net.i2p.crypto.eddsa.math.radix251

Class Radix251FieldElement

java.lang.Object

net.i2p.crypto.eddsa.math.FieldElement

net.i2p.crypto.eddsa.math.radix251.Radix251FieldElement

public class Radix251FieldElement
extends FieldElement

An element t, entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on context.

Field Summary

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

f

Constructor Summary

Constructors

Constructor and Description
Radix251FieldElement(Field f, int[] t)

Method Summary

Methods

Modifier and Type	Method and Description
FieldElement	add(FieldElement val) h = f + g Can overlap h with f or g.
boolean	equals(java.lang.Object obj)
int	hashCode()
FieldElement	invert()
boolean	isNonZero()
FieldElement	multiply(FieldElement val) h = f * g Can overlap h with f or g.
FieldElement	negate() h = -f Preconditions: |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
FieldElement	pow22523()
FieldElement	square() h = f * f Can overlap h with f.
FieldElement	squareAndDouble() h = 2 * f * f Can overlap h with f.
FieldElement	subtract(FieldElement val) h = f - g Can overlap h with f or g.
java.lang.String	toString()

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

addOne, divide, isNegative, subtractOne, toByteArray

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

Radix251FieldElement

public Radix251FieldElement(Field f,
                    int[] t)

Method Detail

isNonZero

public boolean isNonZero()

Specified by:

isNonZero in class FieldElement

add

public FieldElement add(FieldElement val)

h = f + g Can overlap h with f or g. Preconditions: |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. Postconditions: |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.

Specified by:

add in class FieldElement

subtract

public FieldElement subtract(FieldElement val)

h = f - g Can overlap h with f or g. Preconditions: |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. Postconditions: |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.

Specified by:

subtract in class FieldElement

negate

public FieldElement negate()

h = -f Preconditions: |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. Postconditions: |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.

Specified by:

negate in class FieldElement

multiply

public FieldElement multiply(FieldElement val)

h = f * g Can overlap h with f or g. Preconditions: |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. Postconditions: |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. Notes on implementation strategy: Using schoolbook multiplication. Karatsuba would save a little in some cost models. Most multiplications by 2 and 19 are 32-bit precomputations; cheaper than 64-bit postcomputations. There is one remaining multiplication by 19 in the carry chain; one *19 precomputation can be merged into this, but the resulting data flow is considerably less clean. There are 12 carries below. 10 of them are 2-way parallelizable and vectorizable. Can get away with 11 carries, but then data flow is much deeper. With tighter constraints on inputs can squeeze carries into int32.

Specified by:

multiply in class FieldElement

square

public FieldElement square()

h = f * f Can overlap h with f. Preconditions: |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. Postconditions: |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. See multiply(FieldElement) for discussion of implementation strategy.

Specified by:

square in class FieldElement

squareAndDouble

public FieldElement squareAndDouble()

h = 2 * f * f Can overlap h with f. Preconditions: |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. Postconditions: |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. See multiply(FieldElement) for discussion of implementation strategy.

Specified by:

squareAndDouble in class FieldElement

invert

public FieldElement invert()

Specified by:

invert in class FieldElement

pow22523

public FieldElement pow22523()

Specified by:

pow22523 in class FieldElement

hashCode

public int hashCode()

Overrides:

hashCode in class java.lang.Object

equals

public boolean equals(java.lang.Object obj)

Overrides:

equals in class java.lang.Object

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object