We discuss the discrete logarithm problem over the class group Cl( triangle open ) of an imaginary quadratic orde O_ triangle open , which was proposed as a public-key cryptosystem by Buchmann and Williams [8]. While in the meantime there has been found a subexponential algorithm for the computation of discrete logarithms in Cl( triangle open ) [16], this algorithm only has running time L triangle open [1 2, c] and is far less efficient than the number field sieve with L_p [1 3, c] to compute logarithms in F_p. Thus one can choose smaller parameters to obtain the same level of security. It is an open question whether there is an Ltriangle open [1 3, c] algorithm to compute discrete logarithms in arbitrary Cl(triangle open).
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机译：我们讨论了一个虚二次方程O_三角形开的类群Cl（三角形开）上的离散对数问题，这是由Buchmann和Williams提出作为公钥密码系统的[8]。虽然在此期间发现了一种用于计算Cl（三角形开放）中离散对数的次指数算法[16]，但该算法仅具有运行时间L三角形开放[1,2，c]，并且效率远低于数字用L_p [1 3，c]进行现场筛分以计算F_p中的对数。因此，可以选择较小的参数以获得相同的安全级别。是否存在Ltriangle open [1 3，c]算法来计算任意Cl（triangle open）中的离散对数是一个悬而未决的问题。
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