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In this article, we establish a relationship between the confusion coefficient and the autocorrelation function for any Boolean function and give a tight upper bound and a tight lower bound on the confusion coefficient for any (balanced) Boolean function. We also deduce some deep relationships between the sum-of-squares of the confusion coefficient and other cryptographic indicators (the sum-of-squares indicator, hamming weight, algebraic immunity and correlation immunity), respectively. Moreover, we obtain some trade-offs among the sum-of-squares of the confusion coefficient, the signal-to-noise ratio and the redefined transparency order for a Boolean function.<\/jats:p>","DOI":"10.1515\/jmc-2021-0012","type":"journal-article","created":{"date-parts":[[2021,8,7]],"date-time":"2021-08-07T02:31:53Z","timestamp":1628303513000},"page":"1-13","source":"Crossref","is-referenced-by-count":4,"title":["On the confusion coefficient of Boolean functions"],"prefix":"10.1515","volume":"16","author":[{"given":"Yu","family":"Zhou","sequence":"first","affiliation":[{"name":"Science and Technology on Communication Security Laboratory , Chengdu 610041 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianyong","family":"Hu","sequence":"additional","affiliation":[{"name":"Science and Technology on Communication Security Laboratory , Chengdu 610041 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xudong","family":"Miao","sequence":"additional","affiliation":[{"name":"Science and Technology on Communication Security Laboratory , Chengdu 610041 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Han","sequence":"additional","affiliation":[{"name":"Science and Technology on Communication Security Laboratory , Chengdu 610041 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fuzhong","family":"Zhang","sequence":"additional","affiliation":[{"name":"Science and Technology on Communication Security Laboratory , Chengdu 610041 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2021,8,5]]},"reference":[{"key":"2025120600292541401_j_jmc-2021-0012_ref_001","doi-asserted-by":"crossref","unstructured":"Prouff E. 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