14 research outputs found
Decoding Generalized Reed-Solomon Codes and Its Application to RLCE Encryption Schemes
This paper compares the efficiency of various algorithms for implementing
quantum resistant public key encryption scheme RLCE on 64-bit CPUs. By
optimizing various algorithms for polynomial and matrix operations over finite
fields, we obtained several interesting (or even surprising) results. For
example, it is well known (e.g., Moenck 1976 \cite{moenck1976practical}) that
Karatsuba's algorithm outperforms classical polynomial multiplication algorithm
from the degree 15 and above (practically, Karatsuba's algorithm only
outperforms classical polynomial multiplication algorithm from the degree 35
and above ). Our experiments show that 64-bit optimized Karatsuba's algorithm
will only outperform 64-bit optimized classical polynomial multiplication
algorithm for polynomials of degree 115 and above over finite field
. The second interesting (surprising) result shows that 64-bit
optimized Chien's search algorithm ourperforms all other 64-bit optimized
polynomial root finding algorithms such as BTA and FFT for polynomials of all
degrees over finite field . The third interesting (surprising)
result shows that 64-bit optimized Strassen matrix multiplication algorithm
only outperforms 64-bit optimized classical matrix multiplication algorithm for
matrices of dimension 750 and above over finite field . It should
be noted that existing literatures and practices recommend Strassen matrix
multiplication algorithm for matrices of dimension 40 and above. All our
experiments are done on a 64-bit MacBook Pro with i7 CPU and single thread C
codes. It should be noted that the reported results should be appliable to 64
or larger bits CPU architectures. For 32 or smaller bits CPUs, these results
may not be applicable. The source code and library for the algorithms covered
in this paper are available at http://quantumca.org/
Shannon Perfect Secrecy in a Discrete Hilbert Space
The One-time-pad (OTP) was mathematically proven to be perfectly secure by
Shannon in 1949. We propose to extend the classical OTP from an n-bit finite
field to the entire symmetric group over the finite field. Within this context
the symmetric group can be represented by a discrete Hilbert sphere (DHS) over
an n-bit computational basis. Unlike the continuous Hilbert space defined over
a complex field in quantum computing, a DHS is defined over the finite field
GF(2). Within this DHS, the entire symmetric group can be completely described
by the complete set of n-bit binary permutation matrices. Encoding of a
plaintext can be done by randomly selecting a permutation matrix from the
symmetric group to multiply with the computational basis vector associated with
the state corresponding to the data to be encoded. Then, the resulting vector
is converted to an output state as the ciphertext. The decoding is the same
procedure but with the transpose of the pre-shared permutation matrix. We
demonstrate that under this extension, the 1-to-1 mapping in the classical OTP
is equally likely decoupled in Discrete Hilbert Space. The uncertainty
relationship between permutation matrices protects the selected pad, consisting
of M permutation matrices (also called Quantum permutation pad, or QPP). QPP
not only maintains the perfect secrecy feature of the classical formulation but
is also reusable without invalidating the perfect secrecy property. The
extended Shannon perfect secrecy is then stated such that the ciphertext C
gives absolutely no information about the plaintext P and the pad.Comment: 7 pages, 1 figure, presented and published by QCE202
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
Chaves mais pequenas para criptossistemas de McEliece usando codificadores convolucionais
The arrival of the quantum computing era is a real threat to the confidentiality
and integrity of digital communications. So, it is urgent to develop alternative
cryptographic techniques that are resilient to quantum computing. This is the
goal of pos-quantum cryptography. The code-based cryptosystem called
Classical McEliece Cryptosystem remains one of the most promising postquantum
alternatives. However, the main drawback of this system is that the
public key is much larger than in the other alternatives. In this thesis we study
the algebraic properties of this type of cryptosystems and present a new variant
that uses a convolutional encoder to mask the so-called Generalized Reed-
Solomon code. We conduct a cryptanalysis of this new variant to show that
high levels of security can be achieved using significant smaller keys than in
the existing variants of the McEliece scheme. We illustrate the advantages of
the proposed cryptosystem by presenting several practical examples.A chegada da era da computação quântica é uma ameaça real Ã
confidencialidade e integridade das comunicações digitais. É, por isso, urgente
desenvolver técnicas criptográficas alternativas que sejam resilientes Ã
computação quântica. Este é o objetivo da criptografia pós-quântica. O
Criptossistema de McEliece continua a ser uma das alternativas pós-quânticas
mais promissora, contudo, a sua principal desvantagem é o tamanho da chave
pública, uma vez que é muito maior do que o das outras alternativas. Nesta
tese estudamos as propriedades algébricas deste tipo de criptossistemas e
apresentamos uma nova variante que usa um codificador convolucional para
mascarar o código de Generalized Reed-Solomon. Conduzimos uma
criptoanálise dessa nova variante para mostrar que altos nÃveis de segurança
podem ser alcançados usando uma chave significativamente menor do que as
variantes existentes do esquema de McEliece. Ilustramos, assim, as vantagens
do criptossistema proposto apresentando vários exemplos práticos.Programa Doutoral em Matemátic
Energy efficiency analysis of selected public key cryptoschemes
Public key cryptosystems in both classical and post-quantum settings usually involve a lot of computations. The amount as well as the type of computations involved vary among these cryptosystems. As a result, when the computations are performed on processors or devices, they can lead to a wide range of energy consumption. Since a lot of devices implementing these cryptosystems might have a limited source of power or energy, energy consumption by such schemes is an important aspect to be considered.
The Diffie-Hellman key exchange is one of the most commonly used technique in the classical setting of public key cryptographic shceme, and elliptic curve based Diffie-Hellman (ECDH) has been in existence for more than three decades. An elliptic curve based post-quantum version of Diffie-Hellman, called supersingular isogeny based Diffie-Hellman (SIDH) was developed in 2011. For computations involved in ECDH and SIDH, elliptic curve points can be represented in various coordinate systems. In this thesis, a comparative analysis of energy consumption is carried out for the affine and projective coordinate based elliptic curve point addition and doubling used in ECDH and SIDH. We also compare the energy consumption of the entire ECDH and SIDH schemes.
SIDH is one of the more than sixty algorithms currently being considered by NIST to develop and standardize quantum-resistant public key cryptographic algorithms. In this thesis, we use a holistic approach to provide a comprehensive report on the energy consumption and power usage of the candidate algorithms executed on a 64-bit processor
Using Reed-Solomon codes in the (U | U + V ) construction and an application to cryptography
International audience—In this paper we present a modification of Reed-Solomon codes that beats the Guruswami-Sudan 1 − √ R decoding radius of Reed-Solomon codes at low rates R. The idea is to choose Reed-Solomon codes U and V with appropriate rates in a (U | U + V) construction and to decode them with the Koetter-Vardy soft information decoder. We suggest to use a slightly more general version of these codes (but which has the same decoding performance as the (U | U + V)-construction) for being used in code-based cryptography , namely to build a McEliece scheme. The point is here that these codes not only perform nearly as well (or even better in the low rate regime) as Reed-Solomon codes, but also that their structure seems to avoid the Sidelnikov-Shestakov attack which broke a previous McEliece proposal based on generalized Reed-Solomon codes