A Second Pre-image Attack Against Elliptic Curve Only Hash (ECOH)

We present a second pre-image attack on ECOH. Our attack requires 2143 time for ECOH-224 and ECOH-256, 2206 time for ECOH-384, and 2287 time for ECOH-512. The attack sets the checksum block to a fixed value and uses a collision search on the elliptic curve points. 1 An outline of ECOH We first give a description of the essential elements of ECOH. We restrict ourselves to messages that are an integral number of blocks, which is what we use in our attack. For full details, please refer to the ECOH specifications [1]. ECOH divides the message into blocks, maps each block to an elliptic curve point, and adds these points together with two more points. One additional point contains the padding and depends only on the message length. The second additional point depends on the message length and the exclusive-or of all message blocks.