Exploiting cá cược thể thao bet365_cách nạp tiền vào bet365_ đăng ký bet365 math/rsa bug in Go
The bug is really cool: https://groups.google.com/forum/#!topic/golang-dev/MEATuOi_ei4. It impacts not only crypto/tls, but also crypto/openpgp. If you are using Go to sign messages, it's time to change your RSA private keys. Someone asked me to explain cá cược thể thao bet365_cách nạp tiền vào bet365_ đăng ký bet365 bug in layman term, and below is my take.
The RSA function calculates $m^e \pmod{pq}$, where $p$ and $q$ are large prime numbers. Modular operations are expensive, people usually use two tricks to speed cá cược thể thao bet365_cách nạp tiền vào bet365_ đăng ký bet365m up:
a/ Montgomery reduction: calculating 33500 % 99 is hard because 99 is not a nice number. It'll be awesome if we can replace 99 with 100, but that's exactly cá cược thể thao bet365_cách nạp tiền vào bet365_ đăng ký bet365 trick that Montgomery found.
b/ Chinese Remainder Theorem: in high school you were probably asked to find a number $n$ satisfying $n \pmod{2} = 1$, $n \pmod{3} = 5$, and $n \pmod{5} = 7$. Perhaps your teachers didn't tell you, but you can solve this problem using cá cược thể thao bet365_cách nạp tiền vào bet365_ đăng ký bet365 Chinese Remainder Theorem. We can use cá cược thể thao bet365_cách nạp tiền vào bet365_ đăng ký bet365 same trick here, by computing $m^e \pmod{p}…
The RSA function calculates $m^e \pmod{pq}$, where $p$ and $q$ are large prime numbers. Modular operations are expensive, people usually use two tricks to speed cá cược thể thao bet365_cách nạp tiền vào bet365_ đăng ký bet365m up:
a/ Montgomery reduction: calculating 33500 % 99 is hard because 99 is not a nice number. It'll be awesome if we can replace 99 with 100, but that's exactly cá cược thể thao bet365_cách nạp tiền vào bet365_ đăng ký bet365 trick that Montgomery found.
b/ Chinese Remainder Theorem: in high school you were probably asked to find a number $n$ satisfying $n \pmod{2} = 1$, $n \pmod{3} = 5$, and $n \pmod{5} = 7$. Perhaps your teachers didn't tell you, but you can solve this problem using cá cược thể thao bet365_cách nạp tiền vào bet365_ đăng ký bet365 Chinese Remainder Theorem. We can use cá cược thể thao bet365_cách nạp tiền vào bet365_ đăng ký bet365 same trick here, by computing $m^e \pmod{p}…