2,550 research outputs found
Approximate Quantum Error-Correcting Codes and Secret Sharing Schemes
It is a standard result in the theory of quantum error-correcting codes that
no code of length n can fix more than n/4 arbitrary errors, regardless of the
dimension of the coding and encoded Hilbert spaces. However, this bound only
applies to codes which recover the message exactly. Naively, one might expect
that correcting errors to very high fidelity would only allow small violations
of this bound. This intuition is incorrect: in this paper we describe quantum
error-correcting codes capable of correcting up to (n-1)/2 arbitrary errors
with fidelity exponentially close to 1, at the price of increasing the size of
the registers (i.e., the coding alphabet). This demonstrates a sharp
distinction between exact and approximate quantum error correction. The codes
have the property that any components reveal no information about the
message, and so they can also be viewed as error-tolerant secret sharing
schemes.
The construction has several interesting implications for cryptography and
quantum information theory. First, it suggests that secret sharing is a better
classical analogue to quantum error correction than is classical error
correction. Second, it highlights an error in a purported proof that verifiable
quantum secret sharing (VQSS) is impossible when the number of cheaters t is
n/4. More generally, the construction illustrates a difference between exact
and approximate requirements in quantum cryptography and (yet again) the
delicacy of security proofs and impossibility results in the quantum model.Comment: 14 pages, no figure
Encryption of Covert Information into Multiple Statistical Distributions
A novel strategy to encrypt covert information (code) via unitary projections
into the null spaces of ill-conditioned eigenstructures of multiple host
statistical distributions, inferred from incomplete constraints, is presented.
The host pdf's are inferred using the maximum entropy principle. The projection
of the covert information is dependent upon the pdf's of the host statistical
distributions. The security of the encryption/decryption strategy is based on
the extreme instability of the encoding process. A self-consistent procedure to
derive keys for both symmetric and asymmetric cryptography is presented. The
advantages of using a multiple pdf model to achieve encryption of covert
information are briefly highlighted. Numerical simulations exemplify the
efficacy of the model.Comment: 18 pages, 4 figures. Three sentences expanded to emphasize detail.
Typos correcte
The Impact of Quantum Computing on Present Cryptography
The aim of this paper is to elucidate the implications of quantum computing
in present cryptography and to introduce the reader to basic post-quantum
algorithms. In particular the reader can delve into the following subjects:
present cryptographic schemes (symmetric and asymmetric), differences between
quantum and classical computing, challenges in quantum computing, quantum
algorithms (Shor's and Grover's), public key encryption schemes affected,
symmetric schemes affected, the impact on hash functions, and post quantum
cryptography. Specifically, the section of Post-Quantum Cryptography deals with
different quantum key distribution methods and mathematicalbased solutions,
such as the BB84 protocol, lattice-based cryptography, multivariate-based
cryptography, hash-based signatures and code-based cryptography.Comment: 10 pages, 1 figure, 3 tables, journal article - IJACS
Reinforcing Security and Usability of Crypto-Wallet with Post-Quantum Cryptography and Zero-Knowledge Proof
Crypto-wallets or digital asset wallets are a crucial aspect of managing
cryptocurrencies and other digital assets such as NFTs. However, these wallets
are not immune to security threats, particularly from the growing risk of
quantum computing. The use of traditional public-key cryptography systems in
digital asset wallets makes them vulnerable to attacks from quantum computers,
which may increase in the future. Moreover, current digital wallets require
users to keep track of seed-phrases, which can be challenging and lead to
additional security risks. To overcome these challenges, a new algorithm is
proposed that uses post-quantum cryptography (PQC) and zero-knowledge proof
(ZKP) to enhance the security of digital asset wallets. The research focuses on
the use of the Lattice-based Threshold Secret Sharing Scheme (LTSSS), Kyber
Algorithm for key generation and ZKP for wallet unlocking, providing a more
secure and user-friendly alternative to seed-phrase, brain and multi-sig
protocol wallets. This algorithm also includes several innovative security
features such as recovery of wallets in case of downtime of the server, and the
ability to rekey the private key associated with a specific username-password
combination, offering improved security and usability. The incorporation of PQC
and ZKP provides a robust and comprehensive framework for securing digital
assets in the present and future. This research aims to address the security
challenges faced by digital asset wallets and proposes practical solutions to
ensure their safety in the era of quantum computing
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