Category Archives: Number Theory

Q: How good is the Enigma code system compared to today’s publicly available cryptography systems?

Physicist: Freaking terrible. The Enigma machine used a “rolling substitution cypher” which means that it was essentially a (much more) complicated version of “A=1, B=2, C=3, …”.  The problem with substitution cyphers is that if parts of several messages are … Continue reading

Posted in -- By the Physicist, Computer Science, Math, Number Theory, Paranoia | 5 Comments

Q: Is there a formula for finding primes? Do primes follow a pattern?

Physicist: Primes are, for many purposes, basically random.  It’s not easy to “find the next prime” or determine if a given number is prime, but there are tricks.  Which trick depends on the size of the number.  Some of the … Continue reading

Posted in -- By the Physicist, Math, Number Theory | 11 Comments

Learning intro number theory

Physicist: We occasionally get questions about free learning resources.  Khan academy is excellent, and if you poke around you can find a smattering of free class notes and text books, but generally speaking the more more detailed/advanced the material, the … Continue reading

Posted in -- By the Physicist, Brain Teaser, Math, Number Theory | 5 Comments

Q: How do you write algorithms to enycrypt things?

Physicist: There are several algorithms, but almost all of them are all based on “trap-door encryption”.  The idea is that you find some kind of mathematical process that’s easy to run forward, but effectively impossible to run backward, unless you … Continue reading

Posted in -- By the Physicist, Computer Science, Math, Number Theory | 8 Comments

Q: What is the Riemann Hypothesis? Why is it so important?

Physicist: To non-mathematicians this seems like a whole lot of fuss over nothing. There’s a function called the Riemann Zeta function, denoted ““, that’s defined for complex numbers (that is, you can plug in for example, and it’s totally fine).  … Continue reading

Posted in -- By the Physicist, Equations, Math, Number Theory | 3 Comments

Q: How can quantum computers break encryption?

Physicist: What follows is the famous Shor algorithm, which can break any RSA encryption key. The problem: RSA, the most common form of public key encryption, is based on the fact that large numbers are hard to factor.  Without going … Continue reading

Posted in -- By the Physicist, Computer Science, Equations, Math, Number Theory, Physics, Probability, Quantum Theory | 18 Comments