Quickly undoing percentages in your head
I can't remember how exactly it came up, but my son asked me while we were in the car something along
the lines of, "if (some number) was something else minus 20 percent, how much was the original number?"
Of course, with a calculator, this is trivial to work out — if you took off 20%, you computed
(100 - 20) = 80% of the original, so dividing the result by 0.8 will yield the original number.
However, we were in the car without a calculator but after thinking about it for a few minutes, it
occurred to me that adding back 1/4 would yield the original number and, in general, if you reduced
a number by 1/n, you could recover the original by adding back 1/n-1 of the result. I
imagine somebody
tried to teach me this simple rule in primary school, but I didn't pay close enough attention, so I had
to work it out again for myself. Just to make sure I wasn't imagining things, I decided to work out
the algebra to double-check this identity once I had access to a pencil and paper. As it turns out,
demonstrating this algebraically turns out to be somewhat interesting:
Figure 1: Reverse a fractional reduction
More intuitively, if you reduce x by 20% = 1/5, you're computing y = (4/5)x (of course,
you wouldn't do it that way in your head, you'd compute 20% and subtract). To undo this, you multiply
by the reciprocal 5/4, or 1 + 1/4. Of course, this is actually easier done than said.
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I'm the author of the book
"Implementing SSL/TLS Using Cryptography and PKI".
Like the title says, this is a from-the-ground-up examination
of the SSL protocol that provides security, integrity and
privacy to most application-level internet protocols, most notably HTTP.
I include the
source
code to a complete working SSL implementation,
including the most popular cryptographic algorithms
(DES, 3DES, RC4, AES, RSA, DSA, Diffie-Hellman, HMAC, MD5, SHA-1,
SHA-256, and ECC), and show how they all fit together
to provide transport-layer security.
Joshua Davies
Past Posts
- April 30, 2021: A Date Picker Control in Vanilla Javascript
- March 31, 2021: A Web Admin Console for Redis, Part Three
- January 27, 2021: A Web Admin Console for Redis, Part Two
- December 21, 2020: A Web Admin Console for Redis, Part One
- November 30, 2020: What is Procmail and why is it using up all my memory?
- September 30, 2020: Minimal Drag and Drop Support in Javascript
- August 31, 2020: Covariance and Contravariance in Generic Types
- July 31, 2020: How Spread Out Are the Floating Point Numbers?
- June 25, 2020: ERD Diagramming Tool, Part Three
- April 30, 2020: ERD Diagramming Tool, Part Two
- March 31, 2020: ERD Diagramming Tool, Part One
- February 28, 2020: MathJax and "t.setAttribute is not a function"
- December 30, 2019: Solving Systems of Equations with Python
- October 30, 2019: Linear Regression with and without numpy
- September 30, 2019: Reading a Parquet file outside of Spark
- August 30, 2019: UML Diagrams with MetaUML
- July 30, 2019: Clustering in Python
- June 25, 2019: A Walkthrough of a TLS 1.3 Handhsake
- May 31, 2019: A DataType Printer in Java
- April 30, 2019: A Simple HTTP Server in Java, Part 3 - Cookies and Keep Alives
- March 28, 2019: A Simple HTTP Server in Java, Part 2 - POST and SSL
- February 28, 2019: A Simple HTTP Server in Java
- January 29, 2019: Angular CLI Behind the Scenes, Part Two
- September 30, 2018: Angular CLI Behind the Scenes, Part One
- August 31, 2018: Into the MMIX MOR Instruction
- July 24, 2018: Undoing Percentage Changes in your Head
- June 30, 2018: Generating Langford Pairs in Scala
- May 25, 2018: Reflections on Three Years of Reading Knuth
- April 30, 2018: java.lang.NoSuchMethodError: org.junit.vintage. engine.descriptor.RunnerTestDescriptor. getAllDescendants
- March 30, 2018: An Excel Spreadsheet for the Academy Awards
- February 28, 2018: Git for Subversion Users
- January 31, 2018: The Evolution of AngularJS
- December 31, 2017: Numerical Integration in Python
- October 31, 2017: Gradle for Java Developers
- September 29, 2017: Reflections on another year of reading Knuth
- August 30, 2017: SSL OCSP Exchange
- July 27, 2017: A walk-through of an SSL certificate exchange
- June 30, 2017: A walk-through of an SSL key exchange
- May 31, 2017: A walk-through of the SSL handshake
- March 31, 2017: A walk-through of the TCP handshake
- February 28, 2017: The TLS Handshake at a High Level
- January 31, 2017: A Walk-through of a JWT Verification
- August 31, 2016: Reflections on a year of reading Knuth
- July 29, 2016: Matching a private key to a public key
- June 30, 2016: A Completely Dissected GZIP File
- May 31, 2016: Automatic Guitar Tablature Generator, Part 2
- April 28, 2016: Automatic Guitar Tablature Generator, Part 1
- March 31, 2016: Import an encrypted private key into a Java Key Store
- February 26, 2016: Import a private key into a Java Key Store
- January 31, 2016: Debian Linux on MacBook Pro
- December 29, 2015: Is Computer Science necessary or useful for programmers?
