12 research outputs found
On the Implementation of Unified Arithmetic on Binary Huff Curves
Unified formula for computing elliptic curve point addition and doubling are considered to be resistant against simple power-analysis attack. A new elliptic curve formula known as unified binary Huff curve in this regard has appeared into the literature in 2011. This paper is devoted to analyzing the applicability of this elliptic curve in practice. Our paper has two contributions.We provide an efficient implementation of the unified Huff formula in projective coordinates on FPGA. Secondly,
we point out its side-channel vulnerability and show the results of an actual attack. It is claimed that the formula is unified and there will be no power consumption difference when computing point addition and point doubling operations, observable with simple power analysis (SPA). In this paper, we contradict their claim showing actual SPA results on a FPGA platform and propose a modified arithmetic and its suitable implementation technique to overcome the vulnerability
An efficient crypto processor architecture for side-channel resistant Binary Huff Curves on FPGA
<jats:p>This article presents an efficient crypto processor architecture for point multiplication acceleration of side-channel secured Binary Huff Curves (BHC) on FPGA (field-programmable gate array) over GF(2233). We have implemented six finite field polynomial multiplication architectures, i.e., (1) schoolbook, (2) hybrid Karatsuba, (3) 2-way-karatsuba, (4) 3-way-toom-cook, (5) 4-way-toom-cook and (6) digit-parallel-least-significant. For performance evaluation, each implemented polynomial multiplier is integrated with the proposed BHC architecture. Verilog HDL is used for the implementation of all the polynomial multipliers. Moreover, the Xilinx ISE design suite tool is employed as an underlying simulation platform. The implementation results are presented on Xilinx Virtex-6 FPGA devices. The achieved results show that the integration of a hybrid Karatsuba multiplier with the proposed BHC architecture results in lower hardware resources. Similarly, the use of a least-significant-digit-parallel multiplier in the proposed design results in high-speed (in terms of both clock frequency and latency). Consequently, the proposed BHC architecture, integrated with a least-significant-digit-parallel multiplier, is 1.42 times faster and utilizes 1.80 times lower FPGA slices when compared to the most recent BHC accelerator architectures.</jats:p>
Throughput/Area-Efficient Accelerator of Elliptic Curve Point Multiplication over GF(2233) on FPGA
This paper presents a throughput/area-efficient hardware accelerator architecture for elliptic curve point multiplication (ECPM) computation over GF(2233). The throughput of the proposed accelerator design is optimized by reducing the total clock cycles using a bit-parallel Karatsuba modular multiplier. We employ two techniques to minimize the hardware resources: (i) a consolidated arithmetic unit where we combine a single modular adder, multiplier, and square block instead of having multiple modular operators, and (ii) an Itoh–Tsujii inversion algorithm by leveraging the existing hardware resources of the multiplier and square units for multiplicative inverse computation.
An efficient finite-state-machine (FSM) controller is implemented to facilitate control functionalities. To evaluate and compare the results of the proposed accelerator architecture against state-of-the-art solutions, a figure-of-merit (FoM) metric in terms of throughput/area is defined. The implementation results after post-place-and-route simulation are reported for reconfigurable field-programmable gate array (FPGA) devices. Particular to Virtex-7 FPGA, the accelerator utilizes 3584 slices, needs 7208 clock
cycles, operates on a maximum frequency of 350 MHz, computes one ECPM operation in 20.59 s, and the calculated value of FoM is 13.54. Consequently, the results and comparisons reveal that our accelerator suits applications that demand throughput and area-optimized ECPM implementations
A Crypto Accelerator of Binary Edward Curves for Securing Low-Resource Embedded Devices.
This research presents a novel binary Edwards curve (BEC) accelerator designed specifically
for resource-constrained embedded systems. The proposed accelerator incorporates the fixed window
algorithm, a two-stage pipelined architecture, and the Montgomery radix-4 multiplier. As a result,
it achieves remarkable performance improvements in throughput and resource utilization. Experimental
results, conducted on various Xilinx Field Programmable Gate Arrays (FPGAs), demonstrate
impressive throughput/area ratios observed for GF(2233). The achieved ratios for Virtex-4, Virtex-5,
Virtex-6, and Virtex-7 are 12.2, 19.07, 36.01, and 38.39, respectively. Furthermore, the processing
time for one-point multiplication on a Virtex-7 platform is 15.87 μs. These findings highlight the
effectiveness of the proposed accelerator for improved throughput and optimal resource utilizationThis research presents a novel binary Edwards curve (BEC) accelerator designed specifically
for resource-constrained embedded systems. The proposed accelerator incorporates the fixed window
algorithm, a two-stage pipelined architecture, and the Montgomery radix-4 multiplier. As a result,
it achieves remarkable performance improvements in throughput and resource utilization. Experimental
results, conducted on various Xilinx Field Programmable Gate Arrays (FPGAs), demonstrate
impressive throughput/area ratios observed for GF(2233). The achieved ratios for Virtex-4, Virtex-5,
Virtex-6, and Virtex-7 are 12.2, 19.07, 36.01, and 38.39, respectively. Furthermore, the processing
time for one-point multiplication on a Virtex-7 platform is 15.87 μs. These findings highlight the
effectiveness of the proposed accelerator for improved throughput and optimal resource utilizatio
On a new generalization of Huff curves
Recently two kinds of Huff curves were introduced as elliptic curves models and their arithmetic was studied. It was also shown that they are suitable for cryptographic use such as Montgomery curves or Koblitz curves (in Weierstrass form) and Edwards curves.
