Public-Key Cryptography

Public-Key Cryptography = assymetric cryptography
Theory
- Trapdoor function: easy to go in one direction but very difficult and practically impossible in the other direction.
- Most trapdoor function reduces to the same problem in mathematics - *hidden subgroup problem* (this problem abstracts both integer factorization and *discrete logrithm*). See also an explanation here
Usage
- priv could decrypt messages encrypted by pub but not true for the oppsite;
  - Therefore, two sides to communicate require two pairs of priv-pub keys.
InfoSec
- Breaking symmetric-cryptography needs brute-force because its private keys are just bits without structures
- Breaking public-key cryptography has more efficient approaches because those keys are mathematical objects with structures.
  - There's space-time tradeoff but N-bit key has at least N/2-bit security, i.e. requiring $2^{N/2}$ elementary operations to break
  - Therefore, we could say 256-bit ED25519 key has the security level the same as 128-bit symmetric-cryptography key
- Traditional computing power:
  - btc global hash rate ~ 500million TH = $500 * 10^{12}$ hash / sec, \~ $2^{68}$ hash/sec, \~ $2^{93}$ hash/year
  - so > 2^10 year to crash it
- Quantum computing power:
  - [Embedded content]
    -
Example
- RSA
- Elliptic-curve cryptography (ECC) ED25519
ssh-keygen
- ```bash
ssh-keygen -t ed25519 -b 384
```
software/libsodium can be used for encryption/sign/hash/etc.

Public-Key Cryptography and Cryptography/GPG

Public-Key Cryptography and Cryptography/GPG

## 原理相关 - 和其他常见 Public-Key Cryptography 加密方式比较

Theory