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Symmetric cryptosystems with public key based on the symmetric group
Symmetric cryptosystems with public key based on the symmetric group
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机译：基于对称组的具有公开密钥的对称密码系统
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摘要
Symmetric cryptosystems disposable key in the sense that for every message encryption public information is attached to the cryptogram that lets you change the secret key encryption. Such information is therefore a public key. The invention being characterized in that the secret key, said key mater, is a permutation p belonging to the group of algebraic structure (S e,o), where e S is the symmetric group of an ordered set E and o the composition function operation. The permutation p specially composed many disjoint to generate a cyclic subgroup of G Se big order defined by {p1,p2, .., pj, .., P} where pj is the bijection ppoopo ..... with the composition function of o operation iterated j-1 times.G is then modulo a cyclic, the integer a is the lcm integers representing the length of p disjoint. The set of disposable keys is the cyclic subgroup G; the public key being composed of any integer j, or according to a variant of the method, an element w of the Cartesian product of p disjoint if they are selected so that their lengths do not have common divisor . Each integer jw or each element being associated with a permutation and one belonging to G, which is calculated by {a} algorithm p → pjp or {a} → λ.; According to another embodiment, authentication processes in which j or w is a public key and each permutation p 'G belonging to a private key, according to another embodiment (j, p') or (w,w ') are pairs of credentials documents.; According to another use of the algebraic structure (S e,o) and its cyclic subgroups the invention is a symmetric cryptosystem associated with a Latin square characterized in that the secret key is no longer the Latin square form square matrix but a single permutation p disjoint belonging to S e, said permutation for encrypting by composition of the bijection p.展开▼
机译：对称密码系统一次性密钥的意义在于，对于每个消息加密，公共信息都附加在密码上，从而使您可以更改秘密密钥加密。因此，此类信息是公共密钥。本发明的特征在于，秘密密钥，所述密钥主，是属于代数结构（S e，< / Sub> o），，其中 e S 是有序集E的对称组，并且是合成函数操作。排列p特别地由许多不相交组成，以生成由 {p 1， p 2定义的G Se大阶循环子组， ..， p j， ..， P} 其中 p j 是双射 p p o o p o .....具有 o 操作的合成函数，迭代j-1次。 G 然后是模 a 循环模，整数 a 是lcm整数，表示 p 不相交的长度。一次性密钥集是循环子组 G; ，公共密钥由任何整数 j，组成，或者根据方法的变体，元素 <如果选择 p 的笛卡尔积的I> w 不相交，以使它们的长度不具有共同的因数。每个整数 j w 或每个元素与一个排列相关联，并且属于一个属于 G 的元素，其计算公式为 {a} 算法 p → p j p 或 {a } →λ。根据另一个实施例，其中 j 或 w 是公共密钥并且每个排列 p 根据另一实施例，属于私钥的'G （j， p'） 或（w， w '）是一对凭证文件。根据代数结构（S e， o）及其循环子组的另一用途，本发明是与拉丁方相关的对称密码系统。其特征在于秘密密钥不再是拉丁方形式的方阵，而是属于 S e，的单个置换 p 不相交表示通过双射 p组成的加密置换。
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