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Searching for Balanced S-Boxes with High Nonlinearity, Low Differential Uniformity, and Improved DPA-Resistance

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Information Security (ISC 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12472))

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Abstract

Substitution boxes (S-boxes) are one of the most crucial primitives in the field of block ciphers. Recently, differential power analysis (DPA), a very powerful technique which targets implementations of block ciphers, causes the modern block ciphers to be much more vulnerable than ever before. Up to now, the revised transparency order is one of the best metrics to assess the resistance of S-boxes against DPA attacks. In this paper, we present an efficient algorithm to search for cryptographically significant S-boxes with improved DPA-Resistance. Applying our developed algorithm, we generate an \(8\times 8\) balanced S-box with algebraic degree 7, nonlinearity 112, differential uniformity 4, absolute indicator 32, revised transparency order 6.8820 (whereas the Rijndael S-box has revised transparency order 6.9161) and thereby improved resistance towards DPA attacks. Moreover, many other balanced S-boxes with a much better trade-off of cryptographic characteristics than previous works (e.g. S-boxes given by B. Mazumdar and D. Mukhopadhyay in IEEE Trans. Computers 2017) are also captured. The comparison between ours and previous results manifests that our S-boxes are more secure and robust.

This work was partly supported by National Natural Science Foundation of Jiangsu Province (Application No. SBK2020021060) and National Natural Science Foundation of China (No. 61572189).

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Author information

Authors and Affiliations

  1. School of Computer Science and Technology, Nanjing Normal University, Nanjing, China

    Youle Xu & Qichun Wang

Authors
  1. Youle Xu
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  2. Qichun Wang
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Corresponding author

Correspondence to Qichun Wang .

Editor information

Editors and Affiliations

  1. Institute of Cybersecurity and Cryptology, University of Wollongong, Wollongong, NSW, Australia

    Willy Susilo

  2. Singapore Management University, Singapore, Singapore

    Robert H. Deng

  3. Institute of Cybersecurity and Cryptology, University of Wollongong, Wollongong, NSW, Australia

    Fuchun Guo

  4. Institute of Cybersecurity and Cryptology, University of Wollongong, Wollongong, NSW, Australia

    Yannan Li

  5. Informatics, Petra Christian University, Surabaya, Indonesia

    Rolly Intan

Appendices

Appendices

Proposed S-box #2: \(\mathbf {nlf=110,\tau _F=6.8754}\)

[69, 82, 172, 84, 3, 4, 188, 93, 88, 52, 252, 246, 251, 135, 213, 152, 27, 169, 165, 102, 67, 214, 244, 137, 231, 57, 161, 109, 139, 147, 32, 209, 125, 69, 205, 58, 106, 30, 143, 41, 224, 167, 85, 189, 158, 193, 108, 220, 184, 215, 182, 111, 16, 64, 140, 185, 6, 218, 35, 83, 39, 14, 241, 38, 116, 157, 240, 154, 174, 136, 104, 43, 40, 166, 179, 197, 124, 103, 78, 155, 28, 181, 0, 21, 8, 113, 79, 92, 48, 47, 9, 44, 56, 10, 226, 151, 129, 159, 225, 119, 76, 62, 230, 175, 126, 253, 138, 236, 162, 160, 53, 107, 150, 149, 242, 101, 249, 191, 24, 5, 131, 73, 75, 60, 80, 207, 55, 11, 21, 248, 238, 33, 228, 117, 74, 86, 105, 45, 216, 148, 66, 110, 36, 20, 250, 23, 180, 121, 130, 194, 115, 99, 192, 171, 59, 232, 243, 208, 254, 127, 217, 210, 146, 202, 134, 50, 176, 90, 91, 63, 91, 112, 71, 255, 97, 222, 223, 145, 94, 54, 239, 13, 128, 95, 2, 144, 49, 19, 118, 96, 217, 64, 177, 234, 132, 122, 168, 25, 195, 227, 153, 77, 18, 22, 12, 183, 221, 233, 170, 42, 247, 200, 178, 190, 187, 114, 206, 212, 164, 15, 17, 229, 156, 1, 237, 201, 51, 100, 142, 245, 81, 203, 141, 34, 37, 173, 163, 46, 72, 199, 219, 31, 87, 204, 61, 235, 120, 186, 198, 7, 196, 70, 123, 26, 133, 98]

Proposed S-box #3: \(\mathbf {nlf=108,\tau _F=6.8711}\)

[ 69, 82, 172, 84, 3, 4, 188, 93, 88, 52, 252, 246, 251, 135, 213, 152, 27, 169, 165, 102, 67, 214, 244, 137, 231, 49, 161, 109, 139, 147, 32, 209, 125, 73, 205, 58, 106, 30, 143, 41, 224, 163, 85, 189, 158, 193, 108, 220, 184, 215, 182, 111, 16, 64, 140, 185, 6, 218, 35, 87, 39, 14, 241, 38, 116, 157, 240, 154, 174, 136, 104, 43, 40, 166, 179, 197, 124, 103, 78, 155, 28, 181, 0, 21, 8, 113, 79, 92, 48, 47, 9, 44, 56, 10, 226, 151, 129, 159, 225, 119, 76, 62, 230, 175, 126, 253, 138, 236, 162, 160, 53, 107, 150, 149, 242, 101, 249, 191, 24, 5, 131, 73, 75, 60, 80, 207, 55, 11, 29, 248, 238, 33, 228, 117, 74, 86, 105, 45, 216, 148, 66, 110, 36, 20, 250, 23, 180, 121, 130, 194, 119, 99, 192, 171, 59, 232, 243, 208, 254, 127, 217, 210, 146, 202, 134, 50, 176, 90, 91, 63, 211, 112, 67, 255, 97, 222, 223, 145, 94, 54, 239, 13, 128, 95, 2, 144, 49, 19, 118, 96, 89, 64, 177, 234, 132, 122, 168, 25, 195, 227, 153, 77, 18, 22, 12, 183, 221, 233, 170, 42, 247, 200, 178, 190, 187, 114, 206, 212, 164, 15, 17, 229, 156, 1, 237, 201, 51, 100, 142, 245, 81, 203, 141, 34, 37, 173, 167, 46, 72, 199, 219, 31, 87, 204, 61, 235, 120, 186, 198, 7, 196, 70, 123, 26, 133, 98]

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Xu, Y., Wang, Q. (2020). Searching for Balanced S-Boxes with High Nonlinearity, Low Differential Uniformity, and Improved DPA-Resistance. In: Susilo, W., Deng, R.H., Guo, F., Li, Y., Intan, R. (eds) Information Security. ISC 2020. Lecture Notes in Computer Science(), vol 12472. Springer, Cham. https://doi.org/10.1007/978-3-030-62974-8_6

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  • DOI: https://doi.org/10.1007/978-3-030-62974-8_6

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