"ability to see backward (the environment to the left of the player), with a long and narrow expanse of environment available to the right. As the game progresses, the avatar's relative position on the screen gradually shifts to the right, with less visibility to the right and more visibility to the left. The speed of the player also slows as time progresses, and the representation of both the avatar and the wife visibly age. The lack of any victory conditions coupled with the inevitability of death have led some to question whether ""Passage"" is in fact a game at all,"
"change. ""Simon Surprise"" is one of the most difficult games in the unit. Every lens becomes the same color and the player has to memorize the location. ""Simon Rewind"" requires the player to memorize the sequence backwards. During each game, the game will give the player a compliment on a certain number of signals completed. On reaching five and eleven signals, the computer will randomly choose ""Awesome!"", ""Nice!"", ""Sweet!"" or ""Respect!"". On reaching 18 signals, the game will play a victory melody three times. On reaching the ultimate 35 signals, the game will play the victory melody again and will"
"write a heuristic function that always computes the true distance.) As the value of the heuristic increases, A* examines fewer nodes but no longer guarantees an optimal path. In many applications (such as video games) this is acceptable and even desirable, in order to keep the algorithm running quickly. This is a fairly simple and easy-to-understand pathfinding algorithm for tile-based maps. To start off, you have a map, a start coordinate and a destination coordinate. The map will look like this, X being walls, S being the start, O being the finish and _ being open spaces, the numbers along"
"be a required route in order to continue or may be optional and contain rewards for the player, such as a bonus stage, a secret character, extra items or a shortcut to a later part of the game. Some secret entrances are invisible, such as a normal-looking wall that can be walked through, while others give a slight visual clue, such as a cave behind a waterfall. Parent categories: Secret rooms and passages: Secret passage Secret passages, also commonly referred to as hidden passages or secret tunnels, are hidden routes used for stealthy travel, escape, or movement of people and"
"or another manifold. Variants of the game may impose maneuverability constraints on the players, such as a limited range of speed or acceleration. Obstacles may also be used. One of the initial applications of the pursuit-evasion problem was missile guidance systems formulated by Rufus Isaacs at the RAND Corporation. Pursuit-evasion Pursuit-evasion (variants of which are referred to as cops and robbers and graph searching) is a family of problems in mathematics and computer science in which one group attempts to track down members of another group in an environment. Early work on problems of this type modeled the environment geometrically."
"In our daily lives the notion of an ""indirect operation"" is not unusual. Indirection specifies a location identified as the pirate chest in ""Tom_&_Becky's_cave..."" that acts as a ""pointer"" to any other location (including itself): its contents (the treasure map) provides the ""address"" of the ""target"" location ""under_Thatcher's_front_porch"" where the real action is occurring. In the following one must remember that these models are abstract models with two fundamental differences from anything physically real: unbounded numbers of registers each with unbounded capacities. The problem appears most dramatically when one tries to use a counter-machine model to build a RASP that"
"Xyzzy (computing) Xyzzy is a magic word from the ""Colossal Cave Adventure"" computer game. In computing, the word is sometimes used as a metasyntactic variable or as a video game cheat code, the canonical ""magic word"". Modern usage is primarily from one of the earliest computer games, ""Colossal Cave Adventure"", in which the idea is to explore a cave with many rooms, collecting the treasures found there. By typing ""xyzzy"" at the appropriate time, the player could move instantly between two otherwise distant points. As ""Colossal Cave Adventure"" was both one of the first adventure games and one of the"
"bit. A one-way function is a function that is easy to compute but hard to invert. A one-way compression function (also called hash function) should have the following properties: Ideally one would like the ""unfeasibility"" in preimage-resistance and second preimage-resistance to mean a work of about 2 where n is the number of bits in the hash function's output. However, particularly for second preimage-resistance this is a difficult problem. A common use of one-way compression functions is in the Merkle–Damgård construction inside cryptographic hash functions. Most widely used hash functions, including MD5, SHA-1 and SHA-2 use this construction. A hash"
"use straight disks, but others disguise the puzzle in some other form. There is an arcade version by Sega/Andamiro. A 15-disk version of the puzzle appears in the game ""Sunless Sea"" as a lock to a tomb. The player has the option to click through each move of the puzzle in order to solve it, but the game notes that it will take 32767 moves to complete. If an especially dedicated player does click through to the end of the puzzle, it is revealed completing the puzzle does not unlock the door. In ""Yu-Gi-Oh! VRAINS"", a hacking group called ""Knight"
"such an inapproximability result would hold include constraint satisfaction problems, which crop up in a wide variety of disciplines. The conjecture is unusual in that the academic world seems about evenly divided on whether it is true or not. The unique games conjecture can be stated in a number of equivalent ways. The following formulation of the unique games conjecture is often used in hardness of approximation. The conjecture postulates the NP-hardness of the following promise problem known as ""label cover with unique constraints"". For each edge, the colors on the two vertices are restricted to some particular ordered pairs."
