XORn

XORn is a cryptographic concept related to the exclusive OR (XOR) operation and its application in scenarios involving multiple inputs or a sequence of operations. In essence, XORn can refer to a generalized XOR operation where the result is determined by applying the XOR function across more than two operands or through a chained series of XOR operations. For instance, a simple XORn of three bits (A, B, C) would result in 1 if an odd number of the bits are 1, and 0 otherwise. This is analogous to the standard XOR of two bits, where the result is 1 if exactly one of the bits is 1.

The term XORn finds relevance in various areas of computer science and cryptography. It is often encountered in error detection and correction codes, where XOR operations are used to generate parity bits or to verify data integrity. In symmetric-key cryptography, XOR operations are fundamental building blocks in algorithms like stream ciphers and block cipher modes of operation. The chaining of XOR operations, as implied by XORn, can be seen in techniques like the Message Authentication Code (MAC) using XOR, where multiple blocks of data are XORed together. The properties of the XOR operation, such as its self-inverting nature (A XOR A = 0) and associativity, make it a versatile tool for constructing secure and efficient cryptographic primitives.