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Abstract. This paper considers-for the first time-the concept of keyalternating ciphers in a provable security setting. Key-alternating ciphers can be seen as a generalization of a construction proposed by Even and Mansour in 1991. This construction builds a block cipher P X from an n-bit permutation P and two n-bit keys k0 and k1, settingHere we consider a (natural) extension of the EvenMansour construction with t permutations P1, . . . , Pt and t + 1 keys, k0, . . . , kt. We demonstrate in a formal model that such a cipher is secure in the sense that an attacker needs to make at least 2 2n/3 queries to the underlying permutations to be able to distinguish the construction from random. We argue further that the bound is tight for t = 2 but there is a gap in the bounds for t > 2, which is left as an open and interesting problem. Additionally, in terms of statistical attacks, we show that the distribution of Fourier coefficients for the cipher over all keys is close to ideal. Lastly, we define a practical instance of the construction with t = 2 using AES referred to as AES 2 . Any attack on AES 2 with complexity below 2 85 will have to make use of AES with a fixed known key in a non-black box manner. However, we conjecture its security is 2 128 .

Abstract.Online ciphers encrypt an arbitrary number of plaintext blocks and output ciphertext blocks which only depend on the preceding plaintext blocks. All online ciphers proposed so far are essentially serial, which significantly limits their performance on parallel architectures such as modern general-purpose CPUs or dedicated hardware. We propose the first parallelizable online cipher, COPE. It performs two calls to the underlying block cipher per plaintext block and is fully parallelizable in both encryption and decryption. COPE is proven secure against chosenplaintext attacks assuming the underlying block cipher is a strong PRP. We then extend COPE to create COPA, the first parallelizable, online authenticated cipher with nonce-misuse resistance. COPA only requires two extra block cipher calls to provide integrity. The privacy and integrity of the scheme is proven secure assuming the underlying block cipher is a strong PRP. Our implementation with Intel AES-NI on a Sandy Bridge CPU architecture shows that both COPE and COPA are about 5 times faster than their closest competition: TC1, TC3, and McOE-G. This high factor of advantage emphasizes the paramount role of parallelizability on up-to-date computing platforms.