Due to Shor's algorithm, quantum computers are a severe threat for public key cryptography. This motivated the cryptographic community to search for quantum-safe solutions. On the other hand, the impact of quantum computing on secret key cryptography is much less understood. In this paper, we consider attacks where an adversary can query an oracle implementing a cryptographic primitive in a quantum superposition of different states. This model gives a lot of power to the adversary, but recent results show that it is nonetheless possible to build secure cryptosystems in it. We study applications of a quantum procedure called Simon's algorithm (the simplest quantum period finding algorithm) in order to attack symmetric cryptosystems in this model. Following previous works in this direction, we show that several classical attacks based on finding collisions can be dramatically sped up using Simon's algorithm: finding a collision requires Ω(2 n/2 ) queries in the classical setting, but when collisions happen with some hidden periodicity, they can be found with only O(n) queries in the quantum model. We obtain attacks with very strong implications. First, we show that the most widely used modes of operation for authentication and authenticated encryption (e.g. CBC-MAC, PMAC, GMAC, GCM, and OCB) are completely broken in this security model. Our attacks are also applicable to many CAESAR candidates: CLOC, AEZ, COPA, OTR, POET, OMD, and Minalpher. This is quite surprising compared to the situation with encryption modes: Anand et al. show that standard modes are secure with a quantum-secure PRF. Second, we show that Simon's algorithm can also be applied to slide attacks, leading to an exponential speed-up of a classical symmetric cryptanalysis technique in the quantum model.

We derive a new steering inequality based on a fine-grained uncertainty relation to capture EPRsteering for bipartite systems. Our steering inequality improves over previously known ones since it can experimentally detect all steerable two-qubit Werner state with only two measurement settings on each side. According to our inequality, pure entangle states are maximally steerable. Moreover, by slightly changing the setting, we can express the amount of violation of our inequality as a function of their violation of the CHSH inequality. Finally, we prove that the amount of violation of our steering inequality is, up to a constant factor, a lower bound on the key rate of a one-sided device independent quantum key distribution protocol secure against individual attacks. To show this result, we first derive a monogamy relation for our steering inequality. The development of quantum information led to distinguish three forms of non-local correlations in quantum physics [1][2][3][4][5][6]. These are entanglement, steering and Bell non-local correlations. Einstein, Podolsky and Rosen (EPR) introduced entangled quantum states in an attempt to show the incompleteness of quantum physics known as the EPR paradox [1]. The same year, Schrödinger re-expressed the EPR paradox as the possibility of steering (more generally, known as EPRsteering), i.e., when Alice and Bob share an entangled state, Alice can affect Bob's state throught her own measurement. More precisely, a state exhibits EPR-steering if it cannot be modeled as Bob holding an unknown yet definite state, a description known as a local hidden state (LHS) model [4]. Bell-type inequalities can be used to rule out local hidden variable (LHV) models. Similarly, steering inequalities are used to rule out the existence of LHS model and thus, demonstrate steerability.According to Wiseman, Jones and Doherty, the three forms of non-local correlations are also tightly related to the experimental settings required to test them [4]. To test entanglement, both parties need to trust that they perform quantum operations and also trust their measurement devices. In the case of EPR-steering, only one party assumes that he applies a quantum measurement and that his device is not controlled by a third party. Finally, Bell non-locality can be be tested without assuming quantum theory and trusting measurement devices. This leads to a hierarchy in which EPR-steering lies between Bell non-locality and entanglement.Experimental demonstration of Bell's non-locality has been achieved by several experiments [7]. To test EPRsteering, Reid proposed a testable formulation for continuous variable systems based on the position-momentum uncertainty relation [5]. Denote (X, P x ) and (Y, P y ) the position and corresponding momentum of two correlated modes. According to the Reid criterion, one needs to infer the uncertainty (measured by the standard deviation) of the quadrature amplitude X θk = cos[θk]X + sin[θk]P x for k ∈ {1, 2} from the measurement outcome of the correlated amplitude Y φk = cos[φ...