CRAFT: Lightweight Tweakable Block Cipher with Efficient Protection Against DFA Attacks

in IACR Transactions on Symmetric Cryptology (2019), 2019(1), 5-45

Traditionally, countermeasures against physical attacks are integrated into the implementation of cryptographic primitives after the algorithms have been designed for achieving a certain level of ... [more ▼]

Traditionally, countermeasures against physical attacks are integrated into the implementation of cryptographic primitives after the algorithms have been designed for achieving a certain level of cryptanalytic security. This picture has been changed by the introduction of PICARO, ZORRO, and FIDES, where efficient protection against Side-Channel Analysis (SCA) attacks has been considered in their design. In this work we present the tweakable block cipher CRAFT: the efficient protection of its implementations against Differential Fault Analysis (DFA) attacks has been one of the main design criteria, while we provide strong bounds for its security in the related-tweak model. Considering the area footprint of round-based hardware implementations, CRAFT outperforms the other lightweight ciphers with the same state and key size. This holds not only for unprotected implementations but also when fault-detection facilities, side-channel protection, and their combination are integrated into the implementation. In addition to supporting a 64-bit tweak, CRAFT has the additional property that the circuit realizing the encryption can support the decryption functionality as well with very little area overhead. [less ▲]

Alzette: A 64-bit ARX-box

E-print/Working paper (2019)

S-boxes are the only source of non-linearity in many symmetric primitives. While they are often defined as being functions operating on a small space, some recent designs propose the use of much larger ... [more ▼]

S-boxes are the only source of non-linearity in many symmetric primitives. While they are often defined as being functions operating on a small space, some recent designs propose the use of much larger ones (e.g., 32 bits). In this context, an S-box is then defined as a subfunction whose cryptographic properties can be estimated precisely. In this paper, we present a 64-bit ARX-based S-box called Alzette, which can be evaluated in constant time using only 12 instructions on modern CPUs. Its parallel application can also leverage vector (SIMD) instructions. One iteration of Alzette has differential and linear properties comparable to those of the AES S-box, while two iterations are at least as secure as the AES super S-box. Since the state size is much larger than the typical 4 or 8 bits, the study of the relevant cryptographic properties of Alzette is not trivial. [less ▲]

On Degree-d Zero-Sum Sets of Full Rank

E-print/Working paper (2018)

A set S⊆Fn2 is called degree-d zero-sum if the sum ∑s∈Sf(s) vanishes for all n-bit Boolean functions of algebraic degree at most d. Those sets correspond to the supports of the n-bit Boolean functions of ... [more ▼]

A set S⊆Fn2 is called degree-d zero-sum if the sum ∑s∈Sf(s) vanishes for all n-bit Boolean functions of algebraic degree at most d. Those sets correspond to the supports of the n-bit Boolean functions of degree at most n−d−1. We prove some results on the existence of degree-d zero-sum sets of full rank, i.e., those that contain n linearly independent elements, and show relations to degree-1 annihilator spaces of Boolean functions and semi-orthogonal matrices. We are particularly interested in the smallest of such sets and prove bounds on the minimum number of elements in a degree-d zero-sum set of rank n. The motivation for studying those objects comes from the fact that degree-d zero-sum sets of full rank can be used to build linear mappings that preserve special kinds of nonlinear invariants, similar to those obtained from orthogonal matrices and exploited by Todo, Leander and Sasaki for breaking the block ciphers Midori, Scream and iScream. [less ▲]