net.i2p.crypto.eddsa.math.radix251

Class Radix251LittleEndianEncoding

java.lang.Object

net.i2p.crypto.eddsa.math.Encoding

net.i2p.crypto.eddsa.math.radix251.Radix251LittleEndianEncoding

public class Radix251LittleEndianEncoding
extends Encoding

Field Summary

Fields inherited from class net.i2p.crypto.eddsa.math.Encoding

f

Constructor Summary

Constructors

Constructor and Description
Radix251LittleEndianEncoding()

Method Summary

Methods

Modifier and Type	Method and Description
FieldElement	decode(byte[] in) Ignores top bit.
byte[]	encode(FieldElement x) Preconditions: |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. Write p=2^255-19; q=floor(h/p). Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
boolean	isNegative(FieldElement x) Return true if x is in {1,3,5,...,q-2} Return false if x is in {0,2,4,...,q-1} Preconditions: |x| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.

Methods inherited from class net.i2p.crypto.eddsa.math.Encoding

setField

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Radix251LittleEndianEncoding

public Radix251LittleEndianEncoding()

Method Detail

encode

public byte[] encode(FieldElement x)

Preconditions:
|h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.

Write p=2^255-19; q=floor(h/p).
Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).

Proof:
Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.

Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
Then 0 < y < 1.

Write r=h-pq.
Have 0 <= r <= p-1=2^255-20.
Thus 0 <= r+19(2^-255)r < r+19(2^-255)2^255 <= 2^255-1.

Write x=r+19(2^-255)r+y.
Then 0 < x < 2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.

Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.

Specified by:

encode in class Encoding

Returns:

the (b-1)-bit encoding of this FieldElement.

decode

public FieldElement decode(byte[] in)

Ignores top bit.

Specified by:

decode in class Encoding

Returns:

the FieldElement represented by 'val'.

isNegative

public boolean isNegative(FieldElement x)

Return true if x is in {1,3,5,...,q-2}
Return false if x is in {0,2,4,...,q-1}

Preconditions:
|x| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.

Specified by:

isNegative in class Encoding

Returns:

true if x is in {1,3,5,...,q-2}, false otherwise.