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https://github.com/sheroz/rsa
Samples of RSA (Rivest–Shamir–Adleman) asymmetric cipher implementations in Rust
https://github.com/sheroz/rsa
crypto cryptography public-key-cryptography rsa rsa-cipher rsa-cryptography rsa-cryptosystem
Last synced: 1 day ago
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Samples of RSA (Rivest–Shamir–Adleman) asymmetric cipher implementations in Rust
- Host: GitHub
- URL: https://github.com/sheroz/rsa
- Owner: sheroz
- License: mit
- Created: 2023-07-05T20:32:28.000Z (over 1 year ago)
- Default Branch: main
- Last Pushed: 2024-05-27T22:05:04.000Z (6 months ago)
- Last Synced: 2024-05-28T08:00:48.718Z (6 months ago)
- Topics: crypto, cryptography, public-key-cryptography, rsa, rsa-cipher, rsa-cryptography, rsa-cryptosystem
- Language: Rust
- Homepage: https://github.com/sheroz/rsa
- Size: 13.7 KB
- Stars: 2
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- License: LICENSE.txt
Awesome Lists containing this project
README
# RSA (Rivest–Shamir–Adleman) Asymmetric Cipher in Rust
Samples of RSA (Rivest–Shamir–Adleman) public-key cryptosystem implementations for learning purposes
- [src/rsa_gmp.rs](src/rsa_gmp.rs) - uses a [rug](https://crates.io/crates/rug), a high-level interface to the wrapper over [GNU MP / GMP](https://gmplib.org/), a well known arbitrary precision arithmetic library
- [src/rsa_openssl_bn.rs](src/rsa_openssl_bn.rs) - uses an [openssl](https://crates.io/crates/openssl), a safe interface to the popular [OpenSSL library](https://www.openssl.org/)
- [src/rsa_num.rs](src/rsa_num.rs) - uses a [num](https://crates.io/crates/num), a collection of numeric types and traits in pure Rust
## Key generation
1. Choose two distinct primes `p` and `q`
FIPS.186-4, Section: B.3.1 Criteria for IFC Key Pairs
```text
sqrt(2)*2^((nlen/2)-1) <= p <= 2^(nlen/2)-1
sqrt(2)*2^((nlen/2)-1) <= q <= 2^(nlen/2)-1
|p - q| > 2^((nlen/2)-100)
```
where:
`^` is an exponentiation (power) arithmetic operation
`nlen` is the appropriate length for the desired security strength
2. Compute the modulus, `n`
```text
n = p * q
```
3. Compute the totient, `t`
- `Euler's totient function` is used in the original RSA
```text
φ(n) = (p − 1) * (q − 1)
```
which outputs the amount of numbers that are coprime to `n`
- [Carmichael function](https://en.wikipedia.org/wiki/Carmichael_function) is recommended for modern RSA-based cryptosystems, also known as `reduced totient function` or `least universal exponent function`
```text
λ(n) = lcm(p − 1, q − 1)
```
where `lcm()` is the [least common multiple](https://en.wikipedia.org/wiki/Least_common_multiple)
4. Choose a public key exponent, integer `e` (usually `65537` in decimal, or `0x010001` in hex)
```text
1 < e < t
gcd(t, e) = 1
```
5. Compute the [modular multiplicative inverse](https://en.wikipedia.org/wiki/Modular_multiplicative_inverse), `d`
```text
d = (e ^ (−1)) mod t
1 = (d * e) mod t
```
6. Public key
```text
(e, n)
```
7. Private key
```text
(d, n)
```
The numbers `p`, `q`, and `d` must be kept secret
## Encryption
The encryption of the plaintext message, `m`
```text
c = (m ^ e) mod n
```
## Decryption
The decryption of the ciphertext, `c`
```text
D = (c ^ d) mod n
```
## References
- [RSA in Wikipedia](https://en.wikipedia.org/wiki/RSA_(cryptosystem))
- [FIPS 186-4, Key Pair Generation](https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf#page=62)
## Disclaimer
This project was created for research purposes and is not intended for use in production systems.