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82-469: A cryptosystem is considered secure in terms of indistinguishability if no adversary, given an encryption of a message randomly chosen from a two-element message space determined by the adversary, can identify the message choice with probability significantly better than that of random guessing ( 1 ⁄ 2 ). If any adversary can succeed in distinguishing the chosen ciphertext with a probability significantly greater than 1 ⁄ 2 , then this adversary

164-584: A chess championship . On the other hand, players in a game may constitute their own audience as they take their turn to play. Often, part of the entertainment for children playing a game is deciding who is part of their audience and who is a player. A toy and a game are not the same. Toys generally allow for unrestricted play whereas games present rules for the player to follow. Key components of games are goals, rules , challenge , and interaction. Games generally involve mental or physical stimulation, and often both. Many games help develop practical skills , serve as

246-407: A controller or a motion sensitive tool ( console games ). More esoteric devices such as paddle controllers have also been used for input. There are many genres of video game; the first commercial video game, Pong , was a simple simulation of table tennis . As processing power increased, new genres such as adventure and action games were developed that involved a player guiding a character from

328-414: A lawn ; an area of mowed grass (or alternately, on graded soil) generally smaller than a sports field (pitch). Variations of many games that are traditionally played on a sports field are marketed as "lawn games" for home use in a front or back yard. Common lawn games include horseshoes , sholf , croquet , bocce , and lawn bowls . A tabletop game is a game where the elements of play are confined to

410-503: A tarot deck of 78 cards (used in Europe to play a variety of trick-taking games collectively known as Tarot, Tarock or Tarocchi games), or a deck specific to the individual game (such as Set or 1000 Blank White Cards ). Uno and Rook are examples of games that were originally played with a standard deck and have since been commercialized with customized decks. Some collectible card games such as Magic: The Gathering are played with

492-560: A community much larger than the group of players. A city or town may set aside such resources for the organization of sports leagues. Popular sports may have spectators who are entertained just by watching games. A community will often align itself with a local sports team that supposedly represents it (even if the team or most of its players only recently moved in); they often align themselves against their opponents or have traditional rivalries. The concept of fandom began with sports fans. Lawn games are outdoor games that can be played on

574-406: A definition similar to that of IND-CPA. However, in addition to the public key (or encryption oracle, in the symmetric case), the adversary is given access to a decryption oracle which decrypts arbitrary ciphertexts at the adversary's request, returning the plaintext. In the non-adaptive definition, the adversary is allowed to query this oracle only up until it receives the challenge ciphertext. In

656-428: A different game. There are exceptions to this in that some games deliberately involve the changing of their own rules, but even then there are often immutable meta -rules. Rules generally determine the time-keeping system , the rights and responsibilities of the players, scoring techniques, preset boundaries, and each player's goals. The rules of a game may be distinguished from its aims. For most competitive games,

738-559: A few cryptographic algorithms are specifically designed to make ciphertext messages indistinguishable from random bit strings. Most applications don't require an encryption algorithm to produce encrypted messages that are indistinguishable from random bits. However, some authors consider such encryption algorithms to be conceptually simpler and easier to work with, and more versatile in practice—and most IND-CPA encryption algorithms apparently do, in fact, produce encrypted messages that are indistinguishable from random bits. Indistinguishability

820-493: A few known implications, though it is by no means complete. The notation A ⇒ B {\displaystyle A\Rightarrow B} means that property A implies property B. A ⇔ B {\displaystyle A\Leftrightarrow B} means that properties A and B are equivalent . A ⇏ B {\displaystyle A\not \Rightarrow B} means that property A does not necessarily imply property B. Game A game

902-472: A form of exercise, or otherwise perform an educational, simulational , or psychological role. Attested as early as 2600 BC, games are a universal part of human experience and present in all cultures. The Royal Game of Ur , Senet , and Mancala are some of the oldest known games. Ludwig Wittgenstein was probably the first academic philosopher to address the definition of the word game . In his Philosophical Investigations , Wittgenstein argued that

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984-427: A fresh new secret key for each session/conversation (forward secrecy). When used with asymmetric ciphers for key transfer, pseudorandom key generators are nearly always used to generate the symmetric cipher session keys. However, lack of randomness in those generators or in their initialization vectors is disastrous and has led to cryptanalytic breaks in the past. Therefore, it is essential that an implementation use

