Even, Goldreich and Micali showed at Crypto''89 that the existence of signature schemes secure against known message attacks implies the existence of schemes secure against adaptively chosen message attacks. Unfortunately, this transformation leads to a rather impractical scheme. We exhibit a similar security amplification, which takes the given scheme to a new signature scheme that is not even existentially forgeable under adaptively chosen message attacks. Additionally, however, our transformation will be practical: The complexity of the resulting scheme is twice that of the original scheme. The principles of both transformations carry over to block encryption systems. It is shown how they can be used to convert a block encryption system secure against known plaintext attacks to a system secure against chosen plaintext attacks. For both schemes it is shown that if the transformed scheme can be broken given a number, $T$, of encryptions of adaptively chosen plaintexts, then the original scheme can be broken given encryptions of $T$ uniformly chosen plaintexts. In this case, however, the application of the technique of Even, Goldreich and Micali leads to the more efficient scheme. The transformed scheme has the same key length as the original, and ciphertexts are doubled in length. As an example, when applied to DES the transformed scheme is secure against differential cryptanalysis, which relies on the ability to get encryptions of plaintext pairs with proper differences.