wherein said hash value generation unit is operable to convert a format of each of {HEAD ~ the two N dimensional arrays} indicating {TAIL ~ a hash value} for the message data, without changing a norm of the N dimensional array so that a target sub element indicates a predetermined value, the target sub element being one of N sub elements included in the N dimensional array, and 
indicating
wherein said hash value generation unit is operable to convert a format of each of { HEAD ~ the two N dimensional arrays } indicating { TAIL ~ a hash value } for the message data , without changing a norm of the N dimensional array so that a target sub element indicates a predetermined value , the target sub element being one of N sub elements included in the N dimensional array , and
OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH HEAD HEAD HEAD HEAD HEAD HEAD HEAD HEAD HEAD REL TAIL TAIL TAIL TAIL TAIL TAIL TAIL OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH OTH