The present invention aims at providing a novel enciphering and deciphering apparatus and an enciphering and deciphering method related thereto, which are respectively capable of contracting the time required for enciphering and deciphering processes and decreasing the number of logic gates provided in the apparatus. Essentially based on an equation X.sub.k.sup.i=1+.SIGMA.((J=1, i).sub.iC.sub.jX.sub.k-1.sup.j) and also based on an initial value consisting of a group of power raising values X.sub.k0.sup.j corresponding to j=1 through m in relation to k-1=k0, an arithmetic operating unit 21 seeks a second expression Y.sub.k1 by serially computing a group of power raising values X.sub.k.sup.i corresponding to i=1 through m in relation to one unit of k shown in the above equation in a range from k=k0+1 up to k=k1 by applying binomial coefficients stored in a coefficient memory unit 17. Accordingly, once those binomial coefficients corresponding to predetermined integers n and m are stored in memory, thenceforth, it is possible to contract the time required for executing an enciphering or deciphering process related to identical integers n and m.