We present new algorithms for computing the low $n$ bits or the high $n$ bits of the product of two $n$-bit integers. We show that these problems may be solved in asymptotically 75% of the time required to compute the full $2n$-bit product, assuming that the underlying integer multiplication algorithm relies on computing cyclic convolutions of real sequences.

翻译：我们提出了计算两个$n$位整数乘积的低$n$位或高$n$位的新算法。我们证明，假设底层整数乘法算法依赖于计算实数序列的循环卷积，那么这些问题可以在计算完整$2n$位乘积所需时间的渐近75%内解决。