Cryptanalysis of Masked Ciphers: A Not So Random Idea

Abstract

A new approach to the security analysis of hardware-oriented masked ciphers against second-order side-channel attacks is developed. By relying on techniques from symmetric-key cryptanalysis, concrete security bounds are obtained in a variant of the probing model that allows the adversary to make only a bounded, but possibly very large, number of measurements. Specifically, it is formally shown how a boundedquery variant of robust probing security can be reduced to the linear cryptanalysis of masked ciphers. As a result, the compositional issues of higher-order threshold implementations can be overcome without relying on fresh randomness. From a practical point of view, the aforementioned approach makes it possible to transfer many of the desirable properties of first-order threshold implementations, such as their low randomness usage, to the second-order setting. For example, a straightforward application to the block cipher LED results in a masking using less than 700 random bits including the initial sharing. In addition, the cryptanalytic approach introduced in this paper provides additional insight into the design of masked ciphers and allows for a quantifiable trade-off between security and performance.

Second-Order SCA Security with almost no Fresh Randomness

“…Reduction of the number of required fresh masks per cipher round (due to the composition) is of interesting topics as well. We should refer to the relevant study [BDZ20], which addresses some interesting facts with respect to reusing the masks to refresh the shares between consecutive cipher rounds in higher-order td + 1 masked designs. Further, it has been stated in [BKN19], that when each S-box requires n-bit fresh masks, having 16 S-boxes in a second-order implementation of PRINCE, 4n fresh mask bits are adequate to apply instead of 16n bits, i.e., reusing the fresh masks.…”

Resilient uniformity: applying resiliency in masking

“…Figure 1: Representation of a threshold circuit assuming an equal number of input and output shares [1].…”

“…Instead, the Threshold Implementation approach was generalized for second-order security using fresh randomness by the "Consolidating Masking Schemes" (CMS) approach [18]. Only recently a secure extension of the threshold model was proposed for second-order security [1]. Interestingly enough, this extension makes heavy use of the cryptanalytic properties of the shared cipher such as its diffusion layers and nonlinearity of its S-box.…”

“…Further details on this decomposition are given in Appendix A.1. The masking of the S-box is constructed from the masking of G which is inspired from the work by Beyne et al [1] and is detailed in Appendix A.2. This masking consists of seven input shares and seven output shares and is uniform and second-order non-complete.…”

“…We argue that re-using the randomness every 14 rounds is secure as long as the adversary is limited in the number of probing queries. More specifically, we move from the simulation based security model as defined in Section 2.2 to the bounded query model defined by Beyne et al [1] which defines a security model where the adversary is admitted only a limited number of probing queries. In the bounded query model, we make use of linear cryptanalytic security arguments using a trail-wise approach.…”