Unconditionally Secure Quantum Signatures

Abstract

Signature schemes, proposed in 1976 by Diffie and Hellman, have become ubiquitous across modern communications. They allow for the exchange of messages from one sender to multiple recipients, with the guarantees that messages cannot be forged or tampered with and that messages also can be forwarded from one recipient to another without compromising their validity. Signatures are different from, but no less important than encryption, which ensures the privacy of a message. Commonly used signature protocols-signatures based on the Rivest-Adleman-Shamir (RSA) algorithm, the digital signature algorithm (DSA), and the elliptic curve digital signature algorithm (ECDSA)-are only computationally secure, similar to public key encryption methods. In fact, since these rely on the difficulty of finding discrete logarithms or factoring large primes, it is known that they will become completely insecure with the emergence of quantum computers. We may therefore see a shift towards signature protocols that will remain secure even in a post-quantum world. Ideally, such schemes would provide unconditional or information-theoretic security. In this paper, we aim to provide an accessible and comprehensive review of existing unconditionally securesecure signature schemes for signing classical messages, with a focus on unconditionally secure quantum signature schemes.

Free-Space Quantum Signatures Using Heterodyne Measurements

“…Currently used classical digital signature schemes, however, rely on unproven computational assumptions [2], and may become insecure especially if quantum computers can be built [3]. Quantum digital signatures (QDSs) [4][5][6][7][8][9][10], on the other hand, give information-theoretic security [7], loosely speaking based on the fact that nonorthogonal quantum states cannot be perfectly distinguished from each other.The first quantum signature schemes assumed tamperproof, "authenticated" quantum communication links. Intuitively, this could be accomplished using parameter estimation techniques similar to those used in quantum key distribution (QKD).…”

Efficient Unconditionally Secure Signatures Using Universal Hashing

“…Eq. (10) implies that (ω + 1) log(|M|) is the bit-length of the signature. The authors also show that the HSZI scheme provides security proportional to 1/|M|.…”

“…Before we proceed, we first briefly survey the USS schemes which are already proposed in the literature. For a detailed overview, we refer the interested reader to [10] and the references therein.…”

Experimental measurement-device-independent quantum digital signatures

“…Different from encryption, digital signatures play a vital role in software distribution, modern communication and financial transactions, where the integrity of the data against forgery is of utmost importance. While they are currently implemented using public-key cryptography, quantum digital signatures (QDS) have recently been introduced 16 – 18 to allow users to sign a document by quantum means and transfer it to other users with information-theoretical security. Quantum signatures were introduced in ref.…”