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In cryptography, cryptographic hash functions can be divided into two main categories. In the first category are those functions whose designs are based on a mathematical problem and thus their security follows from rigorous mathematical proofs, complexity theory and formal reduction. These functions are called Provably Secure Cryptographic Hash Functions. However this does not mean that such a function could not be broken. To construct them is very difficult and only a few examples were introduced. The practical use is limited. In the second category are functions that are not based on mathematical problems but on an ad hoc basis, where the bits of the message are mixed to produce the hash. They are then believed to be hard to break, but no such formal proof is given. Almost all widely spread hash functions fall in this category. Some of these functions are already broken and are no longer in use. ==Types of security of hash functions== Generally, the ''basic'' security of cryptographic hash functions can be seen from three different angles: pre-image resistance, second pre-image resistance and collision resistance. * Pre-image resistance: given a hash h it should be ''hard'' to find any message m such that h = hash(m). This concept is related to that of one way function. Functions that lack this property are vulnerable to pre-image attacks. * Second pre-image resistance: given an input m1, it should be ''hard'' to find another input, m2 (not equal to m1) such that hash(m1) = hash(m2). This property is sometimes referred to as weak collision resistance. Functions that lack this property are vulnerable to second pre-image attacks. * Collision resistance: it should be ''hard'' to find two different messages m1 and m2 such that hash(m1) = hash(m2). Such a pair is called a (cryptographic) hash collision. This property is sometimes referred to as strong collision resistance. It requires a hash value at least twice as long as what is required for pre-image resistance, otherwise collisions may be found by a birthday attack. 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「Security of cryptographic hash functions」の詳細全文を読む スポンサード リンク
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