So how did Napier's logarithms work?
纳皮尔的对数要怎么使用呢？
I know a lot of logarithms and axioms, but not the language of love.
我认识很多的对数和公理，而不是语言的热爱。
It was also programmed with subroutines for logarithms and trigonometry.
它也用编好的子程序计算对数和三角。
Logarithms were invented to shorten the work of extended numerical computation.
人们发明对数来缩短运算冗长的数值计算工作。
Mr. Ward: "What do you do on a test if you forget how to do inverse logarithms?"
沃兹先生：“如果在考试的时候你忘了怎样做反对数怎么办？”
An eminent mathematician, he is regarded as the inventor of the system of logarithms.
作为一名受人尊敬的数学家，龙比亚被誊为对数的发明者。
It will be assumed that the reader is familiar with logarithms and trigonometric functions.
我们还希望读者能熟悉对数和三角函数。
The model of double logarithms is the best in both simulating and predicting among all these models.
各模型中以双对数型模拟、推算效果最佳。
Reducing everything "mod n" makes it impossible to use the easy techniques that we're used to such as normal logarithms.
对所有的数应用“mod n”的目的是使攻击者不可能使用简单的技术（如过去我们使用的对数）破解它。
Ability to apply advanced mathematical concepts such as exponents, logarithms, quadratic equations, and permutations.
在工作中能运用高等数学概念，如指数，对数，二次方程序和排列。
Based on the computational difficulty of computing discrete logarithms, a dynamic multiple secrets sharing scheme is proposed.
基于单向函数和有限域上离散对数问题提出一种动态多秘密分享方案。
Same with logarithms, roots, transcendentals, and other fundamental mathematical representations that appear nearly everywhere.
同样的，对数，根，超越数，和其他到处出现的基本数学原理。
Logs base e (natural logarithms) appear in the calculation of compound interest, and numerous scientific and mathematical applications.
以e为底的对数（自然对数）出现在复合计算以及大量科学和数学应用程序中。
In this paper, we show that he's digital signature scheme is insecure against forgery if the discrete logarithms problem is solved.
在本论文中，我们证明了假如离散对数的问题解决了，何的数位签章演算法是不安全的。
Based on the computational difficulty in computing discrete logarithms, this paper proposes a dynamic multiple secrets sharing scheme.
基于有限域上离散对数问题提出了一种动态多秘密分享方案。
Integrating logarithms requires a topic that is usually taught in Calculus II and so we won't be integrating a logarithm in this class.
结合对数，通常需要一个教微积分第二，所以我们不会被集成在这个类对数的话题。
The scheme is efficient and practical, and its security is based on the difficulty of computing ellipse curve discrete logarithms problem.
方案的安全性基于求解有限域上椭圆曲线离散对数的困难性。
Logarithms were invented to simplify cumbersome calculations, since exponents can be added or subtracted to multiply or divide their bases.
发明对数是为了简化繁琐的计算，因为用幂指数的相加或相减可以等同于它们的基数的相乘或相除。
In the problem of dynamic access control, we present a secure and efficient scheme, which is based on discrete logarithms and polynomial interpolation.
在用户层次结构的动态存取控制问题上，本文提出了一种安全有效的方案。
As with logarithms integrating inverse trig functions requires a topic usually taught in Calculus II and so we won't be integrating them in this class.
如同对数反三角函数功能整合需要一个主题通常讲授微积分第二，所以我们不会被他们融入这个类。
In this paper, we present a new signature scheme with message recovery and the security of the scheme is based on both factorization and discrete logarithms.
本文设计一种新的具备消息自动恢复特性的数字签名方案，这种方案的安全性同时建立在因子分解和离散对数之上，并对这种方案进行了安全性分析。
In this paper, two schemes for digital signature with message recovery are presented. The security of these schemes is based on factorization and discrete logarithms.
本文设计了两种具有消息恢复的数字签名方案，其安全性都是基于因子分解问题和离散对数问题的。
Based on the zero -knowledge proofs and the computational difficulty of computing discrete logarithms, a dynamic multiple secrets sharing scheme is proposed in this paper.
基于中国剩余定理，零知识证明与有限域上计算离散对数问题的困难性，提出了一种新的动态多秘密分享方案。
You might remember vaguely logarithms from high school math and such but what this suggests for us, the computer scientists, is that this is certainly a smarter, a faster algorithm.
你可能还会依稀记得，高中数学里的对数，这就给了我们这些计算机科学家们，一些启示，即，这种算法更智能，更迅速。
A new key authentication scheme was proposed. This new scheme is based on the intractability of elliptic discrete logarithms. The key is combination of password and private key.
本文利用椭圆曲线上离散对数难解问题，提出了一种新的密钥认证方案，密钥由用户口令和秘密密钥组成。
The other element of the equation, b, turns out to be directly related to T1. It is calculated from the relationship between the logarithms of the attack number, n, and the attack interval, Tn.
至于这个公式里的其他元素，b和T1直接相关，它由袭击次数n的对数和袭击间隔Tn的关系计算得出。
Advanced math — XSLT can perform basic arithmetic easily enough, but it doesn't support trigonometry, exponential functions, logarithms, or other more advanced mathematical operators and functions.
高等数学——XSLT在基本数学方面游刃有余，但它不支持三角学、指数函数、对数或其他更为高级的数学运算符及函数。
Advanced math — XSLT can perform basic arithmetic easily enough, but it doesn't support trigonometry, exponential functions, logarithms, or other more advanced mathematical operators and functions.
高等数学——XSLT在基本数学方面游刃有余，但它不支持三角学、指数函数、对数或其他更为高级的数学运算符及函数。
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