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In present times, Radio‐Frequency Identification (RFID) systems have seen a significant rise in their usage. There has been an increasing interest in developing even lighter RFID protocols suitable for resource‐constrained environments. Ensuring security and privacy remain critical challenges in RFID‐based systems. Recently proposed lightweight authentication schemes, namely LRSAS+ and LRARP+, are ideally suited for constrained devices. However, this article investigates these schemes and reveals certain vulnerabilities: LRSAS+ is susceptible to tag impersonation, desynchronization, and traceability attacks, while LRARP+ can fall prey to traceability and secret disclosure attacks. An enhanced version of these authentication systems is proposed that tackles their inherent weaknesses by leveraging the χper$\chi per$ function. To verify the security of the proposed scheme, a formal analysis is conducted using Gong–Needham–Yahalom logic (GNY logic) and an automated security protocol verification tool, ProVerif. The improved scheme's effectiveness is also compared with multiple contemporary lightweight systems. The results indicate that the enhanced scheme not only meets the security requirements for lightweight authentication schemes but also achieves this with minimal computational overhead. [ABSTRACT FROM AUTHOR]

In this paper, we determine all simple block-transitive 3-designs on 65 points with block stabilizer of order greater than 2, admitting the 2-transitive action of the group S z (8). As a result, we find 23 3-designs on 65 points that have S z (8) as an automorphism group. Also we construct four 3-(3 6 , 1 8 , λ 1 ) designs for λ 1 ∈ { 7 6 8 , 5 1 8 4 , 6 9 1 2 , 9 2 1 6 } and two 3-(3 6 , 1 7 , λ 2 ) designs for λ 2 ∈ { 2 8 8 0 , 8 6 4 0 }. All of these designs have S 6 (2) as the full automorphism group. Some of these designs are flag and anti-flag-transitive. [ABSTRACT FROM AUTHOR]