A key element of any mobile code based distributed system are the security mechanisms available to protect (a) the host against potentially hostile actions of a code fragment under execution and (b) the mobile code against tampering attempts by the executing host. Many techniques for the first problem (a) have been developed. The second problem (b) seems to be much harder: It is the general belief that computation privacy for mobile code cannot be provided without tamper resistant hardware. Furthermore it is doubted that an agent can keep a secret (e.g., a secret key to generate digital signatures). There is an error in reasoning in the arguments supporting these beliefs which we are going to point out. In this paper we describe software-only approaches for providing computation privacy for mobile code in the important case that the mobile code fragment computes an algebraic circuit (a polynomial). We further describe an approach how a mobile agent can digitally sign his..