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Firstly, we put forward a novel secondary construction to obtain 1\u2010resilient functions. Next, we present the relationships between the properties of these constructed 1\u2010resilient functions and that of the initial functions. Based on the construction and a class of bent functions on <jats:italic>n<\/jats:italic> variables, we can obtain a class of (<jats:italic>n<\/jats:italic>\u2009+\u20093)\u2010variable 1\u2010resilient non\u2010separable cryptographic functions with a high algebraic immunity, whose nonlinearity is equal to the bent concatenation bound 2<jats:sup><jats:italic>n<\/jats:italic>\u2009+\u20092<\/jats:sup>\u2009\u2212\u20092<jats:sup>(<jats:italic>n<\/jats:italic>\u2009+\u20092)\/2<\/jats:sup>. Furthermore, we propose a set of 1\u2010resilient non\u2010separable functions on odd number of variables with an optimal algebraic degree, a high algebraic immunity, and a high nonlinearity. 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