In this paper, we will present a new key exchange cryptosystem based on linear algebra, which take less operations but weaker in security than Diffie-Hellman's one.
We develop a public key cryptosystem based on invariants of diagonalizable groups and investigate properties of such cryptosystem first over finite fields, then over number fields and finally over finite rings. We consider the security of these cryptosystem and show that it is necessary to restrict the set of parameters of the system to prevent various attacks (including linear algebra attacks and attacks based on Euclidean algorithm).
This paper presents a new fast public key cryptosystem namel : a key exchange algorithm, a public key encryption algorithm and a digital signature algorithm, based on the difficulty to invert the following function: $$F(x) =(a\times x)Mod(2^p)Div(2^q).$$ Mod is modulo operation , Div is integer division operation , a , p and q are integers where $( p > q )$. We define p and q values for which ModDiv2Inv can be the hardest. We then present ModDiv2Kex, a new fast key exchange algorithm based on ModDiv2Inv. In this paper we also evaluate the hardness of this problem by reducing it to SAT .
All instances of the semidirect key exchange protocol, a generalisation of the famous Diffie-Hellman key exchange protocol, satisfy the so-called "telescoping equality"; in some cases, this equality has been used to construct an attack. In this report we present computational evidence suggesting that an instance of the scheme called `MOBS' is an example of a scheme where the telescoping equality has too many solutions to be a practically viable means to conduct an attack.
In recent years, there have been many studies on quantum computing and the construction of quantum computers which are capable of breaking conventional number theory-based public key cryptosystems. Therefore, in the not-too-distant future, we need the public key cryptosystems that withstand against the attacks executed by quantum computers, so-called post-quantum cryptosystems. A public key cryptosystem based on polar codes (PKC-PC) has recently been introduced whose security depends on the difficulty of solving the general decoding problem of polar code. In this paper, we first implement the …
McEliece cryptosystem represents a smart open key system based on the hardness of the decoding of an arbitrary linear code, which is believed to be able to resist the advent of quantum computers. But the original McEliece cryptosystem, based on Goppa codes, has just very limited interest in practice, partly because it requires a very large public key. In this paper we propose a new general way to reduce the public key size. Unlike most papers on reducing key length of the cryptosystem, where original Goppa codes are substituted by some other codes, we suggest a new method of key size reduction…
The purpose of this paper is to describe and analyze the Cayley-Purser algorithm, which is a public-key cryptosystem proposed by Flannery in 1999. I will present two attacks on it, one of which is apparently new. I will also examine a variant of the Cayley-Purser algorithm that was patented by Slavin in 2008, and show that it is also insecure.
In this paper, we suggest a code-based public key encryption scheme, called McNie. McNie is a hybrid version of the McEliece and Niederreiter cryptosystems and its security is reduced to the hard problem of syndrome decoding. The public key involves a random generator matrix which is also used to mask the code used in the secret key. This makes the system safer against known structural attacks. In particular, we apply rank-metric codes to McNie.
In this paper we show that it is possible to extend the framework of Persichetti's code-based framework and create a secure KEM based on the McEliece protocol. This provides greater flexibility in the application of coding theory as a basis for cryptographic purposes.
In recent years, a lot of research has gone into creating multi-layer chaotic mapping-based cryptosystems. Random-like behavior, a continuous broadband power spectrum, and a weak baseline condition dependency are all characteristics of chaotic systems. Chaos could be helpful in the three functional components of compression, encryption, and modulation in a digital communication system. To successfully use chaos theory in cryptography, chaotic maps must be built in such a way that the entropy they produce can provide the necessary confusion and diffusion. A chaotic map is used in the first laye…
The modified Paillier cryptosystem has become extremely popular and applied in many fields, owning to its additive homomorphism. This cryptosystem provides weak private keys and a strong private key. A weak private key only can decrypt ciphertexts under the corresponding public key. The strong private key can decrypt all ciphertexts even under different public keys. When the modified Paillier cryptosystem is applied in a system, the member, often the system administrator, has the strong private key and can decrypt all ciphertexts. If this system administrator is attacked or compromised, the se…
Goldreich-Goldwasser-Halevi (GGH) public key cryptosystem is an instance of lattice-based cryptosystems whose security is based on the hardness of lattice problems. In fact, GGH cryptosystem is the lattice version of the first code-based cryptosystem, proposed by McEliece. However, it has a number of drawbacks such as; large public key length and low security level. On the other hand, Low Density Lattice Codes (LDLCs) are the practical classes of lattice codes which can achieve capacity on the additive white Gaussian noise (AWGN) channel with low complexity decoding algorithm. This paper intro…
We present public-private key cryptosystem which utilizes the fact that checking whether a partial automaton is carefully synchronizing is $PSPACE$-complete, even in the case of a binary alphabet.
