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Good observation. It looks like the text was copied from page 2 of Boneh's paper, which clearly is wrong, since the multiplicative group modulo pq doesn't even contain a cyclic subgroup of order (p-1)(q-1). The group of quadratic residues has order (p-1)(q-1)/4 since any element has to be a quadratic
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I'm pretty sure there is an error in the section on groups in which DDH is supposed to hold. It mentions a cyclic group of order (p-1)(q-1), where p,q are safe primes which is (I think) supposed to refer to (Z/nZ)* where n=pq. However, if n=pq then (Z/nZ)* will be isomorphic to (Z/pZ)* x (Z/qZ)*
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residue modulo p and modulo q. Furthermore, one would also have to assume that the factorization of the modulus is unknown and hence also the group order. Thus I think it makes sense to remove the claim unless we can find reference that more clearly defines the assumption than Boneh's paper.
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and we'll of course have a subgroup isomorphic to V_4. Would the author of this content please clarify? Likely what was intended was the index 4 subgroup of quadratic residues mod p and mod q.
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from 2007 by User:Blokhead and there are no references, so it is possible that there are other mistakes. I am not qualified to check the accuracy of this section. --
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I have to withdraw a claim I made above. I'm unsure if the factorization of the modulus can be known.
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Knowledge. If you would like to participate, please visit the project page, where you can join
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Decisional Diffie-Hellman (DDH) assumption: Given primes
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382:{\displaystyle (p-1)(q-1)/2}
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