Finding null space of binary matrix in python

In factoring methods based on the quadratic sieve, finding the left null space of a binary matrix (values computed mod 2) is a crucial step. (This is also the null space of the transpose.) Does numpy or scipy have tools to do this quickly?

For reference, here is my current code:

# Row-reduce binary matrix
def binary_rr(m):
    rows, cols = m.shape
    l = 0
    for k in range(min(rows, cols)):
        print(k)
        if l >= cols: break
        # Swap with pivot if m[k,l] is 0
        if m[k,l] == 0:
            found_pivot = False
            while not found_pivot:
                if l >= cols: break
                for i in range(k+1, rows):
                    if m[i,l]:
                        m[[i,k]] = m[[k,i]]  # Swap rows
                        found_pivot = True
                        break

                if not found_pivot: l += 1

        if l >= cols: break  # No more rows

        # For rows below pivot, subtract row
        for i in range(k+1, rows):
            if m[i,l]: m[i] ^= m[k]

        l += 1

    return m

It is pretty much a straightforward implementation of Gaussian elimination, but since it's written in python it is very slow.

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