**modulus**- Obviously the RSA cryptosystem can be broken if its modulus can be factored. (springer.com)
- It is an open question if breaking RSA is equivalent to factoring the modulus. (springer.com)
- The paper presents several modified RSA cryptosystems for which breaking is as difficult as factoring the modulus and gives a general theory for such systems. (springer.com)
- The most efficient method known to solve the RSA problem is by first factoring the modulus N, a task believed to be impractical if N is sufficiently large (see integer factorization). (wikipedia.org)

**ciphertext**- This is perhaps easiest to see by the sheer overkill of the factoring approach: the RSA problem asks us to decrypt one arbitrary ciphertext, whereas the factoring method reveals the private key: thus decrypting all arbitrary ciphertexts, and it also allows one to perform arbitrary RSA private-key encryptions. (wikipedia.org)
- The difficulty of breaking the RSA cipher - recovering a plaintext message given a ciphertext and the public key - is connected to the difficulty of factoring large numbers. (wikipedia.org)
- The decryption of the 1977 ciphertext involved the factoring of a 129-digit number, RSA-129, in order to recover the plaintext. (wikipedia.org)

**toxicity equivalent**- Evaluation of toxicity equivalent factors of paralytic shellfish poisoning toxins in seven human sodium channels types by an automated high throughput electrophysiology system. (fluxionbio.com)
- Taking advantage of the accessibility to pure PSP standards, we calculated the toxicity equivalent factors (TEFs) for nine PSP analogs obtaining reliable TEFs in human targets to fulfill the deficiencies of the official analytic methods and to verify automated patch clamp technology as a fast and reliable screening method for marine toxins that interact with the sodium channel. (fluxionbio.com)
- Then, the measured concentration of each compound is multiplied by its corresponding TEF to produce a TCDD toxicity equivalent (TEQ) concentration. (canceractionny.org)

**TEFs**- Toxic equivalent factors (TEFs) for eight polychlorinated dibenzo-p-dioxin (PCDD) and polychlorinated dibenzofuran (PCDF) congeners were derived with a rainbow trout (Oncorhynchus mykiss) cell line, RTL-W1, and compared with TEFs obtained with a rat hepatoma cell line, H4IIE. (islandscholar.ca)
- These relative toxicity values are called toxicity equivalence factors (TEFs). (canceractionny.org)

**decryption**- Along these same lines, finding the decryption exponent d indeed is computationally equivalent to factoring N, even though the RSA problem does not ask for d. (wikipedia.org)
- That is, it can be shown that if there exists an algorithm that can decrypt arbitrary messages, then this algorithm can be used to factor N. The algorithm processes decryption as fast as Rabin and RSA, however it has much slower encryption since the sender must compute a full exponentiation. (wikipedia.org)

**resistance**- This is largely attributed to the fact that one partial factor is used in the design process, to ensure reliability across all failure modes of the design resistance. (sun.ac.za)
- Due to the South African loading code not covering the sensitivity of the resistance targeted by the currently provided partial factors for the DSM, lowering of the partial factors is recommended. (sun.ac.za)
- A diving watch, also commonly referred to as a diver's or dive watch, is a watch designed for underwater diving that features, as a minimum, a water resistance greater than 1.0 MPa (10 atm), the equivalent of 100 m (330 ft). (wikipedia.org)

**algorithm**- The RSA algorithm raises a message to an exponent, modulo a composite number N whose factors are not known. (wikipedia.org)
- The RSA key setup routine already turns the public exponent e, with this prime factorization, into the private exponent d, and so exactly the same algorithm allows anyone who factors N to obtain the private key. (wikipedia.org)
- This Eurocrypt 2009 paper (link is to a preprint version) proves that solving the RSA problem using a generic ring algorithm is as difficult as factoring. (wikipedia.org)
- Ron Rivest estimated in 1977 that factoring a 125-digit semiprime would require 40 quadrillion years, using the best algorithm known and the fastest computers of the day. (wikipedia.org)

**metric**- Kv can be calculated from Cv using the equation K v = ( 0.865 ) ( C v ) {\displaystyle {K_{v}}=(0.865)({C_{v}})} It can also be obtained directly in metric: The kv factor or value as it is also called is defined in VDI/VDE Richtlinien No. 2173. (wikipedia.org)
- Where they are deducted, the metric is titled equivalent availability factor (EAF). (wikipedia.org)

**Factorization**- This makes essentially equivalent the problems of computing greatest common divisors and factorization of polynomials over the integers and of polynomials over the rational numbers. (wikipedia.org)

**large**- Indeed, there is strong evidence pointing to this conclusion: that a method to break the RSA method cannot be converted necessarily into a method for factoring large semiprimes. (wikipedia.org)

**concentration**- delivery of the appropriate type, concentration, and timely sequence of bioactive growth factors, which promote interactions and functions of cells pertinent to neotissue formation, will enhance the long-term performance of implants, including tissue-engineering constructs. (springer.com)

**method**- By the above method, the RSA problem is at least as easy as factoring, but it might well be easier. (wikipedia.org)
- Dimensional analysis, or more specifically the factor-label method, also known as the unit-factor method, is a widely used technique for such conversions using the rules of algebra. (wikipedia.org)
- While it is not known whether the two problems are mathematically equivalent, factoring is currently the only publicly-known method of directly breaking RSA. (wikipedia.org)

**mathematics**- In mathematics, a factor system (sometimes called factor set) is a fundamental tool of Otto Schreier's classical theory for group extension problem. (wikipedia.org)

