Apparatus for ciphering, including a non-volatile memory, which stores a number from which a private cryptographic key, having a complementary public cryptographic key, is derivable, wherein the number is shorter than the private cryptographic key, and a processor, which is configured to receive an instruction indicating that the private cryptographic key is to be applied to data and, responsively to the instruction, to compute the private cryptographic key using the stored number and to perform a cryptographic operation on the data using the private cryptographic key. Related apparatus and methods are also described.