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Most discussions of Shor's algorithm are for integers but how applicable is it for polynomials? Quite applicable; Shor's algorithm treats the group operation as a blackbox, hence it treats an even characteristic curve just like it does a prime curve. The only practical difference is the cost differential (in terms of qubits, circuit complexity and depth) ...


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This is one of the most poorly written "mainstream" crypto papers I've read. Sorry, McGrew and Viega. Field representation and bit order GCM works in the binary field $GF(2^{128})$. Elements of this field can be represented as polynomials with binary coefficients (i.e. 0 or 1). Using the notation of the paper, here are some examples of field elements: $1$...


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