This paper proposes a new fault attack technique on the LED blockcipher using a single fault injection by combining algebraic

side-channel attack (ASCA) and differential fault attack (DFA). We

name it as algebraic differential fault attack (ADFA). Firstly, a

boolean equation set is constructed for LED using algebraic

techniques. Then, the fault differences of the S-Box inputs in the

last round of LED are deduced by DFA and represented using algebraic

equations by the multiple deductions-based ASCA (MDASCA) technique

proposed in COSADE 2012. Finally, the key is recovered by solving

the equation set with the CryptoMiniSat solver. We show that, as to

ADFA on LED under the single nibble-based fault model, the 64-bit

key can be recovered within one minute on a common PC with a success

rate of 79\\%, which is more efficient than previous work. We modify

the CryptoMiniSat solver to count and output multiple solutions for

the key, and conduct ADFA to calculate the reduced key search space

for DFA. The key search space of LED is reduced to $2^6 \\sim

2^{17}$, which is different from previous work. We also successfully

extend ADFA on LED to other fault models using a single fault

injection, such as byte based fault model and nibble based diagonal

fault model, where traditional DFAs are difficult to work. The

results show that ADFA is an efficient and generic fault analysis

technique which significantly improves DFA.