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229 lines
7.3 KiB
229 lines
7.3 KiB
# <img src="./logo.png" alt="bn.js" width="160" height="160" />
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> BigNum in pure javascript
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[](http://travis-ci.org/indutny/bn.js)
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## Install
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`npm install --save bn.js`
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## Usage
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```js
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const BN = require('bn.js');
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var a = new BN('dead', 16);
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var b = new BN('101010', 2);
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var res = a.add(b);
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console.log(res.toString(10)); // 57047
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```
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**Note**: decimals are not supported in this library.
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## Notation
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### Prefixes
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There are several prefixes to instructions that affect the way the work. Here
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is the list of them in the order of appearance in the function name:
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* `i` - perform operation in-place, storing the result in the host object (on
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which the method was invoked). Might be used to avoid number allocation costs
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* `u` - unsigned, ignore the sign of operands when performing operation, or
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always return positive value. Second case applies to reduction operations
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like `mod()`. In such cases if the result will be negative - modulo will be
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added to the result to make it positive
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### Postfixes
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* `n` - the argument of the function must be a plain JavaScript
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Number. Decimals are not supported.
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* `rn` - both argument and return value of the function are plain JavaScript
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Numbers. Decimals are not supported.
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### Examples
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* `a.iadd(b)` - perform addition on `a` and `b`, storing the result in `a`
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* `a.umod(b)` - reduce `a` modulo `b`, returning positive value
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* `a.iushln(13)` - shift bits of `a` left by 13
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## Instructions
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Prefixes/postfixes are put in parens at the of the line. `endian` - could be
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either `le` (little-endian) or `be` (big-endian).
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### Utilities
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* `a.clone()` - clone number
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* `a.toString(base, length)` - convert to base-string and pad with zeroes
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* `a.toNumber()` - convert to Javascript Number (limited to 53 bits)
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* `a.toJSON()` - convert to JSON compatible hex string (alias of `toString(16)`)
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* `a.toArray(endian, length)` - convert to byte `Array`, and optionally zero
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pad to length, throwing if already exceeding
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* `a.toArrayLike(type, endian, length)` - convert to an instance of `type`,
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which must behave like an `Array`
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* `a.toBuffer(endian, length)` - convert to Node.js Buffer (if available). For
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compatibility with browserify and similar tools, use this instead:
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`a.toArrayLike(Buffer, endian, length)`
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* `a.bitLength()` - get number of bits occupied
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* `a.zeroBits()` - return number of less-significant consequent zero bits
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(example: `1010000` has 4 zero bits)
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* `a.byteLength()` - return number of bytes occupied
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* `a.isNeg()` - true if the number is negative
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* `a.isEven()` - no comments
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* `a.isOdd()` - no comments
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* `a.isZero()` - no comments
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* `a.cmp(b)` - compare numbers and return `-1` (a `<` b), `0` (a `==` b), or `1` (a `>` b)
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depending on the comparison result (`ucmp`, `cmpn`)
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* `a.lt(b)` - `a` less than `b` (`n`)
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* `a.lte(b)` - `a` less than or equals `b` (`n`)
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* `a.gt(b)` - `a` greater than `b` (`n`)
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* `a.gte(b)` - `a` greater than or equals `b` (`n`)
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* `a.eq(b)` - `a` equals `b` (`n`)
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* `a.toTwos(width)` - convert to two's complement representation, where `width` is bit width
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* `a.fromTwos(width)` - convert from two's complement representation, where `width` is the bit width
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* `BN.isBN(object)` - returns true if the supplied `object` is a BN.js instance
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* `BN.max(a, b)` - return `a` if `a` bigger than `b`
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* `BN.min(a, b)` - return `a` if `a` less than `b`
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### Arithmetics
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* `a.neg()` - negate sign (`i`)
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* `a.abs()` - absolute value (`i`)
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* `a.add(b)` - addition (`i`, `n`, `in`)
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* `a.sub(b)` - subtraction (`i`, `n`, `in`)
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* `a.mul(b)` - multiply (`i`, `n`, `in`)
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* `a.sqr()` - square (`i`)
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* `a.pow(b)` - raise `a` to the power of `b`
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* `a.div(b)` - divide (`divn`, `idivn`)
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* `a.mod(b)` - reduct (`u`, `n`) (but no `umodn`)
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* `a.divRound(b)` - rounded division
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### Bit operations
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* `a.or(b)` - or (`i`, `u`, `iu`)
