rsa algorithm research papers



Fast implementations of RSA cryptography
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M Shand, J Vuillemin ,Computer Arithmetic, 1993. Proceedings , 1993
 Ours appears to be the first reported working hardware implementation of RSA to operate in  The
following is a generalization of an original algorithm in [MO 851: Algorithm 6 (Modular Product)
Let A, B, M E N be three integers, each presented by n mdiz p = 2P digits A = [%-1 

A new RSA cryptosystem hardware design based on Montgomery’s algorithm
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 Comput., vol. 42, pp. 693–699, June 1993. [7] N. Shand and J. Vuillemin, Fast implementations
of RSA cryptogra- phy, in Proc. 11th Symp. on Computer Arithmetic, 1993, pp. 252–259.  913
CD Walter, Systolic modular multiplication, IEEE Trans. Comput., vol. 42, pp. 

Hardware implementation of a Montgomery modular multiplier in a systolic array
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 and Paar [3]. The latency of processing elements used to construct the systolic array introduced 
of repetitions for Montgomery’s algorithm is only n + 2 for radix 2 implementations, compared
with  architecture is equally suitable for both types of cryptography, ECC as well as RSA. 

A scalable architecture for modular multiplication based on Montgomery’s algorithm
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 exponentiation [11], [12], which is required in the Diffie-Hellman and RSA public-key  Recent
implementations of the Montgomery Multiplication are focused on elliptic curve cryptography
[15] over  These problems are reduced in systolic architectures [17], [18], at the cost of extra 

Two implementation methods of a 1024-bit RSA cryptoprocessor based on modified Montgomeryalgorithm
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TW Kwon, CS You, WS Heo, YK Kang ,Circuits and Systems, , 2001
 In a systolic implementation  . the addition can be operated by a full adder.  “Hardware
implementation of Montgomery’s modular multiplication algorithm.” IEEE Trans. Conzpzrt.. vol. 
“A new RSA cryptosystem hardware design based on Montgomery’s algorithm.” IEEE Trans. 

FPGA implementation of RSA public-key cryptographic coprocessor
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 Reconfigurable computing allows the designer to respond, in the prototyping stage, to flaws
discovered in implementation or to changes in standards or data formats.  Keywords: RSA
algorithm, Montgomery algorithm, systolic array architecture, FPGA. 

Montgomery modular exponentiation on reconfigurable hardware
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 is at the heart of many practical public-key algorithms such as RSA and discrete  We combine
the Montgomery modular multiplication algorithm with a new systolic array design, which is  the
feasibility and time-space trade-offs of our architecture for implementation on Xilinx 

Two systolic architectures for modular multiplication
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WC Tsai, CB Shung, SJ Wang ,Very Large Scale Integration ( , 2000
 1994. [10] PS Chen, SA Hwang, and CW Wu, A systolic RSA public key cryptosystem, in Proc.
IEEE Int. Symp. Circuits and Systems (ISCAS), May 1996, pp. 408–411. [11] M. Shand and J.
Vuillemin, Fast implementation of RSA cryptog- raphy, in Proc. 11th IEEE Symp. 

High-radix Montgomery modular exponentiation on reconfigurable hardware
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M. Shand and J. Vuillemin, ªFast Implementations of RSA Cryptography,º Proc.  [4] SE
Eldridge and CD Walter, ªHardware Implementation of Montgo- mery’s Modular Multiplication
Algorithm,º IEEE Trans. 

Fast architectures for FPGA-based implementation of RSA encryption algorithm
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This paper proposes new and efficient FPGA based hardware implementations
of RSA algorithm based on a modified Montgomery’s  A systolic approach for the implementation
strategy has been adopted in this paper in order to achieve a high clock frequency. 

Hardware architectures for public key cryptography
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Modular multiplication; 3.3.1. Montgomery’s multiplication method (MMM); 3.3.2. Other
algorithms. 3.4. Architectures for RSA; 3.4.1. Systolic array; 3.4.2. Non-systolic array;
3.4.3. Residue number system; 3.4.4. CRT based implementations. 3.5. 

Design and implementation of a coprocessor for cryptography applications
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A Royo, J Moran, JC Lopez , of the 1997 European conference on , 1997 ,dl.acm.org
 References l:l] PS Chen, SA Hwang, and CW Wu, A systolic RSA Public Key Cryptosystem ,
Proc. of ISCA!J, 1995.  2, pp. 120-126, Feb. I!978 [S] M. Shand, J. Vuillemin, Fast Implementations
of RSA Cryptography. Proceedings 1 lth Symposium on Computer Arithmetic, pp. 

A scalable architecture for RSA cryptography on large FPGAs
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EA Michalski, DA Buell , Logic and Applications, 2006. FPL’06. , 2006
 of the MWRkMM algorithm is based on the use of a systolic array of  FPGA environment, and
demonstrate an efficient implementation for a 1024-bit RSA core consisting of  with both FPGAs
tested allowing for additional functional parallelism through multiple core implementation. 

Modular exponentiation using parallel multipliers
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SH Tang, KS Tsui, PHW Leong , Technology (FPT), 2003. , 2003
 in a Mont- gomery multiplier, and a semi-systolic pipeline scheme were employed to maximize
the clock rate and  is pre-computed as the negative modular inverse of M, ie (-MM’) mod R = 1.
An implementation of Montgomery’s method for RSA typically interleaves 

An efficient implementation of the digital signature algorithm
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Chih-Yuang Su, Shih-Am Hwang, Po-Song Chen, and Cheng-Wen Wu, An Improved
Montgomery’s Algorithm for High  [I31 P. S. Chen, S. A. Hwang, and CW Wu, A systolic RSA public
key  A VLSI implementation of the digital signature scheme is presented in this paper. 

High speed FPGA implementation of RSA encryption algorithm
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O Nibouche, M Nibouche ,Electronics, Circuits and , 2003
 A bit serial parallel implementation of Algorithm 4 is shown in Figure 3. The algorithm is  In Figure
4, a bit-serial architecture that it is fully systolic is depicted.  For RSA cryptography, the two
interleaved modular multiplication operations are the two operations involved in the 

 Towards an FPGA architecture optimized for public-key algorithms
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 Redundant Representation and Systolic Array implementations, the two strategies typically used
to perform high-speed wide-operand addition, were evaluated based on their performance.  [9]
Shand, M. and J. Vuillemin (1993). Fast Implementations of RSA Cryptography. 

Fast algorithm for modular reduction
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QK Kop, CY Hung ,Computers and Digital Techniques, IEE , 1998
 based on this concept has strictly right-to-left communications, and thus leads to very efficient
systolic implementation [ 131.  Applications are found in crypto- systems based on modular
exponentiation, for example, the RSA algorithm [14], the ElGamal signature scheme [15], and 


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