A. K. Lenstra

Publications173
h-index47
Citations11,037
Highly Influential Citations759
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Factoring polynomials with rational coefficients
In this paper 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…
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The XTR Public Key System
TLDR
This paper introduces the XTR public key system, a new method to represent elements of a subgroup of a multiplicative group of a finite field that leads to substantial savings both in communication and computational overhead without compromising security.
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Selecting Cryptographic Key Sizes
TLDR
Recommendations for the determination of key sizes for symmetric cryptosystems, RSA, and discrete logarithm-based cryptosSystems both over finite fields and over groups of elliptic curves over prime fields are offered.
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Factorization of a 768-Bit RSA Modulus
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.
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A random zoo: sloth, unicorn, and trx
TLDR
It is shown how sloth can be used for uncontestable random number generation (unicorn), and how unicorn can be use for a new trustworthy random ellip­ tic curves service (trx) and random-sample.
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Chosen-Prefix Collisions for MD5 and Colliding X.509 Certificates for Different Identities
We present a novel, automated way to find differential paths for MD5. As an application we have shown how, at an approximate expected cost of 250calls to the MD5 compression function, for any two…
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Short Chosen-Prefix Collisions for MD5 and the Creation of a Rogue CA Certificate
TLDR
A more flexible family of differential paths and a new variable birthdaying search space are described, leading to just three pairs of near-collision blocks to generate the collision, enabling construction of RSA moduli that are sufficiently short to be accepted by current CAs.
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Hard Equality Constrained Integer Knapsacks
TLDR
It is demonstrated that the characteristics that make the instances so difficult to solve by branch-and-bound make the solution of a certain reformulation of the problem almost trivial.
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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…
The number field sieve
TLDR
A heuristic run time analysis indicates that the number field sieve is asymptotically substantially faster than any other known factoring method, for the integers that it applies to, and can be modified to handle arbitrary integers.
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