Relativistic quantum cryptography is a sub-field of quantum cryptography, in which in addition to exploiting the principles of quantum physics, the no-superluminal signalling principle of relativity theory stating that information cannot travel faster than light is exploited too. Technically speaking, relativistic quantum cryptography is a sub-field of relativistic cryptography, in which cryptographic protocols exploit the no-superluminal signalling principle, independently of whether quantum properties are used or not. However, in practice, the term relativistic quantum cryptography is used for relativistic cryptography too.
In 1997 and 1998, some important tasks in mistrustful cryptography were shown to be impossible to achieve with unconditional security. Mayers[1] and Lo and Chau[2] showed that unconditionally secure quantum bit commitment was impossible. Lo showed that oblivious transfer and a broad class of secure computations were also impossible to achieve with unconditional security in quantum cryptography.[3] Moreover, Lo and Chau showed that unconditionally secure ideal quantum coin tossing was impossible too.[4] In this context, Kent provided in 1999 the first relativistic cryptographic protocols, for bit commitment and ideal coin tossing, which overcome the assumptions made by Mayers, Lo and Chau, and achieve unconditional security.[5][6] Since then, other unconditionally secure relativistic protocols for bit commitment have been found by Kent and others,[7][8][9][10][11] and other cryptographic tasks have been investigated in the setting of relativistic quantum cryptography.[12][13][14][15][16][17][18]
The no-signalling principle of quantum theory states that information cannot be communicated between two distinct locations L0 and L1 without the transmission of any physical systems, despite any quantum entanglement shared between L0 and L1. This implies, in particular, that without the transmission of any physical systems between L0 and L1, quantum correlation between L0 and L1 cannot be used to transmit information between L0 and L1, even if they are non-locally causal and violate Bell inequalities. According to relativity theory, physical systems cannot travel faster than the speed of light. Thus, it follows from the no-signalling principle that information cannot travel faster than the speed of light. This is called the no-superluminal signalling principle.
The principle of no-superluminal signalling is the key physical principle exploited in relativistic cryptography. It guarantees that the outcome x of a random variable X obtained at some spacetime point P cannot influence the probability that a random variable Y takes some value y at a spacelike separated spacetime point Q. Thus, for example, if two parties Alice and Bob have each two agents, with the first agent of Bob sending a secret message x to a first agent of Alice at the spacetime point P, and with the second agent of Alice sending a secret message y to the second agent of Bob at the spacetime point Q, with P and Q spacelike separated, then Bob can be guaranteed that the message y received from Alice was chosen independently of the message x that he gave Alice, and vice versa. This is a useful mathematical property that is exploited to prove the security of cryptographic protocols in relativistic cryptography.