One important challenge of Quantum Key Distribution (QKD) is to preserve the unconditional security when a scheme is implemented. In Semi Quantum Key Distribution (SQKD), one of the parties is only able of performing classical operations, thus, alleviating the cost of its implementation. Authenticated SQKD (ASQKD) ensures, in addition, better security than SQKD against attacks aiming at the identity of the parties. In this regard, Li et al.have proposed a new ASQKD scheme that ensures better efficiency than the first proposed ASQKD scheme of Yu et al. However, both schemes present loopholes in their security. This study presents a new ASQKD without using entanglement, able to achieve higher security than the schemes of Li et al.and Yu et al. Our scheme is also simpler and demands less advanced quantum devices than ASQKD schemes using entanglement.