Analysis and optimization of the TWINKLE factoring device

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 TWINKLE-assisted factorization of 768 bit numbers is difficult but doable in about 9 months (including the sieving and matrix parts) by a large organization which can use 80000 standard Pentium II PC's and 5000 TWINKLE device

Factoring estimates for a 1024-bit RSA modulus

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 the resulting improved parameter choices from [18]

www.springerreference.com/docs/html/chapterdbid/60497.html Mechanical Computing: The Computational Complexity of Physical Devices

- Mechanism: A machine or part of a machine that performs a particular task computation: the use of a computer for calculation.- Computable: Capable of being worked out by calculation, especially using a computer.- Simulation: Used to denote both the modeling of a physical system by a computer as well as the modeling of the operation of a computer by a mechanical system; the difference will be clear from the context. Definition of the Subject Mechanical devices for computation appear to be largely displaced by the widespread use of microprocessor-based computers that are pervading almost all aspects of our lives. Nevertheless, mechanical devices for computation are of interest for at least three reasons: (a) Historical: The use of mechanical devices for computation is of central importance in the historical study of technologies, with a history dating back thousands of years and with surprising applications even in relatively recent times. (b) Technical & Practical: The use of mechanical devices for computation persists and has not yet been completely displaced by widespread use of microprocessor-based computers. Mechanical computers have found applications in various emerging technologies at the micro-scale that combine mechanical functions with computational and control functions not feasible by purely electronic processing. Mechanical computers also have been demonstrated at the molecular scale, and may also provide unique capabilities at that scale. The physical designs for these modern micro and molecular-scale mechanical computers may be based on the prior designs of the large-scale mechanical computers constructed in the past. (c) Impact of Physical Assumptions on Complexity of Motion Planning, Design, and Simulation: The study of computation done by mechanical devices is also of central importance in providing lower bounds on the computational resources such as time and/or space required to simulate a mechanical syste

Problems

I. Definition of the Subject and Its Importanc

Factorization of RSA-140 using the number field sieve

On February 2, 1999, we completed the factorization of the 140-digit number RSA-140 with the help of the Number Field Sieve factoring method (NFS). This is a new general factoring record. The previous record was established on April 10, 1996 by the factorization of the 130-digit number RSA-130, also with the help of NFS. The amount of computing time spent on RSA-140 was roughly twice that needed for RSA-130, about half of what could be expected from a straightforward extrapolation of the computing time spent on factoring RSA-130. The speed-up can be attributed to a new polynomial selection method for NFS which will be sketched in this paper

Factorization of a 512 bit RSA modulus

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 RS

Cryptanalysis of Algebraic Verifiable Delay Functions

Verifiable Delay Functions (VDF) are a class of cryptographic primitives aiming to guarantee a minimum computation time, even for an adversary with massive parallel computational power. They are useful in blockchain protocols, and several practical candidates have been proposed based on exponentiation in a large finite field: Sloth++, Veedo, MinRoot. The underlying assumption of these constructions is that computing an exponentiation $x^e$ requires at least $\log_2 e$ sequential multiplications. In this work, we analyze the security of these algebraic VDF candidates. In particular, we show that the latency of exponentiation can be reduced using parallel computation, against the preliminary assumptions