The authors are concerned with the processing of encrypted data. For example, could we take an encrypted amount in hundreds of dollars and convert it to yen (that is, multiply it by a known constant, such as 12,689), thus obtaining an encrypted value of the converted amount, without ever knowing the plaintext amount? This particular conversion is multiplicative, so it could be done under the RSA algorithm [1]. More generally, we might want to transform the encrypted vectors X and Y linearly to obtain rX+sY (where r and s are scalars) in encrypted form without decrypting. The method is to use the time-reversal transformations for the encryption of X={x_j(1)}, so x_i(t+1)+x_i(t−1)=f[{x_j(t)}]modk. The indices in f are shifts of the index i, and the transformation is executed a certain number of times starting with x_i(0)=0 and x_i(1)=plaintext. This algorithm is essentially the DES method [2]. If the vector is of dimension n, then the subscripts are taken modulo n. The trick is to take f to be linear, such as fx_i−3+7x_i+2 +63x_i+5. This limits the choice of f severely, creating a security problem. One modification is to permit more arbitrary backgrounds x_i(0). The authors note that for some choices of f, the encryption resembles the finite difference solution of the wave equation, ∂ ² W &slash; ∂ t ² = c ² ∂ ² W &slash; ∂ x ² , so the problem is analogous to the superposition of waves.