1066-429: A game. Muggins , Mexican Train , and Chicken Foot are very popular domino games. Texas 42 is a domino game more similar in its play to a "trick-taking" card game . Variations of traditional dominoes abound: Triominoes are similar in theory but are triangular and thus have three values per tile. Similarly, a game known as Quad-Ominos uses four-sided tiles. Some other games use tiles in place of cards; Rummikub

1148-409: A high degree of luck, which can be directed to some extent by the player through more strategic elements of play and through tenets of probability theory . Such games are thus popular as gambling games; the game of craps is perhaps the most famous example, though liar's dice and poker dice were originally conceived of as gambling games. Domino games are similar in many respects to card games, but

1230-429: A key generation function, E {\displaystyle {\mathcal {E}}} be an encryption function, and D {\displaystyle {\mathcal {D}}} be a decryption function. Let S E = ( K , E , D ) {\displaystyle {\mathcal {S}}{\mathcal {E}}=({\mathcal {K}},{\mathcal {E}},{\mathcal {D}})} be

1312-627: A large area in which to play them, large amounts of strength or stamina, or specialized equipment other than what comes in a box. This class of games includes any game in which the skill element involved relates to manual dexterity or hand-eye coordination, but excludes the class of video games (see below). Games such as jacks , paper football , and Jenga require only very portable or improvised equipment and can be played on any flat level surface, while other examples, such as pinball , billiards , air hockey , foosball , and table hockey require specialized tables or other self-contained modules on which

1394-503: A large number of video games have been created to simulate strategic combat), and the board may be a map on which the players' tokens move. Virtually all board games involve "turn-based" play; one player contemplates and then makes a move, then the next player does the same, and a player can only act on their turn. This is opposed to "real-time" play as is found in some card games, most sports and most video games. Some games, such as chess and Go , are entirely deterministic, relying only on

1476-425: A message does not guarantee that it will remain unchanged while encrypted. Hence, often a message authentication code is added to a ciphertext to ensure that changes to the ciphertext will be noted by the receiver. Message authentication codes can be constructed from an AEAD cipher (e.g. AES-GCM ). However, symmetric ciphers cannot be used for non-repudiation purposes except by involving additional parties. See

1558-486: A message to have the same secret key. All early cryptographic systems required either the sender or the recipient to somehow receive a copy of that secret key over a physically secure channel. Nearly all modern cryptographic systems still use symmetric-key algorithms internally to encrypt the bulk of the messages, but they eliminate the need for a physically secure channel by using Diffie–Hellman key exchange or some other public-key protocol to securely come to agreement on

1640-408: A new type of equilibrium strategy not found in traditional games. The entanglement of player's choices can have the effect of a contract by preventing players from profiting from what is known as betrayal . Games can take a variety of forms, from competitive sports to board games and video games. Many sports require special equipment and dedicated playing fields, leading to the involvement of

1722-614: A number of bits and encrypt them in a single unit, padding the plaintext to achieve a multiple of the block size. The Advanced Encryption Standard (AES) algorithm, approved by NIST in December 2001, uses 128-bit blocks. Examples of popular symmetric-key algorithms include Twofish , Serpent , AES (Rijndael), Camellia , Salsa20 , ChaCha20 , Blowfish , CAST5 , Kuznyechik , RC4 , DES , 3DES , Skipjack , Safer , and IDEA . Symmetric ciphers are commonly used to achieve other cryptographic primitives than just encryption. Encrypting

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1804-444: A pawn on a board, play money , or an intangible item such as a point scored. Games such as hide-and-seek or tag do not use any obvious tool; rather, their interactivity is defined by the environment. Games with the same or similar rules may have different gameplay if the environment is altered. For example, hide-and-seek in a school building differs from the same game in a park; an auto race can be radically different depending on

1886-635: A piece of information that one player knows, and the object is to coerce others into guessing that piece of information without actually divulging it in text or spoken word. Charades is probably the most well-known game of this type, and has spawned numerous commercial variants that involve differing rules on the type of communication to be given, such as Catch Phrase , Taboo , Pictionary , and similar. The genre also includes many game shows such as Win, Lose or Draw , Password and $ 25,000 Pyramid . Video games are computer- or microprocessor -controlled games. Computers can create virtual spaces for

