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18 pages, 951 KiB

Open AccessArticle

A Ciphertext Reduction Scheme for Garbling an S-Box in an AES Circuit with Minimal Online Time

by Xu Yan, Bin Lian, Yunhao Yang, Xiaotie Wang, Jialin Cui, Xianghong Zhao, Fuqun Wang and Kefei Chen

Symmetry 2024, 16(6), 664; https://doi.org/10.3390/sym16060664 - 28 May 2024

Viewed by 800

Abstract

The secure computation of symmetric encryption schemes using Yao’s garbled circuits, such as AES, allows two parties, where one holds a plaintext block m and the other holds a key k, to compute

E n c (k, m)

without [...] Read more.

The secure computation of symmetric encryption schemes using Yao’s garbled circuits, such as AES, allows two parties, where one holds a plaintext block m and the other holds a key k, to compute

E n c (k, m)

without leaking m and k to one another. Due to its wide application prospects, secure AES computation has received much attention. However, the evaluation of AES circuits using Yao’s garbled circuits incurs substantial communication overhead. To further improve its efficiency, this paper, upon observing the special structures of AES circuits and the symmetries of an S-box, proposes a novel ciphertext reduction scheme for garbling an S-box in the last SubBytes step. Unlike the idea of traditional Yao’s garbled circuits, where the circuit generator uses the input wire labels to encrypt the corresponding output wire labels, our garbling scheme uses the input wire labels of an S-box to encrypt the corresponding “flip bit strings”. This approach leads to a significant performance improvement in our garbling scheme, which necessitates only

2^{8}

ciphertexts to garble an S-box and a single invocation of a cryptographic primitive for decryption compared to the best result in previous work that requires

8 \times 2^{8}

ciphertexts to garble an S-box and multiple invocations of a cryptographic primitive for decryption. Crucially, the proposed scheme provides a new idea to improve the performance of Yao’s garbled circuits. We analyze the security of the proposed scheme in the semi-honest model and experimentally verify its efficiency. Full article

(This article belongs to the Special Issue New Advances in Symmetric Cryptography)

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19 pages, 805 KiB

Open AccessArticle

Algebraic Attacks against Grendel: An Arithmetization-Oriented Primitive with the Legendre Symbol

by Jianqiang Ni, Jianhui Zhang, Gaoli Wang, Rui Li and Yanzhao Shen

Symmetry 2023, 15(8), 1563; https://doi.org/10.3390/sym15081563 - 10 Aug 2023

Viewed by 1296

Abstract

The rise of modern cryptographic protocols such as Zero-Knowledge proofs and secure Multi-party Computation has led to an increased demand for a new class of symmetric primitives. Unlike traditional platforms such as servers, microcontrollers, and desktop computers, these primitives are designed to be implemented in arithmetical circuits. In terms of security evaluation, arithmetization-oriented primitives are more complex compared to traditional symmetric cryptographic primitives. The arithmetization-oriented permutation Grendel employs the Legendre Symbol to increase the growth of algebraic degrees in its nonlinear layer. To analyze the security of Grendel thoroughly, it is crucial to investigate its resilience against algebraic attacks. This paper presents a preimage attack on the sponge hash function instantiated with the complete rounds of the Grendel permutation, employing algebraic methods. A technique is introduced that enables the elimination of two complete rounds of substitution permutation networks (SPN) in the sponge hash function without significant additional cost. This method can be combined with univariate root-finding techniques and Gröbner basis attacks to break the number of rounds claimed by the designers. By employing this strategy, our attack achieves a gain of two additional rounds compared to the previous state-of-the-art attack. With no compromise to its security margin, this approach deepens our understanding of the design and analysis of such cryptographic primitives. Full article

(This article belongs to the Special Issue New Advances in Symmetric Cryptography)

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13 pages, 563 KiB

Open AccessArticle

Meet-in-the-Middle Differential Fault Analysis on ITUbee Block Cipher

by Yongze Kang, Qingyuan Yu, Lingyue Qin and Guoyan Zhang

Symmetry 2023, 15(6), 1196; https://doi.org/10.3390/sym15061196 - 2 Jun 2023

Cited by 2 | Viewed by 1458

Abstract

Differential fault analysis (DFA) was introduced by Biham and Shamir. It is a powerful analysis technique to retrieve the secret key by injecting fault into an internal state and utilizing the differences between the correct ciphertexts and the faulty ciphertexts. Based on the idea of meet-in-the-middle, some differential characters can help to recover the key of some symmetric ciphers. At CHES 2011, this technique was utilized to give analyses on AES. In this article, we propose several DFA schemes on ITUbee, a software-oriented block symmetric cipher for resource-constrained devices based on the meet-in-the-middle idea. Our attacks are efficient enough and more powerful than previous works. Furthermore, the attacks in this article break the protection countermeasure, meaning we have to review the protection method on devices for ITUbee. Full article

(This article belongs to the Special Issue New Advances in Symmetric Cryptography)

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