"a good example of this technique. In ""Out Run"", the player drives a Ferrari into depth of the game window. The palms on the left and right side of the street are the same bitmap, but have been scaled to different sizes, creating the illusion that some are closer than others. The angles of movement are ""left and right"" and ""into the depth"" (while still capable of doing so technically, this game did not allow making a U-turn or going into reverse, therefore moving ""out of the depth"", as this did not make sense to the high-speed game play and"
"of the game, which worked as a password to transport the player to a certain part of the game. The mazes started out as extremely simple, but continually grew in complexity until most could not be solved by trial and error. The walls in the mazes were all at 90 degrees, and involved simple commands in any of the four directions to progress, with the player always facing in the direction of the last place he moved. One of the later mazes also featured invisible walls so that the player had to identify whether he was making progress or not"
"is easy to compute in the forward direction, but is difficult to compute in the reverse direction without already knowing the private key (""trapdoor""). Trapdoor permutations can be used for digital signature schemes, where computing the reverse direction with the secret key is required for signing, and computing the forward direction is used to verify signatures. Used directly, this type of signature scheme is vulnerable to key-only existential forgery attack. To create a forgery, the attacker picks a random signature σ and uses the verification procedure to determine the message, ""m"", corresponding to that signature. In practice, however, this type"
"crucial element of the game's various puzzles, as creating holes in the wrong areas could hinder the player's efforts to advance. Dropping the ball into a hole would cause it to return to its starting point. Given the nature of Muddy's ability to move the ball, digging holes in the wrong places could make reaching the gate with the ball completely impossible, requiring Muddy to leave the screen and then return to try again. Along the way, there are many obstacles, such as moving enemies, pipes, barrels, weights, and bosses. Jason Cipriano of MTV praised the games' short and to-the-point"
"as ""Train""). In true Lovecraftian spirit, some Locations are real while others are fictitious. Locations may be in various ""regions"" (color-coded) or ""dimensions"" (indicated by a symbol); this complicates the process of playing a new location, as some are difficult or impossible to travel to from others. Examples: ""Massachusetts State Hospital"", ""R'lyeh"" Playing a Monster requires certain locations which are marked as a ""gate"", and can usually only be used once. Monsters are played face down into a ""mythos threat"", where their strength may be roughly guessed at by the Sanity cost required to play them, but their exact identity"
"Unique games conjecture In computational complexity theory, the unique games conjecture is a conjecture made by Subhash Khot in 2002. The conjecture postulates that the problem of determining the approximate ""value"" of a certain type of game, known as a ""unique game"", has NP-hard algorithmic complexity. It has broad applications in the theory of hardness of approximation. If it is true, then for many important problems it is not only impossible to get an exact solution in polynomial time (as postulated by the P versus NP problem), but also impossible to get a good polynomial-time approximation. The problems for which"
"escape. These are presented from a first-person perspective, with the player being able to move between different pre-determined positions in each room. To escape, the player is tasked with finding various items and solving puzzles, reminiscent of escape-the-room games. At some points, the player may need to combine objects with each other to create the necessary tool to complete a puzzle. The puzzles include various brain teasers, such as baccarat and magic squares. An in-game calculator is provided for math-related problems, and the player can ask characters for hints if they find an Escape room too difficult. All Escape sections"
"of ""Super Mario Bros."", the game has been described as having a ""surprising amount of depth and spatial complexity"" in part due to secret warp zones found through the game. ""Portal"" is a critically acclaimed game that uses warps as its core gameplay mechanic. Warp (gaming) A warp, also known as a portal or teleporter, is an element in video game design that allows a player character instant travel between two locations or levels. Specific areas that allow such travel are referred to as warp zones. A warp zone might be a secret passage, accessible only to players capable of"