1968-465: A play, to make all open endpoints sum to a given number or multiple, or simply to play all dominoes from one's hand onto the board. Sets vary in the number of possible dots on one end, and thus of the number of combinations and pieces; the most common set historically is double-six , though in more recent times "extended" sets such as double-nine have been introduced to increase the number of dominoes available, which allows larger hands and more players in

2050-416: A player toward winning. For instance, an intermediate aim in football is to score goals, because scoring goals will increase one's likelihood of winning the game, but is not alone sufficient to win the game. An aim identifies a sufficient condition for successful action, whereas the rule identifies a necessary condition for permissible action. For example, the aim of chess is to checkmate, but although it

2132-418: A reciprocal cipher, a mathematical involution on each typed-in letter. Instead of designing two kinds of machines, one for encrypting and one for decrypting, all the machines can be identical and can be set up (keyed) the same way. Examples of reciprocal ciphers include: The majority of all modern ciphers can be classified as either a stream cipher , most of which use a reciprocal XOR cipher combiner, or

2214-424: A small area and require little physical exertion, usually simply placing, picking up and moving game pieces. Most of these games are played at a table around which the players are seated and on which the game's elements are located. However, many games falling into this category, particularly party games , are more free-form in their play and can involve physical activity such as mime. Still, these games do not require

2296-413: A small selection of cards that have been collected or purchased individually from large available sets. Some board games include a deck of cards as a gameplay element, normally for randomization or to keep track of game progress. Conversely, some card games such as Cribbage use a board with movers, normally to keep score. The differentiation between the two genres in such cases depends on which element of

2378-405: A source of high entropy for its initialization. A reciprocal cipher is a cipher where, just as one enters the plaintext into the cryptography system to get the ciphertext , one could enter the ciphertext into the same place in the system to get the plaintext. A reciprocal cipher is also sometimes referred as self-reciprocal cipher . Practically all mechanical cipher machines implement

2460-453: A symmetric encryption scheme. The game Guess is defined as: [REDACTED] As many times as it would like, an adversary selects two plaintext messages of its own choosing and provides them to the LR oracle which returns a ciphertext encrypting one of the messages. An adversary's advantage is determined by its probability of guessing the value of b, a value chosen at random at the beginning of

2542-409: A third person perspective through a series of obstacles. This "real-time" element cannot be easily reproduced by a board game, which is generally limited to "turn-based" strategy; this advantage allows video games to simulate situations such as combat more realistically. Additionally, the playing of a video game does not require the same physical skill, strength or danger as a real-world representation of

Ciphertext indistinguishability - Misplaced Pages Continue

2624-457: A true game played for entertainment or a competitive activity describable in principle by mathematical game theory. John Nash proved that games with several players have a stable solution provided that coalitions between players are disallowed. Nash won the Nobel prize for economics for this important result which extended von Neumann's theory of zero-sum games. Nash's stable solution is known as

2706-415: A virtual environment is provided in which the player may be free to do whatever they like within the confines of a particular game's universe. Sometimes, there is a lack of goals or opposition, which has stirred some debate on whether these should be considered "games" or "toys". (Crawford specifically mentions Will Wright 's SimCity as an example of a toy.) Online games have been part of culture from

2788-416: A wide variety of game types. Some video games simulate conventional game objects like cards or dice, while others can simulate environs either grounded in reality or fantastical in design, each with its own set of rules or goals. A computer or video game uses one or more input devices , typically a button / joystick combination (on arcade games ); a keyboard , mouse or trackball ( computer games ); or

2870-458: A worldwide popularity of ball games such as rugby , basketball , soccer (football) , cricket , tennis , and volleyball . Other tools are more idiosyncratic to a certain region. Many countries in Europe, for instance, have unique standard decks of playing cards . Other games such as chess may be traced primarily through the development and evolution of its game pieces. Many game tools are tokens, meant to represent other things. A token may be

2952-493: Is indistinguishable under chosen plaintext attack if every probabilistic polynomial time adversary has only a negligible " advantage " over random guessing. An adversary is said to have a negligible "advantage" if it wins the above game with probability ( 1 2 ) + ϵ ( k ) {\displaystyle \left({\tfrac {1}{2}}\right)\,+\,\epsilon (k)} , where ϵ ( k ) {\displaystyle \epsilon (k)}

