paillier-bigint - npm Package Compare versions

Comparing version 3.0.6 to 3.1.0

package.json

		{
		"name": "paillier-bigint",
		"version": "3.0.6",
		"version": "3.1.0",
		"description": "An implementation of the Paillier cryptosystem using native JS (ECMA 2020) implementation of BigInt",
		@@ -5,0 +5,0 @@ "keywords": [

README.md

		@@ -22,7 +22,7 @@ [![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](https://opensource.org/licenses/MIT)

		D( E(m1) · E(m2) ) mod n^2 = m1 + m2 mod n
		D( E(m<sub>1</sub>) · E(m<sub>2</sub>) ) mod n<sup>2</sup> = m<sub>1</sub> + m<sub>2</sub> mod n

		The product of a ciphertext with a plaintext raising g will decrypt to the sum of the corresponding plaintexts,

		D( E(m1) · g^(m2) ) mod n^2 = m1 + m2 mod n
		D( E(m<sub>1</sub>) · g<sup>m<sub>2</sub></sup> ) mod n<sup>2</sup> = m<sub>1</sub> + m<sub>2</sub> mod n

		@@ -33,5 +33,5 @@ ### (pseudo-)homomorphic multiplication of plaintexts

		D( E(m1)^(m2) mod n^2 ) = m1 · m2 mod n,
		D( E(m<sub>1</sub>)<sup>m<sub>2</sub></sup> mod n<sup>2</sup> ) = m<sub>1</sub> · m<sub>2</sub> mod n,

		D( E(m2)^(m1) mod n^2 ) = m1 · m2 mod n.
		D( E(m<sub>2</sub>)<sup>m<sub>1</sub></sup> mod n<sup>2</sup> ) = m<sub>1</sub> · m<sub>2</sub> mod n.

		@@ -41,3 +41,3 @@ More generally, an encrypted plaintext raised to a constant k will decrypt to the product of the plaintext and the

		D( E(m1)^k mod n^2 ) = k · m1 mod n.
		D( E(m<sub>1</sub>)<sup>k</sup> mod n<sup>2</sup> ) = k · m<sub>1</sub> mod n.

		@@ -54,7 +54,11 @@ However, given the Paillier encryptions of two messages there is no known way to compute an encryption of the product of
		3. Repeat until the bitlength of `n=p·q` is `keyLength`.
		3. Compute `λ = lcm(p-1, q-1)` with `lcm(a, b) = a·b / gcd(a, b)`.
		4. Select a generator `g` in `Z*` of `n^2`. `g` can be computed as follows (there are other ways):
		* Generate randoms `α` and `β` in `Z*` of `n`.
		* Compute `g=( α·n + 1 ) β^n mod n^2`.
		5. Compute `μ=( L( g^λ mod n^2 ) )^(-1) mod n` where `L(x)=(x-1)/n`.
		3. Compute parameters `λ`, `g` and `μ`. Among other ways, it can be done as follows:
		1. Standard approach:
		1. Compute `λ = lcm(p-1, q-1)` with `lcm(a, b) = a·b / gcd(a, b)`.
		2. Generate randoms `α` and `β` in `Z` of `n`, and select generator `g` in `Z` of `n2` as `g = ( α·n + 1 ) βn mod n**2`.
		3. Compute `μ = ( L( g^λ mod n2 ) )(-1) mod n` where `L(x)=(x-1)/n`.
		2. If using p,q of equivalent length, a simpler variant would be:
		1. `λ = (p-1, q-1)`
		2. `g = n+1`
		3. `μ = λ**(-1) mod n`

		@@ -68,10 +72,10 @@ The public (encryption) key is (n, g).

		1. Select random integer `r` in `(1, n^2)`.
		1. Select random integer `r` in `(1, n)`.

		2. Compute ciphertext as: `c = g^m · r^n mod n^2`
		2. Compute ciphertext as: `c = gm · rn mod n2`**

		## Decryption
		Let `c` be the ciphertext to decrypt, where `c` in `(0, n^2)`.
		Let `c` be the ciphertext to decrypt, where `c` in `(0, n**2)`.

		1. Compute the plaintext message as: `m = L( c^λ mod n^2 ) · μ mod n`
		1. Compute the plaintext message as: `m = L( cλ mod n2 ) · μ mod n`

		@@ -78,0 +82,0 @@ ## Installation

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