Concept

Factor base

Related publications (9)

Quadratic Sieving

We propose an efficient variant for the initialisation step of quadratic sieving, the sieving step of the quadratic sieve and its variants, which is also used in sieving-based algorithms for computing class groups of quadratic fields. As an application we ...

American Mathematical Society2016

MicroRNA profiling by simultaneous selective isotachophoresis and hybridization with molecular beacons

Alexandre Louis André Persat

We present and demonstrate a novel assay for the detection and quantification of microRNA (miRNA) that leverages isotachophoresis (ITP) and molecular beacon (MB) hybridization. We use ITP to selectively preconcentrate miRNA from total RNA. We simultaneousl ...

American Chemical Society2011

VSH, an efficient and provable collision-resistant hash function

Arjen Lenstra

We introduce VSH, very smooth hash, a new S-bit hash function that is provably collision-resistant assuming the hardness of finding nontrivial modular square roots of very smooth numbers modulo an S-bit composite. By very smooth, we mean that the smoothnes ...

Springer Verlag2006

Factoring estimates for a 1024-bit RSA modulus

Arjen Lenstra, Pénélope Leyland

We estimate the yield of the number field sieve factoring algorithm when applied to the 1024-bit composite integer RSA-1024 and the parameters as proposed in the draft version [17] of the TWIRL hardware factoring device [18]. We present the details behind ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2003

Analysis of Bernstein's factorization circuit

Arjen Lenstra

D.J. Bernstein has proposed a circuit-based implementation of the matrix step of the number field sieve factorization algorithm (see "Circuits for integer factorization: a proposal", http://cr.yp.to/papers.html#nfscircuit, 2001). These circuits offer an as ...

2002

Analysis and optimization of the TWINKLE factoring device

Arjen Lenstra

We describe an enhanced version of the TWINKLE factoring device and analyse to what extent it can be expected to speed up the sieving step of the quadratic Sieve and number field Sieve factoring algorithms. The bottom line of our analysis is that the TWINK ...

2000

The magic words are squeamish ossifrage [RSA public key cryptography]

Arjen Lenstra, Pénélope Leyland

We describe the computation which resulted in the title of this paper. Furthermore, we give an analysis of the data collected during this computation. From this data, we derive the important observation that in the final stages, the progress of the double ...

1995

The number field sieve

Arjen Lenstra

The number field sieve is an algorithm to factor integers of the form

r^e-s

for small positive

r

and

s

. The authors present a report on work in progress on this algorithm. They informally describe the algorithm, discuss several implementation related ...

Springer Berlin Heidelberg1993

Factoring with two large primes

Arjen Lenstra

We describe a modification to the well-known large prime variant of the multiple polynomial quadratic sieve factoring algorithm. In practice this leads to a speed-up factor of 2 to 2.5. We discuss several implementation-related aspects, and we include some ...

1991

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The number field sieve

Arjen Lenstra

The number field sieve is an algorithm to factor integers of the form

r^e-s

for small positive

r

and

s

. The authors present a report on work in progress on this algorithm. They informally describe the algorithm, discuss several implementation related ...

Springer Berlin Heidelberg1993