Abstract: A computation for batch processing public key encryption method using a processor. The method batch processes an e1.sup.th root of a first message-data signal, M1, as M1.sup.1/e1, and an e2.sup.th root of a second message-data signal, M2,. where e1 and e2 are relatively prime, using the steps of computing an exponent product, e, by multiplying e1 times e2; computing a message product, M, wherein M=M1 .sup.(e/e1) M2.sup.(e/e2) ; computing a batch root, R, wherein R=M.sup.1/e ; computing the euclidean inverse, t, of e2 modulo e1; and computing R.sup.e2*t /(M1.sup.(e2*t-1)/e1 M2.sup.t), thereby generating M1 .sup.(1/e1). For a plurality of message-data signals, the method batch processes a plurality of message-data-signal roots as the e1, e2, . . ., ek, roots for a plurality of message-data signals, M1, M2, . . . Mk, respectively, where the ei and ej are pairwise relatively prime for i.noteq.j.