# If they exist a relation between decisional Diffie-Hellman assumption and composite decisional residuosity assumption

From the cryptographic hardness assumptions, we have DDH and CDR assumptions. It is known that the composite decisional residuosity assumption is related to a factoring problem, while the DDH is related to a discrete logarithm problem. I need to know if there is a method or a mathematical theorems that can provide ways to map from DDH to CDR assumptions and if the mapping between the two assumptions is possible.

• In terms of hardness factoring => CDR and DLog => DDH but DDH doesn't really imply anything by itself (in fact there are groups where DDH is easy but CDH isn't) and CDR only works over rings with composite moduli (?), so I very much doubt there is a direct hardness relation. – SEJPM Dec 6 '19 at 12:47