BinaryIn mathematics and digital electronics, a binary number is a number expressed in the binary numeral system or base-2 numeral system which represents numeric values using two different symbols: typically 0 (zero) and 1 (one). The base-2system is a positional notation with a radix of 2. Because of its straightforward implementation in digital electronic circuitryusing logic gates, the binary system is used internally by almost all modern computers and computer-based devices. Each digit is referred to as a bit.
BitThe bit is a basic unit of information in computing and digital communications.[1] A bit can have only one of two values, and may therefore be physically implemented with a two-state device.
ByteThe byte (/_ba_t/) is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer[1][2] and for this reason it is the smallest addressable unit of memory in many computer architectures.
Co-PrimeTwo numbers are said to be co-prime if they contain no common factor other than one. In other words, if there exists no common number that divides two given numbers, then the two numbers are called coprime (co-prime) numbers. This is at the core of the Totient used to compute the public and private keys in RSA Cryptography. Some guidelines to follow for coprimes are:
Finite FieldsA finite field is a mathematical construct based on a set of axioms which are held to be true. A number of interesting and useful properties arise from finite fields that makes them particularly suitable for use in cryptography, notably in block ciphers.
HexadecimalIn mathematics and computing, hexadecimal (also base 16, or hex) is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0 to 9 to represent values zero to nine, and A,_B,_C,_D,_E,_F (or alternatively a, b, c, d, e, f) to represent values ten to fifteen. Hexadecimal numerals are widely used by computer system designers and programmers. As each hexadecimal digit represents four binary digits (bits), it allows a more human-friendly representation of binary-coded values. One hexadecimal digit represents a nibble (4 bits), which is half of an octet or byte (8 bits). For example, a single byte can have values ranging from 00000000 to 11111111 in binary form, but this may be more conveniently represented as 00 to FF in hexadecimal.
Modular ArithmeticIf you are familiar with boolean logic, you will see that modulo 2 addition is identical to the xor operation. Because of this, we will use the terms "add" and "xor" interchangably, and we will denote the modulo-2 addition operation with a "circle-plus": 1 _ 1 = 0. 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. Usual addition would suggest that the later time should be 7 + 8 = 15, but this is not the answer because clock time "wraps around" every 12 hours; in 12-hour time, there is no "15 o'clock". Likewise, if the clock starts at 12:00 (noon) and 21 hours elapse, then the time will be 9:00 the next day, rather than 33:00. Since the hour number starts over after it reaches 12, this is arithmetic modulo 12. 12 is congruent not only to 12 itself, but also to 0, so the time called "12:00" could also be called "0:00", since 0 _ 12 mod 12.
Number TheoryNumber theory is the study of the properties and construction of numbers, particularly integers. Prime numbers are of particular interest to number theorists and consequently cryptographers as they are considered the "building blocks" of numbers and produce many interesting results which are useful in cryptography.
Prime NumberA prime number is an integer that can only be divided evenly by itself and one. In 300 BC Euclid proved that there are an infinite number of Primes. It is computationally simple to multiply two large Prime numbers together, but infeasible to factor the resulting composite number back into it's Primes. This fact is at the core of the RSA Modulus.
Scientific NotationScientific notation (also referred to as standard form or standard index form) is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. It is commonly used by scientists, mathematicians and engineers, in part because it can simplify certain arithmetic operations. In scientific notation all numbers are written in the form m × 10n