Factorization of a 512-bit RSA modulus

Authors:
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;Joël Marchand;François Morain;Alec Muffett;Chris Putnam;Craig Putnam;Paul Zimmermann
Affiliations:
CWI, Amsterdam, The Netherlands;Lehigh University, Bethlehem, PA;Citibank, Mendham, NJ;CWI, Amsterdam, The Netherlands;Microsoft Research and CWI, San Rafael, CA;Computer Sciences Laboratory, ANU, Canberra, ACT, Australia;CWI, Amsterdam, The Netherlands;Dept. of Computer Science, Utrecht University, The Netherlands;Entrust Technologies Ltd., Ottawa, ON, Canada;SITX Centre of IT resources, École Polytechnique, Palaiseau, France;Microsoft Research Ltd, Cambridge, UK;Laboratoire Gage, École Polytechnique, CNRS, Palaiseau, France;Laboratoire d'Informatique, École Polytechnique, Palaiseau, France;Sun Microsystems, Riverside Way, Watchmoor Park, Camberley, UK;-;-;Inria Lorraine and Loria, Nancy, France
Venue:
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Year:
2000

Citing 18
Cited 28

Status report on factoring (at the Sandia National Labs)

Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
The number field sieve

STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Factoring numbers using singular integers

STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Factoring by electronic mail

EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Factoring with two large primes (extended abstract)

EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
On the factorization of RSA-120

CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Factoring integers using SIMD sieves

EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
A method for obtaining digital signatures and public-key cryptosystems

Communications of the ACM
Some Parallel Algorithms for Integer Factorisation

Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
The Magic Words are Squeamish Ossifrage

ASIACRYPT '94 Proceedings of the 4th International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
A World Wide Number Field Sieve Factoring Record: On to 512 Bits

ASIACRYPT '96 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Factorization of RSA-140 Using the Number Field Sieve

ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Selecting Cryptographic Key Sizes

PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Lattice sieving and trial division

ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Modelling the Yield of Number Field Sieve Polynominals

ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Strategies in Filtering in the Number Field Sieve

ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Factoring Large Numbers with the Twinkle Device (Extended Abstract)

CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
A block Lanczos algorithm for finding dependencies over GF(2)

EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques

Fast computation of linear generators for matrix sequences and application to the block Wiedemann algorithm

Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Subquadratic computation of vector generating polynomials and improvement of the block Wiedemann algorithm

Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
A Practical Architecture for Reliable Quantum Computers

Computer
Quantum Computing: The Final Frontier?

IEEE Intelligent Systems
Note on Fast Computation of Secret RSA Exponents

ACISP '02 Proceedings of the 7th Australian Conference on Information Security and Privacy
Unconditionally Secure Digital Signature Schemes Admitting Transferability

ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Cryptanalysis of the RSA Schemes with Short Secret Exponent from Asiacrypt '99

ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Computation of Discrete Logarithms in F2607

ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Analysis of Bernstein's Factorization Circuit

ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Cryptography 2000±10

Informatics - 10 Years Back. 10 Years Ahead.
A Signcryption Scheme Based on Integer Factorization

ISW '00 Proceedings of the Third International Workshop on Information Security
Efficient and Unconditionally Secure Digital Signatures and a Security Analysis of a Multireceiver Authentication Code

PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Increasing the Bitlength of a Crypto-Coprocessor

CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
The Two Faces of Lattices in Cryptology

CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
A Dedicated Sieving Hardware

PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
Improvements to the general number field sieve for discrete logarithms in prime fields: a comparison with the Gaussian integer method

Mathematics of Computation
A Quantum Logic Array Microarchitecture: Scalable Quantum Data Movement and Computation

Proceedings of the 38th annual IEEE/ACM International Symposium on Microarchitecture
Architectural implications of quantum computing technologies

ACM Journal on Emerging Technologies in Computing Systems (JETC)
On the relations between non-interactive key distribution, identity-based encryption and trapdoor discrete log groups

Designs, Codes and Cryptography
ECM on Graphics Cards

EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Choosing NTRUEncrypt Parameters in Light of Combined Lattice Reduction and MITM Approaches

ACNS '09 Proceedings of the 7th International Conference on Applied Cryptography and Network Security
A kilobit special number field sieve factorization

ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
Factorization of a 768-bit RSA modulus

CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Long-term confidentiality of PKI

Communications of the ACM
Load balanced block lanczos algorithm over GF(2) for factorization of large keys

HiPC'06 Proceedings of the 13th international conference on High Performance Computing
RSA with balanced short exponents and its application to entity authentication

PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
Practical RSA signature scheme based on periodical rekeying for wireless sensor networks

ACM Transactions on Sensor Networks (TOSN)
Scalable hardware for sparse systems of linear equations, with applications to integer factorization

CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems

Quantified Score

Hi-index	0.02

Visualization

Abstract

This paper reports on the factorization of the 512-bit number RSA-155 by the Number Field Sieve factoring method (NFS) and discusses the implications for RSA.