Fermat's factorization methodFermat's factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares: That difference is algebraically factorable as ; if neither factor equals one, it is a proper factorization of N. Each odd number has such a representation. Indeed, if is a factorization of N, then Since N is odd, then c and d are also odd, so those halves are integers. (A multiple of four is also a difference of squares: let c and d be even.
Euclid's lemmaIn algebra and number theory, Euclid's lemma is a lemma that captures a fundamental property of prime numbers, namely: For example, if p = 19, a = 133, b = 143, then ab = 133 × 143 = 19019, and since this is divisible by 19, the lemma implies that one or both of 133 or 143 must be as well. In fact, 133 = 19 × 7. If the premise of the lemma does not hold, i.e., p is a composite number, its consequent may be either true or false. For example, in the case of p = 10, a = 4, b = 15, composite number 10 divides ab = 4 × 15 = 60, but 10 divides neither 4 nor 15.
Disk encryption softwareDisk encryption software is computer security software that protects the confidentiality of data stored on computer media (e.g., a hard disk, floppy disk, or USB device) by using disk encryption. Compared to access controls commonly enforced by an operating system (OS), encryption passively protects data confidentiality even when the OS is not active, for example, if data is read directly from the hardware or by a different OS. In addition crypto-shredding suppresses the need to erase the data at the end of the disk's lifecycle.
Encryption softwareEncryption software is software that uses cryptography to prevent unauthorized access to digital information. Cryptography is used to protect digital information on computers as well as the digital information that is sent to other computers over the Internet. There are many software products which provide encryption. Software encryption uses a cipher to obscure the content into ciphertext. One way to classify this type of software is the type of cipher used.
Hardware-based full disk encryptionHardware-based full disk encryption (FDE) is available from many hard disk drive (HDD/SSD) vendors, including: ClevX, Hitachi, Integral Memory, iStorage Limited, Micron, Seagate Technology, Samsung, Toshiba, Viasat UK, Western Digital. The symmetric encryption key is maintained independently from the computer's CPU, thus allowing the complete data store to be encrypted and removing computer memory as a potential attack vector. Hardware-FDE has two major components: the hardware encryptor and the data store.
Flux qubitIn quantum computing, more specifically in superconducting quantum computing, flux qubits (also known as persistent current qubits) are micrometer sized loops of superconducting metal that is interrupted by a number of Josephson junctions. These devices function as quantum bits. The flux qubit was first proposed by Terry P. Orlando et al. at MIT in 1999 and fabricated shortly thereafter. During fabrication, the Josephson junction parameters are engineered so that a persistent current will flow continuously when an external magnetic flux is applied.
TransmonIn quantum computing, and more specifically in superconducting quantum computing, a transmon is a type of superconducting charge qubit that was designed to have reduced sensitivity to charge noise. The transmon was developed by Robert J. Schoelkopf, Michel Devoret, Steven M. Girvin, and their colleagues at Yale University in 2007. Its name is an abbreviation of the term transmission line shunted plasma oscillation qubit; one which consists of a Cooper-pair box "where the two superconductors are also capacitatively shunted in order to decrease the sensitivity to charge noise, while maintaining a sufficient anharmonicity for selective qubit control".
Charge qubitIn quantum computing, a charge qubit (also known as Cooper-pair box) is a qubit whose basis states are charge states (i.e. states which represent the presence or absence of excess Cooper pairs in the island). In superconducting quantum computing, a charge qubit is formed by a tiny superconducting island coupled by a Josephson junction (or practically, superconducting tunnel junction) to a superconducting reservoir (see figure). The state of the qubit is determined by the number of Cooper pairs that have tunneled across the junction.
Modular arithmeticIn mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801. A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00.
Quantum logic gateIn quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of qubits. They are the building blocks of quantum circuits, like classical logic gates are for conventional digital circuits. Unlike many classical logic gates, quantum logic gates are reversible. It is possible to perform classical computing using only reversible gates.
Challenge–response authenticationIn computer security, challenge–response authentication is a family of protocols in which one party presents a question ("challenge") and another party must provide a valid answer ("response") to be authenticated. The simplest example of a challenge–response protocol is password authentication, where the challenge is asking for the password and the valid response is the correct password. An adversary who can eavesdrop on a password authentication can then authenticate itself by reusing the intercepted password.
SuperconductivitySuperconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike an ordinary metallic conductor, whose resistance decreases gradually as its temperature is lowered, even down to near absolute zero, a superconductor has a characteristic critical temperature below which the resistance drops abruptly to zero.
