Abstract. The authenticated encryptions which resist misuse of initial value (or nonce) at some desired level of privacy are two-pass or Macthen-Encrypt constructions (inherently inefficient but provide full privacy) and online constructions, e.g., McOE, sponge-type authenticated encryptions (such as duplex, AEGIS) and COPA. Only the last one is almost parallelizable with some bottleneck in processing associated data. In this paper, we design a new online secure authenticated encryption, called ELmE or Encrypt-Linear mix-Encrypt, which is completely (twostage) parallel (even in associated data) and pipeline implementable. It also provides full privacy when associated data (which includes initial value) is not repeated. The basic idea of our construction and COPA are based on EME, an Encrypt-Mix-Encrypt type SPRP constructions (secure against chosen plaintext and ciphertext). Unlike EME, we consider online computable efficient linear mixing. Our construction optionally supports intermediate tags, which can be verified faster with less buffer size to provide security against block-wise adversaries which is meaningful in low-end device implementation.