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：我们讨论了虚拟二次orde o_三角形开放的类CL（三角形打开）的离散对数问题，这是由Buchmann和Williams的公钥密码系统[8]。虽然在此期间，在CL（三角形打开）[16]中找到了用于计算离散对数的子统计算法[16]，但该算法仅有运行时间L三角形打开[1 2，C]并且远低于数字效率远远较低使用L_P [1 3，C]的字段筛子来计算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性。它是一个开放的问题是否存在LTRIANGLE OPEN [1 3，C]算法来计算任意CL（三角形）中的离散对数。
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