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See detailOn degree-d zero-sum sets of full rank
Beierle, Christof UL; Biryukov, Alex UL; Udovenko, Aleksei UL

in Cryptography and Communications (2019)

A set π‘†βŠ†π”½π‘›2 is called degree-d zero-sum if the sum βˆ‘π‘ βˆˆπ‘†π‘“(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 ... [more β–Ό]

A set π‘†βŠ†π”½π‘›2 is called degree-d zero-sum if the sum βˆ‘π‘ βˆˆπ‘†π‘“(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 βˆ’ d βˆ’β€‰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 β–²]

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See detailCRAFT: Lightweight Tweakable Block Cipher with Efficient Protection Against DFA Attacks
Beierle, Christof UL; Leander, Gregor; Moradi, Amir et al

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 β–Ό]

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 β–²]

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See detailLightweight AEAD and Hashing using the Sparkle Permutation Family
Beierle, Christof UL; Biryukov, Alex UL; Cardoso Dos Santos, Luan UL et al

in IACR Transactions on Symmetric Cryptology (2019)

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See detailAlzette: A 64-bit ARX-box
Beierle, Christof UL; Biryukov, Alex UL; Cardoso Dos Santos, Luan UL et al

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 β–Ό]

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 β–²]

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See detailNonlinear Approximations in Cryptanalysis Revisited
Beierle, Christof UL; Canteaut, Anne; Leander, Gregor

in IACR Transactions on Symmetric Cryptology (2018), 2018(4), 80-101

This work studies deterministic and non-deterministic nonlinear approximations for cryptanalysis of block ciphers and cryptographic permutations and embeds it into the well-understood framework of linear ... [more β–Ό]

This work studies deterministic and non-deterministic nonlinear approximations for cryptanalysis of block ciphers and cryptographic permutations and embeds it into the well-understood framework of linear cryptanalysis. For a deterministic (i.e., with correlation Β±1) nonlinear approximation we show that in many cases, such a nonlinear approximation implies the existence of a highly-biased linear approximation. For non-deterministic nonlinear approximations, by transforming the cipher under consideration by conjugating each keyed instance with a fixed permutation, we are able to transfer many methods from linear cryptanalysis to the nonlinear case. Using this framework we in particular show that there exist ciphers for which some transformed versions are significantly weaker with regard to linear cryptanalysis than their original counterparts. [less β–²]

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See detailOn Degree-d Zero-Sum Sets of Full Rank
Beierle, Christof UL; Biryukov, Alex UL; Udovenko, Aleksei UL

E-print/Working paper (2018)

A set SβŠ†Fn2 is called degree-d zero-sum if the sum βˆ‘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 β–Ό]

A set SβŠ†Fn2 is called degree-d zero-sum if the sum βˆ‘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 nβˆ’dβˆ’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 β–²]

Detailed reference viewed: 52 (1 UL)