- November 30, 2015: Client certificate authentication vs. password authentication
- October 28, 2015: A Utility for Viewing Java Keystore Contents
- September 29, 2015: Debugging jQuery with Chrome's Developer Tools
- August 26, 2015: Getting Perl, MySQL and Apache to all work together on Mac OS/X
- July 30, 2015: Extract certificates from Java Key Stores for use by CURL
- June 29, 2015: Using the Chrome web developer tools, Part 9: The Console Tab
- May 28, 2015: Using the Chrome web developer tools, Part 8: The Audits Tab
- April 30, 2015: Using the Chrome web developer tools, Part 7: The Resources Tab
- March 30, 2015: Using the Chrome web developer tools, Part 6: The Memory Profiler Tab
- February 27, 2015: Using the Chrome web developer tools, Part 5: The CPU Profiler Tab
- January 31, 2015: Using the Chrome web developer tools, Part 4: The Timeline Tab
- December 31, 2014: Using the Chrome web developer tools, Part 3: The Sources Tab
- October 31, 2014: Using the Chrome web developer tools, Part 2: The Network Tab
- September 30, 2014: Using the Chrome web developer tools, Part 1: The Elements Tab
- August 11, 2014: Unable to find valid certification path to requested target
- June 30, 2014: Sort by a Hierarchy
- May 29, 2014: OpenSSL Tips and Tricks
- April 25, 2014: Heartbleed: What the Heck Happened
- February 28, 2014: Replace Microsoft Money with a Spreadsheet
- January 29, 2014: An Illustrated Guide to the BEAST Attack
- December 21, 2013: Where does GCC look to find its header files?
- October 24, 2013: Planning a Subversion import
- August 28, 2013: Compile and test an iOS app from the command line
- July 31, 2013: The Hidden Costs of Software Reuse
- June 26, 2013: Beware of mvn war:inplace
- May 29, 2013: Block Font Design Using Javascript
- April 4, 2013: Parsing a POM file using only SED
- February 22, 2013: Inside the PDF File Format
- December 31, 2012:How and why rotation matrices work
- November 27, 2012:Date Management in Java
- October 21, 2012:
Installing Debian Without a Network
- August 14, 2012:
My Review of Matt Neuburg's "Programming iOS 5"
- July 16, 2012:
An example OAuth 1.0 Handshake and mini-library
- May 23, 2012:
A Javascript one-liner to display cookie values
- April 27, 2012:
How SSL Certificates Use Digital Signatures
- March 29, 2012:
A breakdown of a GIF decoder
- February 15, 2012:
The design and implementation of LZW (the GIF compression algorithm)
- January 16, 2012:
Calculate the day of week of any date... in your head
- December 4, 2011:
Understanding CRC32
- October 29, 2011:
Efficient Huffman Decoding
- October 4, 2011:
Extract a private key from a Gnu Keyring file
- September 5, 2011:
From Make to Ant to Maven
- July 18, 2011:
A bottom-up look at the Apache configuration file
- July 6, 2011:
Fun with the HTML 5 Canvas Tag
- Jun 16, 2011:
Pain and disfiguration upon all comment spammers
- May 31, 2011:
Use of RSSI and Time-of-Flight Wireless Signal Characteristics for Location Tracking
- May 7, 2011: Implementing SSL
- Apr 24, 2011: Dissecting the GZIP format
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