Quantum Enigma Machine Proposed by Seth Lloyd for Secure Cryptography

Enigma machines are devices that perform cryptography using pseudo-random numbers. The original enigma machine code was broken by detecting hidden patterns in these pseudo-random numbers. This paper proposes a model for a quantum optical enigma machine and shows that the phenomenon of quantum data locking makes such quantum enigma machines provably secure even in the presence of noise and loss. [Arxiv – Quantum enigma machines]

The enigma machine used for cryptography during the second world war was a device which, given a short keyword, produced a pseudorandom output which could be decoded by a second machine using the same keyword. The original enigma machine consisted of a series of rotors through which electrical current could pass in a way that depended on the relative orientation of the rotors. The path taken by the current connected an input symbol to an output system. After each key press the rotors went through a stepping motion that changed the functional relationship between input and output for the next key press. A sender and receiver who prepared their machines using the same initial setting, determined by the keyword, could then exchange encrypted messages. While the enigma machine did a pretty good job of scrambling the input, the outputs deviated sufficiently from pseudorandom sequences that the enigma code could be broken. In general, classical codes based on pseudo-random numbers are secure only if P NP proving the security of such codes is accordingly difficult. This paper proposes a quantum optical version of the enigma machine and shows that it is secure in principle, in the sense that amount of information that Eve can access about the message can be made arbitrarily small, even in the presence of arbitrary amounts of loss.

The security of quantum enigma machines relies on the phenomenon of quantum data locking.

There are several hurdles to overcome in order to make quantum enigma machines secure in practice. Quantum data locking hides large amounts of data with a small key. Consequently, Alice and Bob must be very careful to ensure the security of that key. Data locking is susceptible to plain-text attack: if Eve knows part of the message, she can use that to determine the key and unlock the rest. Alice and Bob can evade the plaintext attack by using data locking to distribute a random secret key: Alice simply sends Bob a random number, known only to her. Performing a fully random unitary is computationally inefficient: in, however, it is shown how locking can be performed using non-random unitaries that can be constructed in time almost linear in n. That is, unlike the classical pseudo-random transformations of the original enigma machine, quantum pseudo-random transformations perform a sufficiently good job of scrambling the message that Eve cannot decipher it. Perhaps the most pressing issue, however, is the ability of quantum enigma machines to function effectively in the presence of noise and loss.

This paper showed that quantum enigma machines, unlike their classical counterparts, are provably secure against eavesdropping. The security of the quantum enigma machine is guaranteed by its ability to spread encoded states over Hilbert space via quantum data locking, thereby limiting the ability of an eavesdropper to obtain information about the encoded message. A quantum enigma machine based on single photons and unary encoding was exhibited and shown to retain its security in the presence of noise and high amounts of loss in the communication channel. The general question of how to define the capacity of quantum enigma machines that render a specified channel secure by the accessible information remains open. Here we exhibited enigmatic quantum coding schemes for the depolarizing and lossy channels: it would be useful to have codes for quantum data locking on general quantum channels. As with any cryptographic system, the security of practically realizable quantum enigma machines must be investigated on a case-by-case basis to probe for possible attacks.

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