def testinvertible1(p=2,n=4,seed=1,maxc=2):
	"""
	cryptography based on non-invertible matrices
	"""
	def getma():
		M=Ms.random_element()
		while M.det()==0:
			M=Ms.random_element()
		return M

	def getmaz():
		M=Ms.random_element()
		while M.det()!=0:
			M=Ms.random_element()
		return M

	if seed:
		set_random_seed(seed)
	K=GF(p)
	Ms=MatrixSpace(K,n,n)
	limr=p**3
	M_0=getmaz()
	N_A,N_B=randint(1,limr),randint(1,limr) #XXX

	M_A=M_0**N_A
	M_B=M_0**N_B
	
	X_A=getma()
	X_B=getma()

	P_A=M_A*X_A
	P_B=M_B*X_B

	S_B=M_B*P_A
	S_A=M_A*P_B


	print(S_B*X_A**(-1)==S_A*X_B**(-1),M_A*M_B==M_B*M_A,M_A*M_B==S_B*X_A**(-1)) 
	soa=[]
	sob=[]
	for Y_M_A in Ms:
		if Y_M_A*P_B != S_A:  continue
		try:
			Y_X_A=Y_M_A.solve_right(P_A)
		except:  continue
		soa += [(Y_M_A,Y_X_A)]
		if len(soa)>=maxc:
			break

	for Y_M_B in Ms:
		if Y_M_B*P_A != S_B:  continue
		try:
			Y_X_B=Y_M_B.solve_right(P_B)
		except:  continue
		sob += [(Y_M_B,Y_X_B)]
		#print(len(sob))
		if len(sob)>=maxc:
			break
	for Y_M_A,Y_X_A in soa:
		for Y_M_B,Y_X_B in sob:
			print(Y_M_A*Y_X_A==P_A,Y_M_A*P_B==S_A,
				Y_M_B*Y_X_B==P_B,Y_M_B*P_A==S_B,
				"secret?",Y_M_A*Y_M_B==M_A*M_B)