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Table 1 Notations

From: Quantum key recovery attack on SIMON32/64

Notation Description
& The bitwise AND operation
The bitwise XOR operation
The cyclic left rotation operation
Round-i The i-th round of SIMON32/64
(Li−1,Ri−1) The input block of Round-i in SIMON32/64
Li[j] The j-th bit of Li(the index of rightmost bit is 0)
Ki−1 The round key of Round-i in SIMON32/64
Δi−1=(ΔLi−1,ΔRi−1) The input difference to Round-i
ΔAndi ΔAndi:=(Li1)&(Li8)((Li)1)&((Li)8)
ΔRoti ΔRoti:=ΔLi2
E(·) The encryption function of 19-round SIMON32/64 with real key k
Ek(·) The encryption function of 19-round SIMON32/64 with guessed key k
\(D_{k}^{j}(\cdot)\) The decryption function that decrypts the given ciphertext in j rounds with key k
\(\mathcal {QMKS}\) The quantum master key exhaustive search attack on 19-round SIMON32/64
\(\mathcal {QRKR}\) The quantum round-key key recovery attack on 19-round SIMON32/64
\(\mathcal {CRKR}\) The key recovery attack on 19-round SIMON32/64 present in (Biryukov et al. 2014)
#iter The number of iteration in a QAA instance
#Toff-C The number of CNOT gate decomposed by Toffoli gate
#Toff-H The number of H gate decomposed by Toffoli gate