I thought this up today. Has anyone ever seen anything like this? It's reminiscent of eliptic curves, but it's not the same as far as I can tell. Take a_n, b_n as elements of a prime-order multiplicative subgroup of a field. Let g be the generator of the subgroup, and lg be discrete log base g. For example, nonzero elements of GF(2^3), g=x. Then we can form a kind of "super-polynomial" A(y) = (a_n)^(y^n) (a_(n-1))^(y^(n-1)) ... (a_0) which we can rewrite as A(y) = g^( (y^n) lg a_n + (y^(n-1)) lg a_(n-1) + ... + lg a_0 ) Since the logs are all mod 7, the exponent is a polynomial in GF(7) and can be given an irreducible modulus with degree d yeilding a representation of GF(7^d). Multiplication of elements in the field is done by exponentiation: A(y) (X) B(y) = A(y)^(lg B(y)) = B(y)^(lg A(y)) Since each of the a_n are polynomials in x over GF(2^3), A(y) is really A(x,y), so it's more fun than just GF(7^d). Since we can stack two of these, we can stack N of them; pick some prime-order subgroup of 7^d and let the log of those elements be the coefficients of a polynomial in z. What happens when you add these things? -- Mike Stay staym@datawest.net staym@clear.net.nz