Montgomery and RNS for RSA Hardware Implementation (original) (raw)
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A Faster Hardware Implementation of RSA Algorithm
2002
The performance of most crypto systems is primarily determined by an efficient implementation of arithmetic operations. When implementing public key cryptography such as RSA the primary requirements are high speed arithmetic computation, small size and low power consumption and resistance to side channel attacks. In this paper an efficient way to explore fast modular operation has been explored, using redundant digit sets with higher radices and making modifications to Montgomery’s Algorithm in order to explore deep pipelining at architecture level which improves the throughput and latency of the system. This paper presents a solution to the problems of existing methods, proposes an actual implementation of the solution and demonstrates the benefit of the proposed approach. I suspect my algorithm to be nearly optimal and challenge the cryptographic community for better results.
Efficient RSA Crypto Processor Using Montgomery Multiplier in FPGA
Advances in Intelligent Systems and Computing, 2019
With the advancement of technology in data communication, security plays a major role in protecting user’s data from adversaries. Cryptography is a technique which consists of various algorithms to provide secure communication during data transfer. One of the most widely used and highly secure algorithm is RSA (Rivest, Adi Shamir and Leonard Adleman). This research is going to focus on designing an efficient crypto processor for RSA on Nexys4, a ready-to-use FPGA (Field Programmable Gate Array) board. There are various techniques in implementing RSA algorithm in hardware platforms. Primary concentration is to implement the algorithm in a high performant manner, and it will be achieved using Montgomery multiplication technique. RSA is a public key cryptography system which involves generation of public key for encryption and private key for decryption. Building blocks of RSA includes: Two multiplier blocks, two blocks to verify the primality of random numbers, one GCD (Greatest Commo...
A new RSA cryptosystem hardware design based on Montgomery's algorithm
IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 1998
In this paper, we propose a new algorithm based on Montgomery's algorithm to calculate modular multiplication that is the core arithmetic operation in an RSA cryptosystem. The modified algorithm eliminates over-large residue and has very short critical path delay that yields a very high-speed processing. The new architecture based on this modified algorithm takes about 1:5n 2 clock cycles on the average to finish one n-bit RSA operation. We have implemented a 512-bit single-chip RSA processor based on the modified algorithm with Compass 0.6-m SPDM CMOS cell library. The simulation results show that the processor can operate up to 125 MHz and deliver the baud rate of 164 Kbits/s on the average.
Hardware modules of the RSA algorithm
Serbian Journal of Electrical Engineering, 2014
This paper describes basic principles of data protection using the RSA algorithm, as well as algorithms for its calculation. The RSA algorithm is implemented on FPGA integrated circuit EP4CE115F29C7, family Cyclone IV, Altera. Four modules of Montgomery algorithm are designed using VHDL. Synthesis and simulation are done using Quartus II software and ModelSim. The modules are analyzed for different key lengths (16 to 1024) in terms of the number of logic elements, the maximum frequency and speed.
Fast Montgomery modular multiplication and RSA cryptographic processor architectures
The Thrity-Seventh Asilomar Conference on Signals, Systems & Computers, 2003, 2003
New, generic silicon architectures for implementing Montgomery's multiplication algorithm are presented. These use Carry Save Adders (CSAs) to perform the large word length additions required by this algorithm when used for RSA encryption and decryption. It is shown that using a four-to-two CSA with two extra registers rather than a five-to-two CSA leads to a useful reduction in the critical path of the multiplier, albeit at the expense of a small increase in circuitry. For operand lengths of 1536-bits and greater, the percentage gain in data throughput rate outweighs the percentage increase in silicon area. Moreover, for a 2048-bit operand length, typical of what is required in many future generation applications, the gain in data throughput is 27.9% compared with a 9.9% increase in area. The practical application of this approach has been demonstrated by applying this to the design of RSA processor architectures with 512-bit and 1024-bit key sizes. The resulting Montgomery multiplier and RSA processor performance results presented are the fastest reported to date in the literature.
