A. K. Lenstra

Publications180
h-index49
Citations11,427
Highly Influential Citations783
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Factoring polynomials with rational coefficients
TLDR
We present a Polynomial-time algorithm to solve the following problem: given a non-zero polynomial fe Q(X) in one variable with rational coefficients, find the decomposition of f into irreducible factors in Z(X). Expand
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  • 349
  • PDF
The XTR Public Key System
This paper introduces the XTR public key system. XTR is based on a new method to represent elements of a subgroup of a multiplicative group of a finite field. Application of XTR in cryptographic… Expand
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  • 38
  • PDF
Selecting Cryptographic Key Sizes
TLDR
We give guidelines for the determination of cryptographic key sizes, based on a set of explicitly formulated hypotheses, combined with existing data points. Expand
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  • 36
Factorization of a 768-Bit RSA Modulus
TLDR
This paper reports on the factorization of the 768-bit RSA-768 by the number field sieve factoring method and discusses some implications for RSA. Expand
  • 430
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Selecting Cryptographic Key Sizes
TLDR
We offer guidelines for the determination of key sizes for symmetric cryptosystems, RSA, and discrete logarithm-based cryptsystems both over finite fields and over groups of elliptic curves. Expand
  • 700
  • 18
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Hard Equality Constrained Integer Knapsacks
We consider the following integer feasibility problem: Given positive integer numbersa0,a1, ... , a n , with gcd( a1,..., a n ) = 1 anda = ( a1,..., a n ), does there exist a vectorx?Z n… Expand
  • 45
  • 15
Chosen-Prefix Collisions for MD5 and Colliding X.509 Certificates for Different Identities
TLDR
We present a novel, automated way to find differential paths for MD5 at an approximate expected cost of 250 calls to the compression function. Expand
  • 179
  • 13
  • PDF
The Development of the Number Field Sieve
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… Expand
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  • 12
The number field sieve
TLDR
The number field sieve is an algorithm to factor integers of the form re − s for small positive r and |s| using arithmetic in an algebraic number field. Expand
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  • 12
  • PDF
A random zoo: sloth, unicorn, and trx
TLDR
We show how sloth can be used for uncontestable random number generation (unicorn), and how unicorn is used for a new trustworthy random ellip­ tic curves service. Expand
  • 61
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