压缩模矩阵乘法
Compressed Modular Matrix Multiplication
摘要：
我们建议将几个整数模一个小素数存储到一个机器字中。模加法是通过对包含数倍模的字进行加法和可能的减法来执行的。模乘不能直接访问，但模点积可以通过整数乘以逆整数来执行。模乘一个字包含一个单一的剩余也是可能的。因此，可以在这种压缩存储器上执行矩阵乘法。我们在这里给出了这样的压缩是可能的素数和矩阵的大小的界限。我们还明确了所需的压缩算术例程的细节。
英文摘要：
We propose to store several integers modulo a small prime into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulo. Modular Multiplication is not directly accessible but modular dot product can be performed by an integer multiplication by the reverse integer. Modular multiplication by a word containing a single residue is a also possible. Therefore matrix multiplication can be performed on such a compressed storage. We here give bounds on the sizes of primes and matrices for which such a compression is possible. We also explicit the details of the required compressed arithmetic routines.
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