Efficient algorithms for computing the Jacobi symbol
Journal of Symbolic Computation
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We examine the implementation of the distributed proof system designed by Minami and Kotz [17]. We find that, although a high-level analysis shows that it preserves confidentiality, the implementation of the cryptographic primitives contains a covert channel that can leak information. Moreover, this channel is present with any traditional choice of public key encryption functions. To remedy this problem, we use the Goldwasser-Micali cryptosystem to implement single-bit re-encryption and show how to make it free of covert channels. We then extend the primitive to support commutative encryption as well. Using this primitive, we design a variant of the Minami-Kotz algorithm that not only is free of covert channels, but also has additional proving power over the original design.