3034-586: Is a negligible function in the security parameter k {\displaystyle k} , that is for every (nonzero) polynomial function poly() there exists k 0 {\displaystyle k_{0}} such that | ϵ ( k ) | < | 1 p o l y ( k ) | {\displaystyle |\epsilon (k)|\;<\;\left|{\tfrac {1}{\mathrm {poly(k)} }}\right|} for all k > k 0 {\displaystyle k\;>\;k_{0}} . Although

3116-626: Is a structured type of play , usually undertaken for entertainment or fun , and sometimes used as an educational tool. Many games are also considered to be work (such as professional players of spectator sports or games) or art (such as jigsaw puzzles or games involving an artistic layout such as mahjong , solitaire , or some video games ). Games are sometimes played purely for enjoyment, sometimes for achievement or reward as well. They can be played alone, in teams, or online; by amateurs or by professionals. The players may have an audience of non-players, such as when people are entertained by watching

3198-510: Is a variant of the Rummy card game family that uses tiles numbered in ascending rank among four colors, very similar in makeup to a 2-deck "pack" of Anglo-American playing cards . Mahjong is another game very similar to Rummy that uses a set of tiles with card-like values and art. Lastly, some games use graphical tiles to form a board layout, on which other elements of the game are played. Settlers of Catan and Carcassonne are examples. In each,

3280-427: Is an important property for maintaining the confidentiality of encrypted communications. However, the property of indistinguishability has in some cases been found to imply other, apparently unrelated security properties. Sometimes these implications go in both directions, making two definitions equivalent; for example, it is known that the property of indistinguishability under adaptive chosen ciphertext attack (IND-CCA2)

3362-443: Is based on the idea of a crossword puzzle , and tic-tac-toe sets with a boxed grid and pieces are available commercially). These games vary widely, from games centering on a design being drawn such as Pictionary and "connect-the-dots" games like sprouts , to letter and word games such as Boggle and Scattergories , to solitaire and logic puzzle games such as Sudoku and crossword puzzles . A guessing game has as its core

Ciphertext indistinguishability - Misplaced Pages Continue

3444-465: Is considered to have an "advantage" in distinguishing the ciphertext, and the scheme is not considered secure in terms of indistinguishability. This definition encompasses the notion that in a secure scheme, the adversary should learn no information from seeing a ciphertext. Therefore, the adversary should be able to do no better than if it guessed randomly. Security in terms of indistinguishability has many definitions, depending on assumptions made about

3526-444: Is equivalent to the property of non-malleability under the same attack scenario (NM-CCA2). This equivalence is not immediately obvious, as non-malleability is a property dealing with message integrity, rather than confidentiality. In other cases, it has been demonstrated that indistinguishability can be combined with certain other definitions, in order to imply still other useful definitions, and vice versa. The following list summarizes

3608-403: Is expected that players will try to checkmate each other, it is not a rule of chess that a player must checkmate the other player whenever possible. Similarly, it is not a rule of football that a player must score a goal on a penalty; while it is expected the player will try, it is not required. While meeting the aims often requires a certain degree of skill and (in some cases) luck, following

3690-418: Is one of the main drawbacks of symmetric -key encryption, in comparison to public-key encryption (also known as asymmetric-key encryption). However, symmetric-key encryption algorithms are usually better for bulk encryption. With exception of the one-time pad they have a smaller key size, which means less storage space and faster transmission. Due to this, asymmetric-key encryption is often used to exchange

3772-426: Is one popular example, where players must succeed in each of four skills: artistry, live performance, trivia, and language. Card games use a deck of cards as their central tool. These cards may be a standard Anglo-American (52-card) deck of playing cards (such as for bridge , poker , Rummy , etc.), a regional deck using 32, 36 or 40 cards and different suit signs (such as for the popular German game skat ),

3854-636: The ISO/IEC 13888-2 standard . Another application is to build hash functions from block ciphers. See one-way compression function for descriptions of several such methods. Many modern block ciphers are based on a construction proposed by Horst Feistel . Feistel's construction makes it possible to build invertible functions from other functions that are themselves not invertible. Symmetric ciphers have historically been susceptible to known-plaintext attacks , chosen-plaintext attacks , differential cryptanalysis and linear cryptanalysis . Careful construction of

3936-474: The Nash equilibrium . If cooperation between players is allowed, then the game becomes more complex; many concepts have been developed to analyze such games. While these have had some partial success in the fields of economics, politics and conflict , no good general theory has yet been developed. In quantum game theory , it has been found that the introduction of quantum information into multiplayer games allows