This project involves an implementation of the Rivest Shamir Adleman (RSA) encryption algorithm in C. It consists of generation of two random prime numbers and a number co- prime to phi(n) also called euler toitent function. These three are used to generate a public key and private key. The user has to enter a message which is encrypted by the public key. The algorithm also decrypts the generated cipher text with the help of the private key and returns the plain text message which was encrypted earlier.
Due to the rapid advances in the development of quantum computers and their susceptibility to errors, there is a renewed interest in error correction algorithms. In particular, error correcting code-based cryptosystems have reemerged as a highly desirable coding technique. This is due to the fact that most classical asymmetric cryptosystems will fail in the quantum computing era. Quantum computers can solve many of the integer factorization and discrete logarithm problems efficiently. However, code-based cryptosystems are still secure against quantum computers, since the decoding of linear cod…
The Rabin cryptosystem has been proposed protect the unique ID (UID) in radio-frequency identification tags. The Rabin cryptosystem is a type of lightweight public key system that is theoretetically quite secure; however it is vulnerable to several side-channel attacks. In this paper, a crashing modulus attack is presented as a new fault attack on modular squaring during Rabin encryption. This attack requires only one fault in the public key if its perturbed public key can be factored. Our simulation results indicate that the attack is more than 50\% successful with several faults in practical…
RSA is one of the most popular Public Key Cryptography based algorithm mainly used for digital signatures, encryption/decryption etc. It is based on the mathematical scheme of factorization of very large integers which is a compute-intensive process and takes very long time as well as power to perform. Several scientists are working throughout the world to increase the speedup and to decrease the power consumption of RSA algorithm while keeping the security of the algorithm intact. One popular technique which can be used to enhance the performance of RSA is parallel programming. In this paper …
Cryptanalysis of a Public-key Cryptosystem Using Lattice Basis Reduction Algorithm
我们提出了一个新的攻击Hwang等人。的密码系统。该密码体制采用超增序列作为私钥,并提出了一种新的算法--置换组合算法来提高背包的密度,以避免低密度攻击。Sattar J. Aboud [Aboud j. Sattar,“An improved knapsack公钥密码学system”,International Journal of Internet Technology and Secured Transactions,Vol.3(3),pp.310-319,2011]使用Shamir对基本Merkle-Hellman密码系统的攻击来破解该密码系统。在本文中,我们介绍了一个直接攻击Hwang等人。的密码体制。通过计算提出的攻击的复杂度,我们表明,不同于Aboud的密码分析,我们的密码分析是更有效和实用。
At Eurocrypt'99, Paillier presented a public-key cryptosystem based on a novel computational problem. It has interested many researchers because it was additively homomorphic. In this paper, we show that there is a big difference between the original Paillier's encryption and some variants. The Paillier's encryption can be naturally transformed into a signature scheme but these variants miss the feature. In particular, we simplify the alternative decryption procedure of Bresson-Catalano-Pointcheval encryption scheme proposed at Asiacrypt'03. The new version is more applicable to cloud computin…
McNie is a code-based public key encryption scheme submitted as a candidate to the NIST Post-Quantum Cryptography standardization. In this paper, we present McNie2-Gabidulin, an improvement of McNie. By using Gabidulin code, we eliminate the decoding failure, which is one of the limitations of the McNie public key cryptosystem that uses LRPC codes. We prove that this new cryptosystem is IND-CPA secure. Suggested parameters are also given which provides low key sizes compared to other known code based cryptosystems with zero decryption failure probability.
In this paper, a novel and efficient hardware implementation of steganographic cryptosystem based on a public-key cryptography is proposed. Digital images are utilized as carriers of secret data between sender and receiver parties in the communication channel. The proposed public-key cryptosystem offers a separable framework that allows to embed or extract secret data and encrypt or decrypt the carrier using the public-private key pair, independently. Paillier cryptographic system is adopted to encrypt and decrypt pixels of the digital image. To achieve efficiency, a proposed efficient paralle…
Recently, a new fast public key exchange protocol was presented by S. Bouftass. The protocol is based on the difficulty of inverting the function $F(x)=\lfloor (zx \mod 2^p)/ 2^q \rfloor$. In this paper, we describe a practical attack against this protocol based on Closest Vector Problem (CVP) and Gaussian lattice reduction.
