https://github.com/pedroalbanese/nums

Microsoft Nothing Up My Sleeve Elliptic curves
https://github.com/pedroalbanese/nums

asymmetric-cryptography digital-signature ecdh elliptic-curves microsoft nums

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Microsoft Nothing Up My Sleeve Elliptic curves

• Host: GitHub
• URL: https://github.com/pedroalbanese/nums
• Owner: pedroalbanese
• License: isc
• Created: 2022-04-16T00:18:15.000Z (over 2 years ago)
• Default Branch: main
• Last Pushed: 2022-05-12T18:14:30.000Z (over 2 years ago)
• Last Synced: 2024-06-20T11:10:06.581Z (6 months ago)
• Topics: asymmetric-cryptography, digital-signature, ecdh, elliptic-curves, microsoft, nums
• Language: Go
• Homepage:
• Size: 41 KB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.md

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README

        
# NUMS

[![ISC License](http://img.shields.io/badge/license-ISC-blue.svg)](https://github.com/pedroalbanese/nums/blob/master/LICENSE.md) 

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[![GitHub release (latest by date)](https://img.shields.io/github/v/release/pedroalbanese/nums)](https://github.com/pedroalbanese/nums/releases)

### Microsoft Nothing Up My Sleeve Elliptic curves

[NUMS](http://www.watersprings.org/pub/id/draft-black-numscurves-01.html) (Nothing Up My Sleeve) curves, which are supported in the MSRElliptic Curve Cryptography Library (a.k.a. MSR ECCLib).

These curves are elliptic curves over a prime field, just like the NIST or Brainpool curves. However, the domain-parameters are choosen using a VERY TIGHT DESIGN SPACE to ensure, that the introduction of a backdoor is infeasable. For a desired size of s bits the prime p is choosen as p = 2^s - c with the smallest c where c>0 and p mod 4 = 3 and p being prime.

## Usage

```

Usage of nums:

  -dec

        Decrypt with Private key

  -derive

        Derive shared secret key

  -enc

        Encrypt with Public key

  -key string

        Private/Public key

  -keygen

        Generate keypair

  -pub string

        Remote's side Public key

  -sign

        Sign with Private key

  -signature string

        Signature

  -verify

        Verify with Public key

```

## Examples

#### Asymmetric keypair generation:

```sh

./nums -keygen 

```

#### Digital signature (ECDSA):

```sh

./nums -sign -key $prvkey < file.ext > sign.txt

sign=$(cat sign.txt)

./nums -verify -key $pubkey -signature $sign < file.ext

```

#### Asymmetric encryption:

```sh

./nums -enc -key $pubkey < file.ext > file.enc

./nums -dec -key $prvkey < file.enc

```

#### Shared key agreement (ECDH):

```sh

./nums -derive -key $prvkey -pub $pubkey

```

## License

This project is licensed under the ISC License.

##### Industrial-Grade Reliability. Copyright (c) 2020-2022 ALBANESE Research Lab.