4018-466: The symmetric case by replacing the public key encryption function with an encryption oracle , which retains the secret encryption key and encrypts arbitrary plaintexts at the adversary's request. The adversarial process of performing a chosen-plaintext attack is usually outlined in the form of a Cryptographic Game . To test for symmetric IND-CPA, the game described above is defined. Let K {\displaystyle {\mathcal {K}}} be

4100-399: The track or street course, even with the same cars. Games are often characterized by their tools and rules. While rules are subject to variations and changes , enough change in the rules usually results in a "new" game. For instance, baseball can be played with "real" baseballs or with wiffleballs . However, if the players decide to play with only three bases, they are arguably playing

4182-532: The ultimate aim is winning: in this sense, checkmate is the aim of chess. Common win conditions are being first to amass a certain quota of points or tokens (as in Settlers of Catan ), having the greatest number of tokens at the end of the game (as in Monopoly ), or some relationship of one's game tokens to those of one's opponent (as in chess's checkmate ). There may also be intermediate aims, which are tasks that move

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4264-695: The "board" is made up of a series of tiles; in Settlers of Catan the starting layout is random but static, while in Carcassonne the game is played by "building" the board tile-by-tile. Hive , an abstract strategy game using tiles as moving pieces, has mechanical and strategic elements similar to chess , although it has no board; the pieces themselves both form the layout and can move within it. Pencil and paper games require little or no specialized equipment other than writing materials, though some such games have been commercialized as board games ( Scrabble , for instance,

4346-417: The adaptive definition, the adversary may continue to query the decryption oracle even after it has received a challenge ciphertext, with the caveat that it may not pass the challenge ciphertext for decryption (otherwise, the definition would be trivial). A scheme is IND-CCA1/IND-CCA2 secure if no adversary has a non-negligible advantage in winning the above game. Sometimes we need encryption schemes in which

4428-446: The adversary knows M 0 , M 1 and PK , the probabilistic nature of E means that the encryption of M b will be only one of many valid ciphertexts, and therefore encrypting M 0 , M 1 and comparing the resulting ciphertexts with the challenge ciphertext does not afford any non-negligible advantage to the adversary. While the above definition is specific to an asymmetric key cryptosystem, it can be adapted to

4510-502: The best strategic move based on the roll of two dice . Trivia games have a great deal of randomness based on the questions a person gets. German-style board games are notable for often having rather less of a luck factor than many board games. Board game groups include race games , roll-and-move games, abstract strategy games , word games , and wargames , as well as trivia and other elements. Some board games fall into multiple groups or incorporate elements of other genres: Cranium

4592-552: The capabilities of the attacker. It is normally presented as a game , where the cryptosystem is considered secure if no adversary can win the game with significantly greater probability than an adversary who must guess randomly. The most common definitions used in cryptography are indistinguishability under chosen plaintext attack (abbreviated IND-CPA), indistinguishability under (non-adaptive) chosen ciphertext attack (IND-CCA1), and indistinguishability under adaptive chosen ciphertext attack (IND-CCA2). Security under either of

4674-474: The ciphertext string is indistinguishable from a random string by the adversary. If an adversary is unable to tell if a message even exists, it gives the person who wrote the message plausible deniability . Some people building encrypted communication links prefer to make the contents of each encrypted datagram indistinguishable from random data, in order to make traffic analysis more difficult. Some people building systems to store encrypted data prefer to make

4756-470: The data indistinguishable from random data in order to make data hiding easier. For example, some kinds of disk encryption such as TrueCrypt attempt to hide data in the innocent random data left over from some kinds of data erasure . As another example, some kinds of steganography attempt to hide data by making it match the statistical characteristics of the innocent "random" image noise in digital photos. To support such deniable encryption systems,

4838-467: The dice has a profound impact on the outcome of the game, however dice games are differentiated in that the dice do not determine the success or failure of some other element of the game; they instead are the central indicator of the person's standing in the game. Popular dice games include Yahtzee , Farkle , Bunco , liar's dice / Perudo , and poker dice . As dice are, by their very nature, designed to produce random numbers , these games usually involve

