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Factorization of a 768-Bit RSA Modulus [chapter]

Thorsten Kleinjung, Kazumaro Aoki, Jens Franke, Arjen K. Lenstra, Emmanuel Thomé, Joppe W. Bos, Pierrick Gaudry, Alexander Kruppa, Peter L. Montgomery, Dag Arne Osvik, Herman te Riele, Andrey Timofeev (+1 others)
2010 Lecture Notes in Computer Science  
This paper reports on the factorization of the 768-bit number RSA-768 by the number field sieve factoring method and discusses some implications for RSA.  ...  Part of this paper was inspired by Col. Hans Landa.  ...  We acknowledge the help of Cyril Bouvier during filtering and merging experiments.  ... 
doi:10.1007/978-3-642-14623-7_18 fatcat:237trz7ofzdmhbacw6ab5wd4ju

Universal Security [chapter]

Arjen K. Lenstra, Thorsten Kleinjung, Emmanuel Thomé
2013 Lecture Notes in Computer Science  
In this note a universal security measure is proposed that puts all cryptographic primitives on the same footing, thereby making it easier to get comparable security across the board.  ...  Acknowledgements We gratefully acknowledge usage of Wikipedia and gladly blame its contributors for any errors in our data.  ...  The 2009 factorization of a 768-bit modulus took roughly a year on 2000 cores running at 2GHz. With N (1024) N (768) ≈ 1200, a 1024-bit modulus can be factored within two million 2GHz core-years.  ... 
doi:10.1007/978-3-642-42001-6_9 fatcat:4dj5nww6xnf67ow6ssh2okbdxq

Fast RSA-type cryptosystem modulo p k q [chapter]

Tsuyoshi Takagi
1998 Lecture Notes in Computer Science  
68-bit modulus p2q for 256-bit primes p and q, then the decryption process of the proposed cryptosystem is about 3 times faster than that of RSA cryptosystem using Quisquater-Couvreur method.  ...  We propose a cryptosystem modulo pkq based on the RSA cryptosystem.  ...  Therefore, if we choose the 768-bit modulus p2q with 256-bit primes p and q, neither of the factoring algorithms is feasible, so the scheme is secure for cryptographic purposes.  ... 
doi:10.1007/bfb0055738 fatcat:u3nisbrleja4djy3i3zq7opjey

On the Design of RSA with Short Secret Exponent [chapter]

Hung-Min Sun, Wu-Chuan Yang, Chi-Sung Laih
1999 Lecture Notes in Computer Science  
As an example, we can construct a secure RSA system with p of 256 bits, q of 768 bits, d of 256 bits, and e of 880 bits.  ...  Compared with a typical RSA system in which e is the same order of magnitude as N if d is first selected, these variants of RSA have the advantage that the overall computation can be significantly reduced  ...  As an example, we can construct a secure RSA with p of 256 bits, q of 768 bits, d of 256 bits, and e of 880 bits.  ... 
doi:10.1007/978-3-540-48000-6_13 fatcat:k4rahko5dbgxlhyrvd4rr2g5xq

An Overview of Cryptanalysis of RSA Public key System

Berlin K, Dhenakaran S.S
2017 International Journal of Engineering and Technology  
The main principle of RSA is providing tough security from the difficulty of factoring large integers.  ...  It secured sensitive data while the transmission of secrets through the improper channel like internet. It key sizes 1024 to 4096, 768 bit key had been broken.  ...  From the above reference table, RSA has 80 bits of strength for 1024 modulus size and 2048 bits of RSA modulus size has the strength of 112bits approximately.  ... 
doi:10.21817/ijet/2017/v9i5/170905312 fatcat:avttklyuu5exrifhnsjonfyzn4

A Generalize Estimating the Ø(n) of Upper-Lower Bound to RSA Public Key Crytosystem

Jie Fang, Chenglian Liu
2018 International Journal of Network Security  
The RSA-200 (663 bits) was factored by Bahr et al. on May 9, 2005, while he RSA-210 (696 bits) was factored by Propper on September 26, 2013.  ...  The RSA-768 (270 decimal digits) was factored by Kleinjung et al. on December 12, 2009, while the RSA-704 (212 decimal digits) was factored by Bai et al. on July 2, 2012.  ...  This work is partially supported from Fujian Provincial Department of Education, the education and scientific research projects for young and middle-  ... 
dblp:journals/ijnsec/FangL18 fatcat:a7ct73ptqna5hgvvlifdk5yjtm

Parallelizing RSA Algorithm on Multicore CPU and GPU

Heba MohammedFadhil, Mohammed Issam Younis
2014 International Journal of Computer Applications  
Public key algorithms are extensively known to be slower than symmetric key alternatives in the a r e a of cryptographic algorithms for the reason of their basis in modular arithmetic.  ...  This paper proposes a hybrid system to parallelize the RSA for multicore CPU and many cores GPUs with variable key size.  ...  Therefore, two primes p and q should be chosen to have just about the same bit length to guarantee that any efforts to factor the modulus are computationally infeasible.  ... 
doi:10.5120/15211-3704 fatcat:mtaybtpmivfi5bmnaufi3xqh7a

Computing Power, Key Length and Cryptanalysis. An Unending Battle? [article]

