13 research outputs found
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
Secure Key Encapsulation Mechanism with Compact Ciphertext and Public Key from Generalized Srivastava code
Code-based public key cryptosystems have been found to be an interesting option in the area of Post-Quantum Cryptography. In this work, we present a key encapsulation mechanism (KEM) using a parity check matrix of the Generalized Srivastava code as the public key matrix. Generalized Srivastava codes are privileged with the decoding technique of Alternant codes as they belong to the family of Alternant codes. We exploit the dyadic structure of the parity check matrix to reduce the storage of the public key. Our encapsulation leads to a shorter ciphertext as compared to DAGS proposed by Banegas et al. in Journal of Mathematical Cryptology which also uses Generalized Srivastava code. Our KEM provides IND-CCA security in the random oracle model. Also, our scheme can be shown to achieve post-quantum security in the quantum random oracle model
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 à
confidencialidade e integridade das comunicações digitais. É, por isso, urgente
desenvolver técnicas criptográficas alternativas que sejam resilientes à
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 níveis 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
A Modified Symmetric Key Fully Homomorphic Encryption Scheme Based on Read-Muller Code
Homomorphic encryption became popular and powerful cryptographic primitive for various cloud computing applications. In the recent decades several developments has been made. Few schemes based on coding theory have been proposed but none of them support unlimited operations with security. We propose a modified Reed-Muller Code based symmetric key fully homomorphic encryption to improve its security by using message expansion technique. Message expansion with prepended random fixed length string provides one-to-many mapping between message and codeword, thus one-to many mapping between plaintext and ciphertext. The proposed scheme supports both (MOD 2) additive and multiplication operations unlimitedly. We make an effort to prove the security of the scheme under indistinguishability under chosen-plaintext attack (IND-CPA) through a game-based security proof. The security proof gives a mathematical analysis and its complexity of hardness. Also, it presents security analysis against all the known attacks with respect to the message expansion and homomorphic operations
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
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
Theoretical analysis of decoding failure rate of non-binary QC-MDPC codes
In this paper, we study the decoding failure rate (DFR) of non-binary QC-MDPC codes using theoretical tools, extending the results of previous binary QC-MDPC code studies. The theoretical estimates of the DFR are particularly significant for cryptographic applications of QC-MDPC codes. Specifically, in the binary case, it is established that exploiting decoding failures makes it possible to recover the secret key of a QC-MDPC cryptosystem. This implies that to attain the desired security level against adversaries in the CCA2 model, the decoding failure rate must be strictly upper-bounded to be negligibly small. In this paper, we observe that this attack can also be extended to the non--binary case as well, which underscores the importance of DFR estimation. Consequently, we study the guaranteed error-correction capability of non-binary QC-MDPC codes under one-step majority logic (OSML) decoder and provide a theoretical analysis of the 1-iteration parallel symbol flipping decoder and its combination with OSML decoder. Utilizing these results, we estimate the potential public-key sizes for QC-MDPC cryptosystems over for various security levels. We find that there is no advantage in reducing key sizes when compared to the binary case
Cryptanalysis of Ivanov-Krouk-Zyablov cryptosystem
Recently, F.Ivanov, E.Krouk and V.Zyablov proposed new cryptosystem based of Generalized Reed--Solomon (GRS) codes over field extensions. In their approach, the subfield images of GRS codes are masked by a special transform, so that the resulting public codes are not equivalent to subfield images of GRS code but burst errors still can be decoded. In this paper, we show that the complexity of message-recovery attack on this cryptosystem can be reduced due to using burst errors, and the secret key of Ivanov-Krouk-Zyablov cryptosystem can successfully recovered in polynomial time with a linear-algebra based attack and a square-based attack