4920-440: The elements of games, such as play , rules, and competition, all fail to adequately define what games are. From this, Wittgenstein concluded that people apply the term game to a range of disparate human activities that bear to one another only what one might call family resemblances . As the following game definitions show, this conclusion was not a final one and today many philosophers, like Thomas Hurka , think that Wittgenstein

5002-402: The following game between an adversary and a challenger. For schemes based on computational security , the adversary is modeled by a probabilistic polynomial time Turing machine , meaning that it must complete the game and output a guess within a polynomial number of time steps. In this definition E ( PK , M ) represents the encryption of a message M under the key PK : A cryptosystem

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5084-432: The functions for each round can greatly reduce the chances of a successful attack. It is also possible to increase the key length or the rounds in the encryption process to better protect against attack. This, however, tends to increase the processing power and decrease the speed at which the process runs due to the amount of operations the system needs to do. Most modern symmetric-key algorithms appear to be resistant to

5166-419: The game is foremost in its play; a board game using cards for random actions can usually use some other method of randomization, while Cribbage can just as easily be scored on paper. These elements as used are simply the traditional and easiest methods to achieve their purpose. Dice games use a number of dice as their central element. Board games often use dice for a randomization element, and thus each roll of

5248-409: The game is played. The advent of home video game systems largely replaced some of these, such as table hockey, however air hockey, billiards, pinball and foosball remain popular fixtures in private and public game rooms. These games and others, as they require reflexes and coordination, are generally performed more poorly by intoxicated persons but are unlikely to result in injury because of this; as such

5330-682: The game which determines the message that is encrypted in the LR oracle. Therefore, its advantage is defined as: Adv S E i n d − c p a ⁡ ( A ) = 2 ⋅ Pr [ G u e s s S E A ⇒ t r u e ] − 1 {\displaystyle \operatorname {Adv} _{\mathcal {SE}}^{\mathrm {ind-cpa} }(A)=2\cdot \Pr \left[\mathrm {Guess} _{\mathcal {SE}}^{A}\Rightarrow \mathrm {true} \right]-1} Indistinguishability under non-adaptive and adaptive Chosen Ciphertext Attack (IND-CCA1, IND-CCA2) uses

5412-464: The game, and can provide either very realistic, exaggerated or impossible physics, allowing for elements of a fantastical nature, games involving physical violence, or simulations of sports. Lastly, a computer can, with varying degrees of success, simulate one or more human opponents in traditional table games such as chess , leading to simulations of such games that can be played by a single player. In more open-ended video games, such as sandbox games ,

5494-408: The games are popular as drinking games . In addition, dedicated drinking games such as quarters and beer pong also involve physical coordination and are popular for similar reasons. Board games use as a central tool a board on which the players' status, resources, and progress are tracked using physical tokens. Many also involve dice or cards. Most games that simulate war are board games (though

5576-436: The generic device is instead a set of tiles called dominoes , which traditionally each have two ends, each with a given number of dots, or "pips", and each combination of two possible end values as it appears on a tile is unique in the set. The games played with dominoes largely center around playing a domino from the player's "hand" onto the matching end of another domino, and the overall object could be to always be able to make

5658-410: The lack of any formidable opposition. Many games described as "single-player" may be termed actually puzzles or recreations . A multiplayer game is a game of several players who may be independent opponents or teams. Games with many independent players are difficult to analyze formally using game theory as the players may form and switch coalitions . The term "game" in this context may mean either

5740-404: The latter definition implies security under the previous ones: a scheme which is IND-CCA1 secure is also IND-CPA secure, and a scheme which is IND-CCA2 secure is both IND-CCA1 and IND-CPA secure. Thus, IND-CCA2 is the strongest of the three definitions of security. For a probabilistic asymmetric key encryption algorithm , indistinguishability under chosen plaintext attack (IND-CPA) is defined by

5822-440: The outcome. Many other games involving a high degree of luck do not allow direct attacks between opponents; the random event simply determines a gain or loss in the standing of the current player within the game, which is independent of any other player; the "game" then is actually a "race" by definitions such as Crawford's. Most other board games combine strategy and luck factors; the game of backgammon requires players to decide

5904-453: The player does". This is often referred to as gameplay . Major key elements identified in this context are tools and rules that define the overall context of game. Games are often classified by the components required to play them (e.g. miniatures , a ball , cards , a board and pieces , or a computer ). In places where the use of leather is well-established, the ball has been a popular game piece throughout recorded history, resulting in

