This paper introduces NORX, a novel authenticated encryption scheme supporting arbitrary parallelism degree and based on ARX primitives, yet not using modular additions. NORX has a unique parallel architecture based on the monkeyDuplex construction, with an original domain separation scheme for a simple processing of header/payload/trailer data. Furthermore, NORX specifies a dedicated datagram to facilitate interoperability and avoid users the trouble of defining custom encoding and signalling. NORX was optimized for efficiency in both software and hardware, with a SIMD-friendly core, almost byte-aligned rotations, no secret-dependent memory lookups, and only bitwise operations. On a Haswell processor, a serial version of NORX runs at 2.51 cycles per byte. Simulations of a hardware architecture for 180 nm UMC ASIC give a throughput of approximately 10 Gbps at 125 MHz.