212 research outputs found
An efficient and secure RSA--like cryptosystem exploiting R\'edei rational functions over conics
We define an isomorphism between the group of points of a conic and the set
of integers modulo a prime equipped with a non-standard product. This product
can be efficiently evaluated through the use of R\'edei rational functions. We
then exploit the isomorphism to construct a novel RSA-like scheme. We compare
our scheme with classic RSA and with RSA-like schemes based on the cubic or
conic equation. The decryption operation of the proposed scheme turns to be two
times faster than RSA, and involves the lowest number of modular inversions
with respect to other RSA-like schemes based on curves. Our solution offers the
same security as RSA in a one-to-one communication and more security in
broadcast applications.Comment: 18 pages, 1 figur
SHIELD: Scalable Homomorphic Implementation of Encrypted Data-Classifiers
Homomorphic encryption (HE) systems enable computations on encrypted data, without decrypting and without knowledge of the secret key. In this work, we describe an optimized Ring Learning With Errors (RLWE) based implementation of a variant of the HE system recently proposed by Gentry, Sahai and Waters (GSW). Although this system was widely believed to be less efficient than its contemporaries, we demonstrate quite the opposite behavior for a large class of applications. We first highlight and carefully exploit the algebraic features of the system to achieve significant speedup over the state-of-the-art HE implementation, namely the IBM homomorphic encryption library (HElib). We introduce several optimizations on top of our HE implementation, and use the resulting scheme to construct a homomorphic Bayesian spam filter, secure multiple keyword search, and a homomorphic evaluator for binary decision trees. Our results show a factor of 10× improvement in performance (under the same security settings and CPU platforms) compared to IBM HElib for these applications. Our system is built to be easily portable to GPUs (unlike IBM HElib) which results in an additional speedup of up to a factor of 103.5× to offer an overall speedup of 1,035×
A Fast Implementation of Elliptic Curve Cryptosystem with Prime Order Defined over F(p8)
Public key cryptosystem has many uses, such as to sign digitally, to realize electronic commerce. Especially, RSA public key cryptosystem has been the most widely used, but its key for ensuring sufficient security reaches about 2000 bits long. On the other hand, elliptic curve cryptosystem(ECC) has the same security level with about 7-fold smaller length key. Accordingly, ECC has been received much attention and implemented on various processors even with scarce computation resources. In this paper, we deal with an elliptic curve which is defined over extension field F(p2c) and has a prime order, where p is the characteristic and c is a non negative integer. In order to realize a fast software implementation of ECC adopting such an elliptic curve, a fast implementation method of definition field F(p2c) especially F(p8) is proposed by using a technique called successive extension. First, five fast implementation methods of base field F(p2) are introduced. In each base field implementation, calculation costs of F(p2)-arithmetic operations are evaluated by counting the numbers of F(p)-arithmetic operations. Next, a successive extension method which adopts a polynomial basis and a binomial as the modular polynomial is proposed with comparing to a conventional method. Finally, we choose two prime numbers as the characteristic, and consider several implementations for definition field F(p8) by using five base fields and two successive extension methods. Then, one of these implementations is especially selected and implemented on Toshiba 32-bit micro controller TMP94C251(20MHz) by using C language. By evaluating calculation times with comparing to previous works, we conclude that proposed method can achieve a fast implementation of ECC with a prime order
Enhancing Speed Performance of the Cryptographic Algorithm Based on the Lucas Sequence
Computer information and network security has recently become a popular subject
due to the explosive growth of the Internet and the migration of commerce practices
to the electronic medium. Thus the authenticity and privacy of the information transmitted
and the data stored on networked computers is of utmost importance. The
deployment of network security procedures requires the implementation of cryptographic
functions. More specifically, these include encryption, decryption, authentication,
digital signature algorithms and message-digest functions. Performance has
always been the most critical characteristic of a cryptographic function, which determines
its effectiveness.Since the discovery of public-key cryptography, very few convincingly secure asymmetric
schemes have been discovered despite considerable research efforts. Utilizing
the properties of Lucas functions introduced a public key system based on Lucas functions
instead of exponentiation, which offer a good alternative to the most publicly
used exponential public key system RSA.
LUC cryptosystem algorithm based on the quadratic and cubic polynomial, is
introduced in this thesis with a new formula to distinguishing between the cubic
polynomial roots. Reducing the calculation time of the algorithm, in sequential and
parallel platforms, using the doubling-rule technique combined with a new scheme
led to a strong improvement of the LUC algorithm speed.
The computation time analysis shows that whene doubling with remainder technique
is used, the improvement of the speed rises rapidly compared to the standard
implementation of the LUC algorithm and LUC algorithm with doubling rule. Furthermore
the algorithm is still keeping its simplicity of non-multiplicative and nonexponentiation
public-key cryptosystem. The improved algorithm is applied on the
lab-PC for the sequential platform, and cluster-computing machine for the parallel
platform, which lead to a substantial time reduction and an enhancement of the
algorithm speed in both platforms
Finding Small Solutions of the Equation and Its Applications to Cryptanalysis of the RSA Cryptosystem
In this paper, we study the condition of finding small solutions of the equation . The framework is derived from Wiener\u27s small private exponent attack on RSA and May-Ritzenhofen\u27s investigation about the implicit factorization problem, both of which can be generalized to solve the above equation. We show that these two methods, together with Coppersmith\u27s method, are equivalent for solving in the general case. Then based on Coppersmith\u27s method, we present two improvements for solving in some special cases. The first improvement pays attention to the case where either or is large enough. As the applications of this improvement, we propose some new cryptanalysis of RSA, such as new results about the generalized implicit factorization problem, attacks with known bits of the prime factor, and so on. The motivation of these applications comes from oracle based complexity of factorization problems. The second improvement assumes that the value of is known. We present two attacks on RSA as its applications. One focuses on the case with known bits of the private exponent together with the prime factor, and the other considers the case with a small difference of the two prime factors. Our new attacks on RSA improve the previous corresponding results respectively, and the correctness of the approach is verified by experiments
Multivariate public key cryptography with polynomial composition
This paper presents a new public key cryptography scheme using multivariate polynomials over a finite field. Each multivariate polynomial from the public key is obtained by secretly and repeatedly composing affine transformations with series of quadratic polynomials (in a single variable). The main drawback of this scheme is the length of the public key
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