How to Break Cryptography | Infinite Series
PBS Infinite Series・2 minutes read
Cracking secure messages involves factoring large numbers, crucial for breaking RSA cryptography using prime numbers as keys. Euler's work on prime numbers and modular arithmetic plays a vital role, with quantum computers excelling at finding periods to decrypt messages.
Insights
- Understanding prime numbers and modular arithmetic is essential for breaking RSA cryptography, with Euler's contributions playing a significant role in this process.
- Quantum computers' proficiency in finding periods is a key factor in their advantage over traditional computers in cracking secure messages encrypted using RSA cryptography.
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Recent questions
How do computers crack secure messages?
By factoring huge numbers.
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Summary
00:00
"Breaking RSA: Prime Numbers and Quantum Computing"
- Cracking secure messages involves factoring huge numbers, a challenging task for computers.
- RSA cryptography relies on prime numbers as keys to decrypt messages.
- Euler's work on prime numbers and modular arithmetic is crucial in breaking RSA cryptography.
- Modular arithmetic involves counting in a circle and operations with remainders when dividing numbers.
- The period in modular arithmetic is essential, indicating when a sequence of numbers repeats.
- Finding the period of a number mod N is crucial in factoring large numbers.
- Steps to factor large numbers involve selecting a number, computing its period, and using algebraic equations.
- The greatest common divisor of specific calculations helps identify prime factors of large numbers.
- Quantum computers excel at finding periods, a crucial step in breaking RSA cryptography.
- Combining the digits of e and pi algebraically can lead to rational numbers, with examples like e to the pi i plus 1 equals 0 and pi to the ninth divided by e to the eighth being close to 10 but not exactly.
14:10
"Reddles' Challenge: e, pi, and infinity"
- The computation of e to the sixth minus pi to the fifth minus pi to the fourth is close to 0 but not exactly 0, resembling the number 10 when done by hand. Reddles won a challenge t-shirt for a comprehensive response to a question about the uncountable length of numbers produced by swapping infinitely many digits between e and pi, with proofs involving binary representation and Cantor's diagonalization argument.
