Session E1: Hardening Crypto CCS’17, October 30-November 3, 2017, Dallas, TX, USA Beer Bounds for Block Cipher Modes of Operation via Nonce-Based Key Derivation Shay Gueron Yehuda Lindell University of Haifa and Amazon Web Services Bar-Ilan University
[email protected] [email protected] ABSTRACT block size of 3DES is 64 bits, and thus collisions occur at just 232 Block cipher modes of operation provide a way to securely en- blocks, or 32GB of data, which can be transferred in under an hour crypt using a block cipher. The main factors in analyzing modes on a fast Internet connection, and in seconds within a data center. of operation are the level of security achieved (chosen-plaintext At rst sight, this problem of birthday collisions is a problem security, authenticated encryption, nonce-misuse resistance, and that is only of relevance for 3DES. Modern block ciphers, like AES, 64 so on) and performance. When measuring the security level of a have a block size of 128, and the birthday bound is thus 2 , which mode of operation, it does not suce to consider asymptotics, and corresponds to a whopping 1 million Petabytes of data. However, a concrete analysis is necessary. This is especially the case today, in reality, birthday collisions are a concern, even for AES or other when encryption rates can be very high, and so birthday bounds 128-bit block ciphers. This is because the standard NIST recom- may be approached or even reached. mendation is to stop using a key when the probability of some −32 48 In this paper, we show that key-derivation at every encryp- leakage exceeds 2 .