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* `a.and(b)` - and (`i`, `u`, `iu`, `andln`) (NOTE: `andln` is going to be replaced
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with `andn` in future)
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* `a.xor(b)` - xor (`i`, `u`, `iu`)
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* `a.setn(b)` - set specified bit to `1`
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* `a.shln(b)` - shift left (`i`, `u`, `iu`)
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* `a.shrn(b)` - shift right (`i`, `u`, `iu`)
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* `a.testn(b)` - test if specified bit is set
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* `a.maskn(b)` - clear bits with indexes higher or equal to `b` (`i`)
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* `a.bincn(b)` - add `1 << b` to the number
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* `a.notn(w)` - not (for the width specified by `w`) (`i`)
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### Reduction
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* `a.gcd(b)` - GCD
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* `a.egcd(b)` - Extended GCD results (`{ a: ..., b: ..., gcd: ... }`)
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* `a.invm(b)` - inverse `a` modulo `b`
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## Fast reduction
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When doing lots of reductions using the same modulo, it might be beneficial to
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use some tricks: like [Montgomery multiplication][0], or using special algorithm
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for [Mersenne Prime][1].
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### Reduction context
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To enable this tricks one should create a reduction context:
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```js
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var red = BN.red(num);
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```
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where `num` is just a BN instance.
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Or:
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```js
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var red = BN.red(primeName);
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```
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Where `primeName` is either of these [Mersenne Primes][1]:
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* `'k256'`
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* `'p224'`
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* `'p192'`
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* `'p25519'`
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Or:
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```js
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var red = BN.mont(num);
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```
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To reduce numbers with [Montgomery trick][0]. `.mont()` is generally faster than
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`.red(num)`, but slower than `BN.red(primeName)`.
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### Converting numbers
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Before performing anything in reduction context - numbers should be converted
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to it. Usually, this means that one should:
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* Convert inputs to reducted ones
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* Operate on them in reduction context
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* Convert outputs back from the reduction context
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Here is how one may convert numbers to `red`:
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```js
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var redA = a.toRed(red);
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```
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Where `red` is a reduction context created using instructions above
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Here is how to convert them back:
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```js
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var a = redA.fromRed();
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```
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### Red instructions
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Most of the instructions from the very start of this readme have their
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counterparts in red context:
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* `a.redAdd(b)`, `a.redIAdd(b)`
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* `a.redSub(b)`, `a.redISub(b)`
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* `a.redShl(num)`
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* `a.redMul(b)`, `a.redIMul(b)`
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* `a.redSqr()`, `a.redISqr()`
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* `a.redSqrt()` - square root modulo reduction context's prime
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* `a.redInvm()` - modular inverse of the number
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* `a.redNeg()`
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* `a.redPow(b)` - modular exponentiation
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### Number Size
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Optimized for elliptic curves that work with 256-bit numbers.
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There is no limitation on the size of the numbers.
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## LICENSE
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This software is licensed under the MIT License.
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Copyright Fedor Indutny, 2015.
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Permission is hereby granted, free of charge, to any person obtaining a
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copy of this software and associated documentation files (the
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"Software"), to deal in the Software without restriction, including
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without limitation the rights to use, copy, modify, merge, publish,
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distribute, sublicense, and/or sell copies of the Software, and to permit
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persons to whom the Software is furnished to do so, subject to the
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following conditions:
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The above copyright notice and this permission notice shall be included
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in all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
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OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN
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NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
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DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
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OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
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USE OR OTHER DEALINGS IN THE SOFTWARE.
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[0]: https://en.wikipedia.org/wiki/Montgomery_modular_multiplication
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[1]: https://en.wikipedia.org/wiki/Mersenne_prime
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