  We illustrate through example 1 and 2 that the condition at theorem 1 in [8]
dissatisfies necessity, and the converse proposition of fact 1.1 in [8] does
not hold, namely the condition Z/M - L/Ak < 1/(2 Ak^2) is not sufficient for
f(i) + f(j) = f(k). Illuminate through an analysis and ex.3 that there is a
logic error during deduction of fact 1.2, which causes each of fact 1.2, 1.3, 4
to be invalid. Demonstrate through ex.4 and 5 that each or the combination of
qu+1 > qu * D at fact 4 and table 1 at fact 2.2 is not sufficient for f(i) +
f(j) = f(k), property 1, 2, 3, 4, 5 each are invalid, and alg.1 based on fact 4
and alg.2 based on table 1 are disordered and wrong logically. Further,
manifest through a repeated experiment and ex.5 that the data at table 2 is
falsified, and the example in [8] is woven elaborately. We explain why Cx = Ax
* W^f(x) (% M) is changed to Cx = (Ax * W^f(x))^d (% M) in REESSE1+ v2.1. To
the signature fraud, we point out that [8] misunderstands the existence of T^-1
and Q^-1 % (M-1), and forging of Q can be easily avoided through moving H.
Therefore, the conclusion of [8] that REESSE1+ is not secure at all (which
connotes that [8] can extract a related private key from any public key in
REESSE1+) is fully incorrect, and as long as the parameter Omega is fitly
selected, REESSE1+ with Cx = Ax * W^f(x) (% M) is secure.