Traditional methods in public key cryptography are based on number theory, and suffer from problems such as dealing with very large numbers, making key creation cumbersome. Here, we propose a new public key cryptosystem based on strings only, which avoids the difficulties of the traditional number theory approach. The security mechanism for public and secret keys generation is ensured by a recursive encoding mechanism embedded in a quasi-commutative-random function, resulted from the composition of a quasi-commutative function with a pseudo-random function. In this revised version of the paper…
We propose BQTRU, a non-commutative NTRU-like cryptosystem over quaternion algebras. This cryptosystem uses bivariate polynomials as the underling ring. The multiplication operation in our cryptosystem can be performed with high speed using quaternions algebras over finite rings. As a consequence, the key generation and encryption process of our cryptosystem is faster than NTRU in comparable parameters. Typically using Strassen's method, the key generation and encryption process is approximately $16/7$ times faster than NTRU for an equivalent parameter set. Moreover, the BQTRU lattice has a hy…
A verifiable multi-secret sharing (VMSS) scheme enables the dealer to share multiple secrets, and the deception of both participants and the dealer can be detected. After analyzing the security of VMSS schemes proposed by Mashhadi and Dehkordi in 2015, we illustrate that they cannot detect some deception of the dealer. By using nonhomogeneous linear recursion and LFSR public key cryptosystem, we introduce two new VMSS schemes. Our schemes can not only overcome the drawback mentioned above, but also have shorter private/public key length at the same safety level. Besides, our schemes have dynam…
ITRU cryptosystem is a public key cryptosystem and one of the known variants of NTRU cryptosystem. Instead of working in a truncated polynomial ring, ITRU cryptosystem is based on the ring of integers. The authors claimed that ITRU has better features comparing to the classical NTRU, such as having a simple parameter selection algorithm, invertibility, and successful message decryption, and better security. In this paper, we present an attack technique against the ITRU cryptosystem, and it is mainly based on a simple frequency analysis on the letters of ciphertexts.
Braid group is a very important non-commutative group. It is also an important tool of quantum field theory, and has good topological properties. This paper focuses on the provable security research of cryptosystem over braid group, which consists of two aspects: One, we proved that the Ko's cryptosystem based on braid group is secure against chosen-plaintext-attack(CPA) which proposed in CRYPTO2000, while it dose not resist active attack. The other is to propose a new public key cryptosystem over braid group which is secure against adaptive chosen-ciphertext-attack(CCA2). Our proofs are based…
A repair of the Faure-Loidreau (FL) public-key code-based cryptosystem is proposed. The FL cryptosystem is based on the hardness of list decoding Gabidulin codes which are special rank-metric codes. We prove that the recent structural attack on the system by Gaborit et al. is equivalent to decoding an interleaved Gabidulin code. Since all known polynomial-time decoders for these codes fail for a large constructive class of error patterns, we are able to construct public keys that resist the attack. It is also shown that all other known attacks fail for our repair and parameter choices. Compare…
This paper presents a key recovery attack on the cryptosystem proposed by Lau and Tan in a talk at ACISP 2018. The Lau-Tan cryptosystem uses Gabidulin codes as the underlying decodable code. To hide the algebraic structure of Gabidulin codes, the authors chose a matrix of column rank $n$ to mix with a generator matrix of the secret Gabidulin code. The other part of the public key, however, reveals crucial information about the private key. Our analysis shows that the problem of recovering the private key can be reduced to solving a multivariate linear system over the base field, rather than so…
We propose a framework for threshold cryptosystems under a permissionless-economic model in which the participants are rational profit-maximizing entities. To date, threshold cryptosystems have been considered under permissioned settings with a limited adversary. Our framework relies on an escrow service that slashes and redistributes deposits to incentivize participants to adhere desired behaviors. Today, more than ever, sophisticated escrow services can be implemented over public blockchains like Ethereum, without additional trust assumptions. The key threat to rational threshold cryptosyste…
In this paper, a code-based public-key cryptosystem based on interleaved Goppa codes is presented. The scheme is based on encrypting several ciphertexts with the same Goppa code and adding a burst error to them. Possible attacks are outlined and the key size of several choices of parameters is compared to those of known schemes for the same security level. For example, for security level 128 bits, we obtain a key size of 696 Kbits whereas the classical McEliece scheme based on Goppa codes using list decoding requires a key size of 1935 Kbits.