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Solving 112-bit prime ECDLP on game consoles using sloppy reduction

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Video game console

A video game console is an electronic device that outputs a video signal or image to display a video game that can be played with a game controller. These may be home consoles, which are generally placed in a permanent location connected to a television or other display devices and controlled with a separate game controller, or handheld consoles, which include their own display unit and controller functions built into the unit and which can be played anywhere. Hybrid consoles combine elements of both home and handheld consoles.

Handheld game console

A handheld game console, or simply handheld console, is a small, portable self-contained video game console with a built-in screen, game controls and speakers. Handheld game consoles are smaller than home video game consoles and contain the console, screen, speakers, and controls in one unit, allowing people to carry them and play them at any time or place. In 1976, Mattel introduced the first handheld electronic game with the release of Auto Race.

Sixth generation of video game consoles

In the history of video games, the sixth generation era (sometimes called the 128-bit era; see "bits and system power" below) is the era of computer and video games, video game consoles, and handheld gaming devices available at the turn of the 21st century, starting on November 27, 1998. Platforms in the sixth generation include consoles from four companies: the Sega Dreamcast (DC), Sony PlayStation 2 (PS2), Nintendo GameCube (GC), and Microsoft Xbox.

Nintendo video game consoles

The Japanese multinational consumer electronics company Nintendo has developed seven home video game consoles and multiple portable consoles for use with external media, as well as dedicated consoles and other hardware for their consoles. , in addition to Nintendo Switch, Nintendo has sold over 863.07 million hardware units. The company's first console, the Color TV-Game, was a success in Japan but was never released outside of Japan.

Seventh generation of video game consoles

The seventh generation of home video game consoles began on November 22, 2005, with the release of Microsoft's Xbox 360 home console. This was followed by the release of Sony's PlayStation 3 on November 17, 2006, and Nintendo's Wii on November 19, 2006. Each new console introduced new technologies. The Xbox 360 offered games rendered natively at high-definition video (HD) resolutions, the PlayStation 3 offered HD movie playback via a built-in 3D Blu-ray Disc player, and the Wii focused on integrating controllers with movement sensors as well as joysticks.

Elliptic-curve cryptography

Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide equivalent security. Elliptic curves are applicable for key agreement, digital signatures, pseudo-random generators and other tasks. Indirectly, they can be used for encryption by combining the key agreement with a symmetric encryption scheme.

PlayStation (console)

The PlayStation (abbreviated as PS, commonly known as the PS1/PS one or its codename PSX) is a home video game console developed and marketed by Sony Computer Entertainment. It was released in Japan on 3 December 1994, in North America on 9 September 1995, in Europe on 29 September 1995, and in Australia on 15 November 1995. As a fifth-generation console, the PlayStation primarily competed with the Nintendo 64 and the Sega Saturn.

Finite field

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are given by the integers mod p when p is a prime number. The order of a finite field is its number of elements, which is either a prime number or a prime power.

Prime number

A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4.

First generation of video game consoles

In the history of video games, the first generation era refers to the video games, video game consoles, and handheld video game consoles available from 1972 to 1983. Notable consoles of the first generation include the Odyssey series (excluding the Magnavox Odyssey 2), the Atari Home Pong, the Coleco Telstar series and the Color TV-Game series. The generation ended with the Computer TV-Game in 1980, but many manufacturers had left the market prior due to the market decline in the year of 1977 and the start of the second generation of video game consoles.