Composite based on at least one metallic reinforcing element comprising a metallic surface and on a rubber composition based on at least a. an epoxidized diene elastomer, b. a reinforcing filler, and c. a system for crosslinking the epoxidized diene elastomer comprising at least: - a polyacid compound selected from organopolyphosphorus compounds of general formula and polysulfonic acids of general formula, and - a polyphenol compound comprising at least one aromatic ring comprising 6 carbon atoms and at least two hydroxyl -OH functions on the same aromatic ring, in which - A represents a covalent bond or a hydrocarbon group comprising at least 1 carbon atom, which is optionally substituted and optionally interrupted by one or more heteroatoms, and - the R symbols represent, independently of one another, a hydrocarbon group comprising at least 1 carbon atom or a hydrogen atom; in which - A' represents a covalent bond or a hydrocarbon group comprising at least 1 carbon atom, which is optionally substituted and optionally interrupted by one or more heteroatoms. a. an epoxidized diene elastomer, b. a reinforcing filler, and c. a system for crosslinking the epoxidized diene elastomer comprising at least: - a polyacid compound selected from organopolyphosphorus compounds of general formula and polysulfonic acids of general formula, and - a polyphenol compound comprising at least one aromatic ring comprising 6 carbon atoms and at least two hydroxyl -OH functions on the same aromatic ring, in which - A represents a covalent bond or a hydrocarbon group comprising at least 1 carbon atom, which is optionally substituted and optionally interrupted by one or more heteroatoms, and - the R symbols represent, independently of one another, a hydrocarbon group comprising at least 1 carbon atom or a hydrogen atom; in which - A' represents a covalent bond or a hydrocarbon group comprising at least 1 carbon atom, which is optionally substituted and optionally interrupted by one or more heteroatoms. - a polyacid compound selected from organopolyphosphorus compounds of general formula and polysulfonic acids of general formula, and - a polyphenol compound comprising at least one aromatic ring comprising 6 carbon atoms and at least two hydroxyl -OH functions on the same aromatic ring, in which - A represents a covalent bond or a hydrocarbon group comprising at least 1 carbon atom, which is optionally substituted and optionally interrupted by one or more heteroatoms, and - the R symbols represent, independently of one another, a hydrocarbon group comprising at least 1 carbon atom or a hydrogen atom; in which - A' represents a covalent bond or a hydrocarbon group comprising at least 1 carbon atom, which is optionally substituted and optionally interrupted by one or more heteroatoms. - A represents a covalent bond or a hydrocarbon group comprising at least 1 carbon atom, which is optionally substituted and optionally interrupted by one or more heteroatoms, and - the R symbols represent, independently of one another, a hydrocarbon group comprising at least 1 carbon atom or a hydrogen atom; in which - A' represents a covalent bond or a hydrocarbon group comprising at least 1 carbon atom, which is optionally substituted and optionally interrupted by one or more heteroatoms. - A' represents a covalent bond or a hydrocarbon group comprising at least 1 carbon atom, which is optionally substituted and optionally interrupted by one or more heteroatoms.