This paper develops a mathematically grounded framework for Differential Fault Analysis (DFA) on lightweight symmetric primitives, focusing on the NIST-standardized authenticated encryption scheme sf Ascon and the NSA’s lightweight block cipher sf Aradi. We characterize fault propagation in the underlying substitution permutation network (SPN) by modeling the nonlinear substitution layer in Algebraic Normal Form (ANF), enabling a precise description of the differential relations induced by injected faults. To minimize fault and complexity for key recovery, we formulate the selection of effective fault patterns as a combinatorial optimization problem, where the coverage of key-dependent variables by observable differentials is expressed as a Set Covering Problem (SCP). Solving the resulting SCP via an Integer Linear Programming (ILP) model yields an optimized fault injection strategy. For sf Ascon , we show that full key recovery under an encryption oracle requires only 72 faulty queries specifically, 71 single bit-flip faults and one multi-bit bit-reset fault. This is well below the nonce-misuse bound of 256 queries specified in the NIST standard. In the decryption oracle setting, the proposed optimization reduces the number of faulty decryptions by 54.5% compared with previous analyses, requiring at most 320 (expected 272) queries for half-key recovery instead of 704. Applying the same framework to sf Aradi enables full key recovery with 64 faulty decryption queries when the fault location is known, while for the unknown-location setting the ILP-based model remains effective with a simulation based fault complexity of 168. Overall, these results show that combining algebraic cryptanalysis with combinatorial optimization provides a systematic method to minimize fault complexity and assess the fault resilience of lightweight cryptographic primitives.