**tend**- Newer plants tend to have significantly higher availability factors, but preventive maintenance is as important as improvements in design and technology. (wikipedia.org)

**open**- A simplified version of the definition is: The kv factor of a valve indicates "The water flow in m3/h, at a pressure drop across the valve of 1 kg /cm2 when the valve is completely open. (wikipedia.org)
- In 2015, the same RSA-129 number was factored in about one day, with the CADO-NFS open source implementation of number field sieve, using a commercial cloud computing service for about $30. (wikipedia.org)

**probability**- Normal probability distributions were used for the thickness and model factor variables. (sun.ac.za)

**nuclear**- The yield required of a nuclear weapon to destroy a hard and deeply buried target is reduced by a factor of 15 to 25 by enhanced ground-shock coupling if the weapon is detonated a few meters below the surface. (nap.edu)
- For urban targets, civilian casualties from a nuclear earth-penetrator weapon are reduced by a factor of 2 to 10 compared with those from a surface burst having 25 times the yield. (nap.edu)
- Originally the term availability factor was used only for power plants that depended on an active, controlled supply of fuel, typically fossil or later also nuclear. (wikipedia.org)

**private key**- The public key is then (n, g, h) and the private key is the factors (p, q). (wikipedia.org)

**reliability**- By convention, such zero production periods are counted against the capacity factor but not against the availability factor, which thus remains defined as depending on an active, controlled supply of fuel, along with factors concerning reliability and maintenance. (wikipedia.org)
- Availability (Reliability Engineering) Capacity factor Generating Availability Data System (Electricity Industry) High availability List of energy storage projects Utilization factor Forced outage rate Institute of Electrical and Electronics Engineers. (wikipedia.org)

**thus**- Thus, the capacity of enzymes responsible for the activation of the carcinogenic PAHs has been regarded as one of the factors affecting the risk to chemical carcinogenesis. (aacrjournals.org)
- Units for volume, however, can be factored into the base units of length (m3), thus they are considered derived or compound units. (wikipedia.org)

**directly**- Physics 90 fulfills prerequisite requirements for PHYS 115, though Physics 90 is not directly equivalent to Physics 30. (usask.ca)

**growth**- Realization and appreciation that growth factors are essential in tissue development, regeneration, and maintenance as well as crucial mediators/regulators of pertinent cellular- and molecular-level events has motivated new directions in bioengineering research. (springer.com)
- This chapter summarizes the current knowledge of the role of growth factors in the biology/physiology of two tissues, specifically, vascular tissue and bone. (springer.com)
- Shibuya M. Vascular endothelial growth factor-dependent and -independent regulation of angiogenesis. (springer.com)

**problem**- When that decision is wholly motivated by factors other than age, the problem that prompted the ADEA's passage inaccurate and stigmatizing stereotypes about older workers' productivity and competence disappears. (cornell.edu)
- This unrefereed preprint purports that solving the RSA problem using a Straight line program is as difficult as factoring provided e has a small factor. (wikipedia.org)
- This Asiacrypt 2007 paper (link is to a preprint version) proves that solving the RSA problem using an oracle to some certain other special cases of the RSA problem is easier than factoring. (wikipedia.org)

**system**- In fact, a factor system constitutes a realisation of the cocycles in the second cohomology group in group cohomology. (wikipedia.org)
- A cocycle or (Noether) factor system is a map c:G × G → L* satisfying c ( h , k ) g c ( h k , g ) = c ( h , k g ) c ( k , g ) . {\displaystyle c(h,k)^{g}c(hk,g)=c(h,kg)c(k,g). (wikipedia.org)

**depth**- a is the depth of equivalent rectangular stress block, and this is also where i start getting a little confused. (physicsforums.com)
- After a series of trials undertaken by the Swiss Laboratory for Horology in Neuchâtel in May 1937, the watch was certified as being able to withstand a pressure of 1.37 MPa (13.5 atm), equivalent to a depth of 135 m (443 ft), without any water intake whatsoever. (wikipedia.org)

**value**- e The temperature factor is fixed at this value. (wikipedia.org)

**several**- In Western practice, decisions on the selection and prioritization of news are made by editors on the basis of their experience and intuition, although analysis by J. Galtung and M. Ruge showed that several factors are consistently applied across a range of news organizations. (wikipedia.org)

**given**- The capacity factor for a given period can never exceed the availability factor for the same period. (wikipedia.org)

**require**- Everything else being equal, plants that are run less frequently have higher availability factors because they require less maintenance and because more inspections and maintenance can be scheduled during idle time. (wikipedia.org)

**time**- The availability factor of a power plant is the amount of time that it is able to produce electricity over a certain period, divided by the amount of the time in the period. (wikipedia.org)
- But efficient factoring algorithms had not been studied much at the time, and a lot of progress was made in the following decades. (wikipedia.org)

**cannot**- A wind turbine cannot operate in wind speeds above a certain limit, which counts against its availability factor. (wikipedia.org)

**appropriate**- It may be more appropriate to apply different partial factors to the three failure modes. (sun.ac.za)

**list**- Focusing on newspapers and broadcast news, Galtung and Ruge devised a list describing what they believed were significant contributing factors as to how the news is constructed. (wikipedia.org)

**difference**- The distinction between the formal, publicized policy in Thurston and the undisclosed factor here is not such a difference, since an employer's reluctance to acknowledge its reliance on the forbidden factor should not cut against imposing a penalty. (cornell.edu)
- The difference arises when the plant is run at less than full capacity, in which case the capacity factor is less than the availability factor. (wikipedia.org)