In this work, we introduce the new generalized Huff curves with , which contains the generalized Huff\u27s model with of Joye-Tibouchi-Vergnaud and the generalized Huff curves with of Wu-Feng as a special case.
The addition law in projective coordinates is as fast as in the previous particular cases. More generally all good properties of the previous particular Huff curves, including completeness and independence of two of the four curve parameters, extend to the new generalized Huff curves. We verified that the method of Joye-Tibouchi-Vergnaud for computing of pairings can be generalized over the new curve
Batch Binary Weierstrass
Bitslicing is a programming technique that offers several attractive features,
such as timing attack resistance, high amortized performance in batch
computation, and architecture independence. On the symmetric crypto side, this
technique sees wide real-world deployment, in particular for block ciphers with
naturally parallel modes. However, the asymmetric side lags in application,
seemingly due to the rigidity of the batch computation requirement. In this
paper, we build on existing bitsliced binary field arithmetic results to develop
a tool that optimizes performance of binary fields at any size on a given
architecture. We then provide an ECC layer, with support for arbitrary binary
curves. Finally, we integrate into our novel dynamic OpenSSL engine,
transparently exposing the batch results to the OpenSSL library and linking
applications to achieve significant performance and security gains for key pair
generation, ECDSA signing, and (half of) ECDH across a wide range of curves,
both standardized and non-standard
User-controlled cyber-security using automated key generation
Traditionally, several different methods are fully capable of providing an adequate degree of security to the threats and attacks that exists for revealing different keys. Though almost all the traditional methods give a good level of immunity to any possible breach in security keys, the biggest issue that exist with these methods is the dependency over third-party applications. Therefore, use of third-party applications is not an acceptable method to be used by high-security applications. For high-security applications, it is more secure that the key generation process is in the hands of the end users rather than a third-party. Giving access to third parties for high-security applications can also make the applications more venerable to data theft, security breach or even a loss in their integrity. In this research, the evolutionary computing tool Eureqa is used for the generation of encryption keys obtained by modelling pseudo-random input data. Previous approaches using this tool have required a calculation time too long for practical use and addressing this drawback is the main focus of the research. The work proposes a number of new approaches to the generation of secret keys for the encryption and decryption of data files and they are compared in their ability to operate in a secure manner using a range of statistical tests and in their ability to reduce calculation time using realistic practical assessments. A number of common tests of performance are the throughput, chi-square, histogram, time for encryption and decryption, key sensitivity and entropy analysis. From the results of the statistical tests, it can be concluded that the proposed data encryption and decryption algorithms are both reliable and secure. Being both reliable and secure eliminates the need for the dependency over third-party applications for the security keys. It also takes less time for the users to generate highly secure keys compared to the previously known techniques.The keys generated via Eureqa also have great potential to be adapted to data communication applications which require high security
Elliptic Curve Arithmetic for Cryptography
The advantages of using public key cryptography over secret key
cryptography include the convenience of better key management and
increased security. However, due to the complexity of the
underlying number theoretic algorithms, public key cryptography
is slower than conventional secret key cryptography, thus
motivating the need to speed up public key cryptosystems.
A mathematical object called an elliptic curve can be used in the
construction of public key cryptosystems. This thesis focuses on
speeding up elliptic curve cryptography which is an attractive
alternative to traditional public key cryptosystems such as RSA.
Speeding up elliptic curve cryptography can be done by speeding
up point arithmetic algorithms and by improving scalar
multiplication algorithms. This thesis provides a speed up of
some point arithmetic algorithms. The study of addition chains
has been shown to be useful in improving scalar multiplication
algorithms, when the scalar is fixed. A special form of an
addition chain called a Lucas chain or a differential addition
chain is useful to compute scalar multiplication on some elliptic
curves, such as Montgomery curves for which differential addition
formulae are available. While single scalar multiplication may
suffice in some systems, there are others where a double or a
triple scalar multiplication algorithm may be desired. This
thesis provides triple scalar multiplication algorithms in the
context of differential addition chains. Precomputations are
useful in speeding up scalar multiplication algorithms, when the
elliptic curve point is fixed. This thesis focuses on both
speeding up point arithmetic and improving scalar multiplication
in the context of precomputations toward double scalar
multiplication. Further, this thesis revisits pairing
computations which use elliptic curve groups to compute pairings
such as the Tate pairing. More specifically, the thesis looks at
Stange's algorithm to compute pairings and also pairings on
Selmer curves. The thesis also looks at some aspects of the
underlying finite field arithmetic