翻訳と辞書 Words near each other ・ Ellipsoolithus ・ Ellipsoptera ・ Ellipsuella ・ Ellipta ・ Elliptera ・ Ellipteroides ・ Elliptic algebra ・ Elliptic boundary value problem ・ Elliptic cohomology ・ Elliptic complex ・ Elliptic coordinate system ・ Elliptic curve ・ Elliptic curve cryptography ・ Elliptic curve Diffie–Hellman ・ Elliptic Curve Digital Signature Algorithm ・ Elliptic curve only hash ・ Elliptic curve point multiplication ・ Elliptic curve primality ・ Elliptic cylindrical coordinates ・ Elliptic divisibility sequence ・ Elliptic filter ・ Elliptic flow ・ Elliptic function ・ Elliptic gamma function ・ Elliptic Gauss sum ・ Elliptic geometry ・ Elliptic hypergeometric series ・ Elliptic integral ・ Elliptic operator ・ Elliptic orbit Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Elliptic curve only hash ： ウィキペディア英語版 Elliptic curve only hash The elliptic curve only hash (ECOH) algorithm was submitted as a candidate for SHA-3 in the NIST hash function competition. However, it was rejected in the beginning of the competition since a second pre-image attack was found. The ECOH is based on the MuHASH hash algorithm, that has not yet been successfully attacked. However, MuHASH is too inefficient for practical use and changes had to be made. The main difference is that where MuHASH applies a random oracle , ECOH applies a padding function. Assuming random oracles, finding a collision in MuHASH implies solving the discrete logarithm problem. MuHASH is thus a provably secure hash, i.e. we know that finding a collision is at least as hard as some hard known mathematical problem. ECOH does not use random oracles and its security is not strictly directly related to the discrete logarithm problem, yet it is still based on mathematical functions. ECOH is related to the Semaev's problem of finding low degree solutions to the summation polynomial equations over binary field, called the Summation Polynomial Problem. An efficient algorithm to solve this problem has not been given so far. Although the problem was not proven to be NP-hard, it is assumed that such an algorithm does not exist. Under certain assumptions, finding a collision in ECOH may be also viewed as an instance of the subset sum problem. Besides solving the Summation Polynomial Problem, there exists another way how to find second pre-images and thus collisions, Wagner's generalized birthday attack. ECOH is a nice example of hash function that is based on mathematical functions (with the provable security approach) rather than on classical ad hoc mixing of bits to obtain the hash. == The algorithm == Given $n$, ECOH divides the message $M$ into $n$ blocks $M\_0,\backslash ldots,M\_$. If the last block is incomplete, it is padded with single 1 and then appropriate number of 0. Let furthermore $P$ be a function that maps a message block and an integer to an elliptic curve point. Then using the mapping $P$, each block is transformed to an elliptic curve point $P\_i$, and these points are added together with two more points. One additional point $X\_1$ contains the padding and depends only on the message length. The second additional point $X\_2$ depends on the message length and the XOR of all message blocks. The result is truncated to get the hash $H$. $\backslash begin$ P_i &:= P^ *(M_i, n)\\ Q & P_i + X_1 + X_2\\ R &{}:= f(Q) \end{align} The two extra points are computed by $P\text{'}$ and $P^$ * . $Q$ adds all the elliptic curve points and the two extra points together. Finally, the result is passed through an output transformation function f to get the hash result $R$. To read more about this algorithm, see ("ECOH: the Elliptic Curve Only Hash" ). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Elliptic curve only hash」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.