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<p>Integral cryptanalysis is a pivotal technique in symmetric-key cryptography. This paper enhances the integral key-recovery analysis of the Feistel-based cipher Zodiac by introducing a systematic framework for identifying optimal key recovery attack paths. This framework leverages the conversion relationship between zero-correlation linear and integral distinguishers, seamlessly integrating distinguisher construction with key recovery into a coherent process. During the key recovery phase, we apply the partial-sum technique to reduce computational complexity and adaptively adjust the number of distinguisher rounds to optimize performance. We reduce the computational complexity of the full-round attack on Zodiac-192 from <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2^{190}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>2</mn> <mn>190</mn> </msup> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(2^{87}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>2</mn> <mn>87</mn> </msup> </math></EquationSource> </InlineEquation>. Our analysis also identifies two 14-round integral distinguishers: the longest known for Zodiac. Interestingly, we identify that the optimal full-round key recovery is achieved by pairing the partial-sum technique with the 13-round distinguisher, not the longer 14-round one. This result clearly demonstrates that the longest distinguisher does not guarantee the most efficient key recovery attack. Also we performed a non-standard extension (adding one round) on Zodiac, achieving the first 17-round key recovery attack on Zodiac-192.</p>

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Improved integral cryptanalysis of block cipher Zodiac

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月5日

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  • Yi Guo,
  • Danping Shi,
  • Lei Hu,
  • Xu Guo,
  • Zhiru Chen

摘要

Integral cryptanalysis is a pivotal technique in symmetric-key cryptography. This paper enhances the integral key-recovery analysis of the Feistel-based cipher Zodiac by introducing a systematic framework for identifying optimal key recovery attack paths. This framework leverages the conversion relationship between zero-correlation linear and integral distinguishers, seamlessly integrating distinguisher construction with key recovery into a coherent process. During the key recovery phase, we apply the partial-sum technique to reduce computational complexity and adaptively adjust the number of distinguisher rounds to optimize performance. We reduce the computational complexity of the full-round attack on Zodiac-192 from \(2^{190}\) 2 190 to \(2^{87}\) 2 87 . Our analysis also identifies two 14-round integral distinguishers: the longest known for Zodiac. Interestingly, we identify that the optimal full-round key recovery is achieved by pairing the partial-sum technique with the 13-round distinguisher, not the longer 14-round one. This result clearly demonstrates that the longest distinguisher does not guarantee the most efficient key recovery attack. Also we performed a non-standard extension (adding one round) on Zodiac, achieving the first 17-round key recovery attack on Zodiac-192.