The　authors　propose　a　new　type　of　hash　iterative　structure-the　ring-iterative　structure　with　feedback　which　is　subdivided　into　the　single　feedback　ring　iteration　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　equivalent　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　modification,　endless　loop　on　message　modification　and　incompatibility　of　the　sufficient　conditions,　to　the　multi-block　differential　collision　attack.　Argue　the　ineffectiveness　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　structure　and　the　zipper-iterative　structure.