RSA (Rivest, Shamir, Adleman) is one of the most widely used cryptographic algorithms worldwide to perform data encryption and decryption. An essential step in RSA computation lies on its modular multiplication which is relatively expensive and time consuming to be implemented in hardware. This paper proposes two modular multiplication architectures based on modified serial montgomery algorithm for 2048-bit RSA. By limiting the integer modulo that has sequence of A094358, a very simple and fast modular multiplication hardware can be developed. The first archictecture which incorporates 2048-bit adders performes better in term of latency (19010 Logic Cells, 2048 clock cycles or 0.0022 s), while the second architecture utilizing multiple smaller 128-bit adders offers less area consumption (8926 Logic Cells, 36864 clock cycles or 0.0031 s). An area multiplied with squared latency (AT 2) can be used as trade-off parameter for choosing the most suitable design for certain need. For prototyping purpose, we have successfully synthesized and implemented our proposed designs written in VHDL using Altera Quartus II with Cyclone II EP2C70F896C6 FPGA as a target board.
Montgomery modular multiplier architectures and hardware implementations for an RSA cryptosystem
2003
This paper describes and analyses the Montgomery Multiplication Algorithm and proposes two scalable, systolic architectures and hardware implementations based on this algorithm in order to be used for an RSA module. The Conventional Architecture uses the original version of Montgomery Multiplication Algorithm and the Optimized Architecture a modified version of the algorithm. The second architecture is considerably better than the first one Both architectures follow Carry -Save redundant logic and in comparison with other known architecture give interesting results in term of clock frequency, Multiplication time and chip Covered area..
Reducing Runtime of RSA Processors Based On High-Radix Montgomery Multipliers.
International Journal of Engineering Sciences & Research Technology, 2013
Depends on various requirements the paper presents & optimized Rivest processor which satisfies circuit area, operating time. we also introduces 3 multiplier based data path using different intermediate data forms: 1) single form, 2) wide variety of arithmetic components. A total of 242 datapaths for 1024 radix. We can reduce the RSA runtime up to 0.24ms. As a result, the faste in less than 1.0 ms.
EFFICIENT ASIC ARCHITECTURE OF RSA CRYPTOSYSTEM
This paper presents a unified architecture design of the RSA cryptosystem i.e. RSA cryptoaccelerator along with key-pair generation. A structural design methodology for the same is proposed and implemented. The purpose is to design a complete cryptosystem efficiently with reduced hardware redundancy. Individual modular architectures of RSA, Miller-Rabin Test and Extended Binary GCD algorithm are presented and then they are integrated. Standard algorithm for RSA has been used. The RSA datapath has further been transformed into DPA resistant design. The simulation and implementation results using 180nm technology are shown and prove the validity of the architecture.
Efficient FPGA Implementation of RSA Coprocessor Using Scalable Modules
The 9th International Conference on Future Networks and Communications (FNC'14)/The 11th International Conference on Mobile Systems and Pervasive Computing (MobiSPC'14)/Affiliated Workshops/EICM 2014, At Canada, Volume: 34, 2014
RSA Cryptosystem is considered the first practicable secure algorithm that can be used to protect information during the communication. The significance of high security and efficient implementations of RSA have formed the base of many cryptographic engineering researches. In fact, the implementation of RSA Cryptosystem is heavily based on modular arithmetic and exponentiation involving large prime numbers. In this paper, we propose an efficient FPGA design and architecture for RSA cryptosystem using ALTERA FPGA Hardware Kit. The proposed design comprises six levels: random two prime numbers, parallel multiplication of the prime numbers and their decremented values, get encryption key, get decryption key, encryption and decryption levels. As the modular multiplication is considered as the heart of RSA computations, Interleaved Algorithm was particularly chosen as an efficient solution to speed up the modular multiplication. The experimental part of this work has been synthesized for...