An FFT extension of the elliptic curve method of factorization
An FFT extension of the elliptic curve method of factorization
RSA Signature Algorithm for Microcontroller Implementation
CARDIS '98 Proceedings of the The International Conference on Smart Card Research and Applications
Approximate Integer Common Divisors
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Some baby-step giant-step algorithms for the low hamming weight discrete logarithm problem
Mathematics of Computation
Modern Computer Algebra
Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
Fast fourier transform algorithms with applications
Fast fourier transform algorithms with applications
Space- and time-efficient polynomial multiplication
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
The LLL Algorithm: Survey and Applications
The LLL Algorithm: Survey and Applications
An in-place truncated fourier transform and applications to polynomial multiplication
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Cryptanalysis of the RSA subgroup assumption from TCC 2005
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
Implementing Gentry's fully-homomorphic encryption scheme
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Fully homomorphic encryption over the integers with shorter public keys
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Fully Homomorphic Encryption without Squashing Using Depth-3 Arithmetic Circuits
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Cryptography in subgroups of Zn
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Fully homomorphic encryption over the integers
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
BKZ 2.0: better lattice security estimates
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
Cryptanalysis of RSA with private key d less than N0.292
IEEE Transactions on Information Theory
Attacking RSA---CRT signatures with faults on montgomery multiplication
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
Side channel attack to actual cryptanalysis: breaking CRT-RSA with low weight decryption exponents
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
Protecting data confidentiality in cloud systems
Proceedings of the Fourth Asia-Pacific Symposium on Internetware
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At EUROCRYPT '10, van Dijk et al. presented simple fully- homomorphic encryption (FHE) schemes based on the hardness of approximate integer common divisors problems, which were introduced in 2001 by Howgrave-Graham. There are two versions for these problems: the partial version (PACD) and the general version (GACD). The seemingly easier problem PACD was recently used by Coron et al. at CRYPTO '11 to build a more efficient variant of the FHE scheme by van Dijk et al.. We present a new PACD algorithm whose running time is essentially the "square root" of that of exhaustive search, which was the best attack in practice. This allows us to experimentally break the FHE challenges proposed by Coron et al. Our PACD algorithm directly gives rise to a new GACD algorithm, which is exponentially faster than exhaustive search. Interestingly, our main technique can also be applied to other settings, such as noisy factoring and attacking low-exponent RSA.