Fine-tuning the ISO/IEC Standard Lightmac

LightMAC, by Luykx et al., is a block cipher based message authentication code (MAC). The simplicity of design and low overhead allows it to have very compact implementations. As a result, it has been recently chosen as an ISO/IEC standard MAC for lightweight applications. LightMAC has been shown to achieve query-length independent security bound of O(q^2/2^n) when instantiated with two independently keyed n-bit block ciphers, where q denotes the number of MAC queries and the query-length is upper bounded by (n-s)2^s bits for a fixed counter size s. In this paper, we aim to minimize the number of block cipher keys in LightMAC. First, we show that the original LightMAC instantiated with a single block cipher key, referred as 1k-LightMAC, achieves security bound of O(q^2/2^n) while the query-length is at least (n-s) bits and at most min{(n-s)2^{n/4},(n-s)2^s} bits. Second, we show that a minor variant of 1k-LightMAC, dubbed as LightMAC-ds, achieves security bound of O(q^2/2^n) while query-length is upper bounded by (n-s)2^{s-1} bits. Of independent interest, our security proof of 1k-LightMAC employs a novel sampling approach, called the reset-sampling, as a subroutine within the H-coefficient proof setup.