In a system 300, a server 310 provides a cryptographic function F to an execution device in an obfuscated form. The function F composes output of a plurality of the mapping tables Ti(0≦i≦n; n≧1) using an Abelian group operator . A processor 312 chooses tables O and C such that C[x]O[x]=0, ∀x±Di and creates tables T′i, 0≦i≦m; n≦m≦n+1, where for 0≦i≦n, each Table T′i represents the respective corresponding table T,j and at least one table T′o1, 0≦01, ≦n, being formed through an Abelian composition of To1 and O, and at least one table T′c10≦c1,≦m, c1#oj, being formed through an Abelian composition that includes C. Means 314 are used for providing the tables T′i, to the executing device. The executing device 320 includes means 324 for receiving the tables and a processor 322 for forming a function F′ that is functionally equivalent to the cryptographic function F by an Abelian composition of the tables T′i.