The authors propose a new type of hash iterative structure-the ring-iterative structure with feed- back which is subdivided into the single feedback ring it- eration and the multiple feedback ring iteration, namely SFRI and MFRI. Prove that SFRI is at least equivalent to the MD structure in security, and MFRI is at least equiv- alent to SFRI in security (property 1 makes people incline to believe MFRI is more secure than MD). Analyze the resistance of MFRI, which results from the joint event on message modi¯cation, endless loop on message modi¯ca- tion and incompatibility of the su±cient conditions, to the multi-block di®erential collision attack. Argue the ine®ec- tiveness of the D-way second preimage attack on MFRI. Discuss the time and space expenses of MFRI, and point out the advantage of MFRI over the tree-iterative struc- ture and the zipper-iterative structure.