5986-1332: The rules of a game merely requires knowledge of the rules and some careful attempt to follow them; it rarely (if ever) requires luck or demanding skills. A game's tools and rules will result in its requiring skill, strategy, luck , or a combination thereof, and are classified accordingly. Games of skill include games of physical skill, such as wrestling , tug of war , hopscotch , target shooting , and games of mental skill such as checkers and chess . Games of strategy include checkers, chess, Go , arimaa , and tic-tac-toe , and often require special equipment to play them. Games of chance include gambling games ( blackjack , Mahjong , roulette , etc.), as well as snakes and ladders and rock, paper, scissors ; most require equipment such as cards or dice . However, most games contain two or all three of these elements. For example, American football and baseball involve both physical skill and strategy while tiddlywinks , poker , and Monopoly combine strategy and chance. Many card and board games combine all three; most trick-taking games involve mental skill, strategy, and an element of chance, as do many strategic board games such as Risk , Settlers of Catan , and Carcassonne . Most games require multiple players. However, single-player games are unique in respect to

6068-401: The same cryptographic keys for both the encryption of plaintext and the decryption of ciphertext . The keys may be identical, or there may be a simple transformation to go between the two keys. The keys, in practice, represent a shared secret between two or more parties that can be used to maintain a private information link. The requirement that both parties have access to the secret key

6150-400: The secret key for symmetric-key encryption. Symmetric-key encryption can use either stream ciphers or block ciphers . Stream ciphers encrypt the digits (typically bytes ), or letters (in substitution ciphers) of a message one at a time. An example is ChaCha20 . Substitution ciphers are well-known ciphers, but can be easily decrypted using a frequency table . Block ciphers take

6232-556: The strategy element for their interest. Such games are usually described as having " perfect information "; the only unknown is the exact thought processes of one's opponent, not the outcome of any unknown event inherent in the game (such as a card draw or die roll). Children's games, on the other hand, tend to be very luck-based, with games such as Candy Land and Chutes and Ladders having virtually no decisions to be made. By some definitions, such as that by Greg Costikyan , they are not games since there are no decisions to make which affect

6314-437: The threat of post-quantum cryptography . Quantum computers would exponentially increase the speed at which these ciphers can be decoded; notably, Grover's algorithm would take the square-root of the time traditionally required for a brute-force attack , although these vulnerabilities can be compensated for by doubling key length. For example, a 128 bit AES cipher would not be secure against such an attack as it would reduce

6396-415: The time required to test all possible iterations from over 10 quintillion years to about six months. By contrast, it would still take a quantum computer the same amount of time to decode a 256 bit AES cipher as it would a conventional computer to decode a 128 bit AES cipher. For this reason, AES-256 is believed to be "quantum resistant". Symmetric-key algorithms require both the sender and the recipient of

6478-408: The type of challenges a player faces. Unlike a game with multiple players competing with or against each other to reach the game's goal, a one-player game is a battle solely against an element of the environment (an artificial opponent), against one's own skills, against time, or against chance. Playing with a yo-yo or playing tennis against a wall is not generally recognized as playing a game due to

6560-473: The very earliest days of networked and time-shared computers. Early commercial systems such as Plato were at least as widely famous for their games as for their strictly educational value. In 1958, Tennis for Two dominated Visitor's Day and drew attention to the oscilloscope at the Brookhaven National Laboratory ; during the 1980s, Xerox PARC was known mainly for Maze War , which

6642-445: Was offered as a hands-on demo to visitors. Modern online games are played using an Internet connection; some have dedicated client programs, while others require only a web browser . Some simpler browser games appeal to more casual game-playing demographic groups (notably older audiences) that otherwise play very few video games. Symmetric encryption Symmetric-key algorithms are algorithms for cryptography that use

6724-753: Was wrong and that Bernard Suits' definition is a good answer to the problem. French sociologist Roger Caillois , in his book Les jeux et les hommes (Games and Men) (1961), defined a game as an activity that must have the following characteristics: Game designer Chris Crawford defined the term in the context of computers. Using a series of dichotomies : Crawford's definition may thus be rendered as: an interactive, goal-oriented activity made for money, with active agents to play against, in which players (including active agents) can interfere with each other. Other definitions, however, as well as history, show that entertainment and games are not necessarily undertaken for monetary gain. Games can be characterized by "what

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