In this paper we propose Differential Fault Attack (DFA) on two Fully Homomorphic Encryption (FHE) friendly stream ciphers Rasta and$\text{FiLIP}_{\text{DSM}}$. Design criteria of Rasta rely on affine layers and nonlinear layers, whereas$\text{FiLIP}_{\text{DSM}}$relies on permutations and a nonlinear filter function. Here we show that the secret key of these two ciphers can be recovered by injecting only 1 bit fault in the initial state. Our DFA on full round (# rounds$=6$) Rasta with 219 block size requires only one block (i.e., 219 bits) of normal and faulty keystream bits. In the case of our DFA on FiLIP-430 (one instance of$\text{FiLIP}_{\text{DSM}}$), we need 30000 normal and faulty keystream bits.

In this article, we propose key recovery attack on two stream ciphers: Kreyvium and FLIP$_{530}(42,128,360)$using Differential Fault Attack (DFA) technique. These two ciphers are being used in Fully Homomorphic Encryption (FHE) due to their low error growth during keystream generation. Kreyvium is an NFSR-based stream cipher and FLIP is a permutation-based stream cipher. We first show that the complete state of the Kreyvium can be recovered by injecting 3 faults and considering 450 many keystream bits. In case of FLIP, we show that if there is a 1-bit fault in the state of the cipher then from 9000 normal and faulty keystream bits the state (i.e., the secret key) of the cipher can be recovered. For single bit fault, one will require to solve a system of equations for each 530 possible fault locations to recover the correct key of FLIP. To the best of our knowledge, this is the first article which analyzes the security of these two FHE supported stream ciphers under DFA and it has been observed that DFA completely reveals the secret keys of these two ciphers with very minimal faults.

Boolean functions are usually studied under the assumption that each input bit is considered independent and identically distributed. However, in the case of some stream ciphers, a keystream bit is generated by using a nonlinear Boolean function with inputs from a restricted domain. At Eurocrypt 2016, one such stream cipher (FLIP) has been proposed, where a Boolean function on n variables was exploited with inputs of weight n/2 only. Recently, Carlet et al. studied several properties of such functions and obtained certain bounds on linear approximations of direct sum in the restricted domain. In this paper, we observe that for a direct sum like f = f1+ f2, the inputs to each sub-function f1, f2do not follow a uniform distribution in the restricted domain. In this regard, we study the properties of the Boolean functions by considering a general probability distribution on the inputs. We further obtain several bounds related to the biases of direct sums. Finally, we obtain a lower bound on the bias of the nonlinear filter function of FLIP. Our results provide a general framework to study security parameters of ciphers over restricted domain.

In this study, the authors construct two different distinguishers on Grain‐v1 with 112 and 114 initialisation rounds. Their first distinguisher can distinguish Grain‐v1 with 112 initialisation rounds from a uniform random source for 99% of the randomly chosen keys from full key space. The second one can distinguish Grain‐v1 from a random source for 73% of the randomly chosen keys for one‐fourth of the total key space (2 78 keys out of 2 80 keys). Our results improve upon the earlier distinguishers. The technique used for the distinguishers is conditional differential cryptanalysis. The existing works in this direction considered only one bit difference in the initialisation vector. However, for the first time, they could handle complicated conditions for the 2‐bit difference to obtain better cryptanalytic results. Extending their technique by allowing the 1‐bit difference in the pair of keys (i.e. related keys) and the 4‐bit difference in IVs, they could observe the non‐randomness till 116 initialisation rounds with a success in 62% cases.