A Related-Key Chosen-IV Distinguishing Attack on Full Sprout Stream Cipher

Sprout is a new lightweight stream cipher proposed at FSE 2015. According to its designers, Sprout can resist time-memory-data trade-off (TMDTO) attacks with small internal state size. However, we find a weakness in the updating functions of Sprout and propose a related-key chosen-IV distinguishing attacks on full Sprout. Under the related-key setting, our attacks enable the adversary to detect non-randomness on full 320-round Sprout with a practical complexity of $\tilde{O}(2^4)$ and find collisions in 256 output bits of full Sprout with a complexity of $\tilde{O}(2^7)$. Furthermore, when considering possible remedies, we find that only by modifying the updating functions and output function seems unlikely to equip Sprout with better resistance against this kind of distinguisher. Therefore, it is necessary for designers to give structural modifications

Some results on Sprout

Sprout is a lightweight stream cipher proposed by Armknecht and Mikhalev at FSE 2015. It has a Grain-like structure with two State Registers of size 40 bits each, which is exactly half the state size of Grain v1. In spite of this, the cipher does not appear to lose in security against generic Time-Memory-Data Tradeoff attacks due to the novelty of its design. In this paper, we first present improved results on Key Recovery with partial knowledge of the internal state. We show that if 50 of the 80 bits of the internal state are guessed then the remaining bits along with the Secret Key can be found in a reasonable time using a SAT solver. Thereafter we show that it is possible to perform a distinguishing attack on the full Sprout stream cipher in the multiple IV setting using around $2^{40}$ randomly chosen IVs on an average. The attack requires around $2^{48}$ bits of memory. Thereafter we will show that for every Secret Key, there exist around $2^{30}$ IVs for which the LFSR used in Sprout enters the all zero state during the Keystream generating phase. Using this observation, we will first show that it is possible to enumerate Key-IV pairs that produce keystream bits with period as small as 80. We will then outline a simple Key recovery attack that takes time equivalent to $2^{66.7}$ encryptions with negligible memory requirement. This although is not the best attack reported against this cipher in terms of the Time complexity, it is the best in terms of the memory required to perform the attack

On Ciphers that Continuously Access the Non-Volatile Key

Due to the increased use of devices with restricted resources such as limited area size, power or energy, the community has developed various techniques for designing lightweight ciphers. One approach that is increasingly discussed is to use the cipher key that is stored on the device in non-volatile memory not only for the initialization of the registers but during the encryption/decryption process as well. Recent examples are the ciphers Midori (Asiacrypt’15) and Sprout (FSE’15). This may on the one hand help to save resources, but also may allow for a stronger key involvement and hence higher security. However, only little is publicly known so far if and to what extent this approach is indeed practical. Thus, cryptographers without strong engineering background face the problem that they cannot evaluate whether certain designs are reasonable (from a practical point of view) which hinders the development of new designs. In this work, we investigate this design principle from a practical point of view. After a discussion on reasonable approaches for storing a key in non-volatile memory, motivated by several commercial products we focus on the case that the key is stored in EEPROM. Here, we highlight existing constraints and derive that some designs, based on the impact on their throughput, are better suited for the approach of continuously reading the key from all types of non-volatile memory. Based on these findings, we improve the design of Sprout for proposing a new lightweight stream cipher that (i) has a significantly smaller area size than almost all other stream ciphers and (ii) can be efficiently realized using common non-volatile memory techniques. Hence, we see our work as an important step towards putting such designs on a more solid ground and to initiate further discussions on realistic designs