SPDZ基础使用手册（深度学习视角）

基本类型

深度学习中最常使用的便是秘密定点数sfix，有关定点数的高级运算协议请参阅Paper: Secure Computation With Fixed-Point Numbers.

容器类型

SPDZ的深度学习框架主要基于TensorFlow实现，其中使用的容器是张量Tensor，在库中的定义如下：

def Tensor(cls, shape):
    """
    Type-dependent tensor of any dimension::
        a = sfix.Tensor([10, 10])
    """
    if len(shape) == 1:
        return Array(shape[0], cls)
    else:
        return MultiArray(shape, cls)

可以看出使用Tensor在大多数情况就是在使用MultiArray，类比Python基础类型的多维列表。

这里举一个例子：

a = sint.Tensor([3, 10, 10])    #创建张量，类型为sint，内容是3个10×10的矩阵
a[0].input_from(0)    #第一个矩阵从第0方读取数据
a[1].input_from(1)    #第二个矩阵从第1方读取数据
a[2][:] = a[0][:] * a[1][:]    #第三个矩阵由前两个矩阵元素对应相乘实现；[:] 表示选择这个矩阵的所有元素。

MultiArray的其它用法

assign(other, base=0)

        Assign container to content. Not implemented for floating-point.

                Parameters other – container of matching size and type

assign_all(value)

        Assign the same value to all entries.

                Parameters value – convertible to relevant basic type

assign_part_vector(vector, base=0)

        Assign vector from range of the first dimension, including all entries in further dimensions.                 Parameters

                        • vector – updated entries

                        • base – index in first dimension (regint/cint/int)

assign_vector(vector, base=0)

               Assign vector to content. Not implemented for floating-point.

                        Parameters

                                • vector – vector of matching size convertible to relevant basic type

                                • base – compile-time (int)

direct_mul(other, reduce=True, indices=None, res_type=None)

        Matrix multiplication in the virtual machine. Unlike dot(), this only works for sint and sfix, and it returns a vector instead of a data structure.

                Parameters

                        • self – Matrix / 2-dimensional MultiArray

                        • other – Matrix / 2-dimensional MultiArray

                        • indices – 4-tuple of regint vectors for index selection (default is complete multiplication)

                Returns Matrix as vector of relevant type (row-major)

PS: 不常用，因为泛用性很差，只能针对二维数组；也是库里自带函数的通病，以至于很多tf的很多高级函数在库中都是不存在的。

dot(other, res_params=None, n_threads=None)

        Matrix-matrix and matrix-vector multiplication.

                Parameters

                • self – two-dimensional

                • other – Matrix or Array of matching size and type

                • n_threads – number of threads (default: all in same thread)

        Return type Matrix or Array of appropriate size and type

input_from(player, budget=None, raw=False, **kwargs)

        Fill with inputs from player if supported by type.

                Parameters player – public (regint/cint/int)

randomize(*args, n_threads=None)

        Randomize according to data type. If it is sfix, the following will sample an individual         uniformly random entry of the multi-array M roughly in the range [