Improved Trial Division Algorithm by Lagrange?s Interpolation Function

Nowadays data communication over the internetgrowths the security risk on the side of receiver and transmitter. To reduce risk level, cryptography technique has been used which is based on aprivate and public key in disquiet of endorsement. The process of encryption and decryption improved the capacity of data security. Asymmetric cryptography technique provides renowned RSA public key cryptography technique. The success story of RSA algorithm depends on the prime factor. For the estimation of theprime factor used various mathematical functions. In this paper,Lagrange?s interpolation derivation for the estimation of aprime factoris used. The estimated prime factor is very complex and reduces the complexity of prime factor

Utilizing the Double-Precision Floating-Point Computing Power of GPUs for RSA Acceleration

Asymmetric cryptographic algorithm (e.g., RSA and Elliptic Curve Cryptography) implementations on Graphics Processing Units (GPUs) have been researched for over a decade. The basic idea of most previous contributions is exploiting the highly parallel GPU architecture and porting the integer-based algorithms from general-purpose CPUs to GPUs, to offer high performance. However, the great potential cryptographic computing power of GPUs, especially by the more powerful floating-point instructions, has not been comprehensively investigated in fact. In this paper, we fully exploit the floating-point computing power of GPUs, by various designs, including the floating-point-based Montgomery multiplication/exponentiation algorithm and Chinese Remainder Theorem (CRT) implementation in GPU. And for practical usage of the proposed algorithm, a new method is performed to convert the input/output between octet strings and floating-point numbers, fully utilizing GPUs and further promoting the overall performance by about 5%. The performance of RSA-2048/3072/4096 decryption on NVIDIA GeForce GTX TITAN reaches 42,211/12,151/5,790 operations per second, respectively, which achieves 13 times the performance of the previous fastest floating-point-based implementation (published in Eurocrypt 2009). The RSA-4096 decryption precedes the existing fastest integer-based result by 23%

Optimizing MAKWA on GPU and CPU

We present here optimized implementations of the MAKWA password hashing function on an AMD Radeon HD 7990 GPU, and compare its efficiency with an Intel i7 4770K CPU for systematic dictionary attacks. We find that the GPU seems to get more hashing done for a given budget, but not by a large amount (the GPU is less than twice as efficient as the CPU). Raising the MAKWA modulus size to 4096 bits, instead of the default 2048 bits, should restore the balance in favour of the CPU. We also find that power consumption, not hardware retail price, is likely to become the dominant factor for industrialized, long-term attacking efforts

Low-Overhead Techniques For Secure And Reliable Gpu Computing

In recent years, Graphics Processing Units (GPUs) have become a de facto choice to accelerate the computations in various domains such as machine learning, security, financial and scientific computing. GPUs leverage the inherent data parallelism in the target applications to provide high throughput at superior energy efficiency. Due to the rising usage of GPUs for a large number of applications, they are facing new challenges, especially in the security and reliability domains. From the security side, recently several microarchitectural attacks targeting GPUs have been demonstrated. These attacks leak the secret information stored on GPUs, for example, the parameters of a neural network (NN) model and the private user information. From the reliability side, the innovations to improve GPU memory systems are making them more susceptible to errors. My dissertation research focuses on addressing these security and reliability challenges in GPUs while minimizing the associated overhead of the proposed protection mechanisms. To improve GPU security, we focus on the previously demonstrated correlation timing attack. Such an attack exploits the deterministic nature of the coalescing mechanism in GPUs to correlate the execution time and the number of accesses. Consequently, an attacker can recover the encryption keys stored on GPUs. Therefore, to counter the correlation timing attack, we first introduce a randomized coalescing defense scheme (RCoal). RCoal randomizes the coalescing logic such that the attacker fails to correlate the execution time and the number of accesses. As a result, RCoal thwarts the correlation timing attack. Next, we propose a bucketing-based coalescing defense scheme, BCoal, which minimizes the variation in the number of memory accesses by generating a predetermined number (called buckets) of memory accesses. With low variation in the number of memory accesses, the attacker cannot correlate the application execution time and the secret information, thus failing the correlation timing attack. BCoal generates less memory traffic than RCoal and, therefore, is performance efficient. To improve GPU reliability, we address the data memory faults in GPU caches and DRAM. Existing reliability mechanisms of redundancy and check-pointing fail to scale with the increasing memory/computational demands on GPUs and quickly become impractical. To address this problem, we study a wide range of applications to nd that a very small fraction of the data memory is most vulnerable to faults. This small fraction of the data is not only highly accessed but also highly shared across GPU threads. Consequently, we propose and develop two reliability schemes to detect-only and to detect/correct faults in this most vulnerable data while incurring low overhead. The focus of ongoing and future work is to improve the reliability of machine learning applications