A. Dasso, A. Funes, D. Riesco, G. Montejano
2020 arXiv   pre-print
We review here ways to determine the security, given an span of time, of a factoring-based encryption method, such as RSA, by establishing a relation between the processing power needed to break a given  ...  On the other hand, Bit Length (BL) can be considered a metric to measure the strength of an asymmetric encryption method.  ...  The size of an RSA key refers either to the bit-length of the RSA modulus or the number of decimal digits of the number (n in equation (1) and ¡Error!  ... 
arXiv:2011.00985v1 fatcat:qs45vgk775hxnfzc2kcmzpfari

Two efficient RSA multisignature schemes [chapter]

Sangjoon Park, Sangwoo Park, Kwangjo Kim, Dongho Won
1997 Lecture Notes in Computer Science  
The first one causes bit expansion in block size of a multisignature, but the bit length of the expansion is no more greater than the number of signers regardless of their RSA modulus.  ...  The second one has no bit expansion, in which all signers have a RSA modulus with the same bit size and the same most significant 1 bits pattern.  ...  All users must have a RSA modulus of a fixed length, k bits, the most significant i bits of which are the same.  ... 
doi:10.1007/bfb0028477 fatcat:cszys65l2ze7hmxvrvwmhexg7i

Incorporating Error Detection in an RSA Architecture [chapter]

L. Breveglieri, I. Koren, P. Maistri, M. Ravasio
2006 Lecture Notes in Computer Science  
(p-1)(q-1) A faulty signature allows to factor the modulus N easily (and thus recover the private key) FDTC 2005 Incorporating Error Detection in an RSA Architecture 6 The Basic RSA Architecture  ...  detection rate out of hundreds of tests Undetected faults: Transient double faults Random 16-bit value injected once in two different 16-bit blocks of the same word at a random time 0% detection  ... 
doi:10.1007/11889700_7 fatcat:bdcsuk7ywne23aw7upqwsawbjm

Efficient variant of RSA cryptosystem

Yun-fei LI, Qing LIU, Lin HAO, Bao-lin ZHOU
2010 Journal of Computer Applications  
We describe an efficient combination of two variants of RSA cryptosystem (MPrime and Rebalanced RSA) analysed by Boneh and Schacham [2] .  ...  The decryption process resultant is (for 2048-bits moduli) about 8 times faster than that presented by Quisquater and Couvreur [9] and about 27 times faster than original cryptosystem.  ...  Acknowledgements We would like to thank Paulo Barreto and Leon Achjian Jr for their comments and support during the development of this work.  ... 
doi:10.3724/sp.j.1087.2010.02393 fatcat:hpeqcbbga5dvlcsemkmp7ykewy

Factorization of a 512-Bit RSA Modulus [chapter]

Stefania Cavallar, Bruce Dodson, Arjen K. Lenstra, Walter Lioen, Peter L. Montgomery, Brian Murphy, Herman te Riele, Karen Aardal, Jeff Gilchrist, Gérard Guillerm, Paul Leyland, Jöel Marchand (+4 others)
2000 Lecture Notes in Computer Science  
This paper reports on the factorization of the 768-bit number RSA-768 by the number field sieve factoring method and discusses some implications for RSA.  ...  Part of this paper was inspired by Col. Hans Landa.  ...  We acknowledge the help of Cyril Bouvier during filtering and merging experiments.  ... 
doi:10.1007/3-540-45539-6_1 fatcat:xxt34apgbrfp7o73tvgya7blnm

Ron was wrong, Whit is right [article]

Arjen K. Lenstra, James P. Hughes, Maxime Augier, Joppe W. Bos, Thorsten Kleinjung, Christophe Wachter
2012 IACR Cryptology ePrint Archive  
We found that the vast majority of public keys work as intended. A more disconcerting finding is that two out of every one thousand RSA moduli that we collected offer no security.  ...  We performed a sanity check of public keys collected on the web. Our main goal was to test the validity of the assumption that different random choices are made each time keys are generated.  ...  Hughes participated in this project in his individual capacity without sponsorship of his employer or any other party.  ... 
dblp:journals/iacr/LenstraHABKW12 fatcat:dqr7g5hvezafbdgtmys6kbvj7q

Mathematical Attack of RSA by Extending the Sum of Squares of Primes to Factorize a Semi-Prime

Anthony Overmars, Sitalakshmi Venkatraman
2020 Mathematical and Computational Applications  
The security of RSA relies on the computationally challenging factorization of RSA modulus with being a large semi-prime consisting of two primes for the generation of RSA keys in commonly adopted cryptosystems  ...  We present the algorithm showing the simplicity of steps that use rudimentary arithmetic operations requiring minimal memory, with search cycle time being a factor for very large semi-primes, which can  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/mca25040063 fatcat:go6vdxizvnbhdozlc5jvnyrldq

A new public key cryptosystem based on higher residues

David Naccache, Jacques Stern
1998 Proceedings of the 5th ACM conference on Computer and communications security - CCS '98  
The deterministic version is practically oriented: encryption amounts to a single exponentiation w.r.t. a modulus with at least 768 bits and a 160-bit exponent.  ...  This paper describes a new public-key cryptosystem based on the hardness of computing higher residues modulo a composite RSA integer.  ...  Acknowledgements The paper grew out of a previous version which did not include the probabilistic case of our scheme.  ... 
doi:10.1145/288090.288106 dblp:conf/ccs/NaccacheS98 fatcat:czqcxtkprzazxe2rfsrcjyecaq
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