フィールドの詳細

• t

  final int[] t

  Variable is package private for encoding.

コンストラクタの詳細

• Ed25519FieldElement

  public Ed25519FieldElement​(Field f,
                             int[] t)

  Creates a field element.

  パラメータ:

  f - The underlying field, must be the finite field with p = 2^255 - 19 elements

  t - The 2^25.5 bit representation of the field element.

メソッドの詳細

• isNonZero

  public boolean isNonZero​()

  Gets a value indicating whether or not the field element is non-zero.

  定義:

  isNonZero クラス内 FieldElement

  戻り値:

  1 if it is non-zero, 0 otherwise.

• add

  public FieldElement add​(FieldElement val)

  h = f + g

  TODO-CR BR: h is allocated via new, probably not a good idea. Do we need the copying into temp variables if we do that?

  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.

  定義:

  add クラス内 FieldElement

  パラメータ:

  val - The field element to add.

  戻り値:

  The field element this + val.

• subtract

  public FieldElement subtract​(FieldElement val)

  h = f - g

  Can overlap h with f or g.

  TODO-CR BR: See above.

  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.

  定義:

  subtract クラス内 FieldElement

  パラメータ:

  val - The field element to subtract.

  戻り値:

  The field element this - val.

• negate

  public FieldElement negate​()

  h = -f

  TODO-CR BR: see above.

  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.

  定義:

  negate クラス内 FieldElement

  戻り値:

  The field element (-1) * this.

• 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.

  定義:

  multiply クラス内 FieldElement

  パラメータ:

  val - The field element to multiply.

  戻り値:

  The (reasonably reduced) field element this * val.

• 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.

  定義:

  square クラス内 FieldElement

  戻り値:

  The (reasonably reduced) square of this field element.

• 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.

  定義:

  squareAndDouble クラス内 FieldElement

  戻り値:

  The (reasonably reduced) square of this field element times 2.

• invert

  public FieldElement invert​()

  Invert this field element.

  The inverse is found via Fermat's little theorem:
  a^p congruent a mod p and therefore a^(p-2) congruent a^-1 mod p

  定義:

  invert クラス内 FieldElement

  戻り値:

  The inverse of this field element.

• pow22523

  public FieldElement pow22523​()

  Gets this field element to the power of (2^252 - 3). This is a helper function for calculating the square root.

  TODO-CR BR: I think it makes sense to have a sqrt function.

  定義:

  pow22523 クラス内 FieldElement

  戻り値:

  This field element to the power of (2^252 - 3).

• hashCode

  public int hashCode​()

  オーバーライド:

  hashCode クラス内 java.lang.Object

• equals

  public boolean equals​(java.lang.Object obj)

  オーバーライド:

  equals クラス内 java.lang.Object

• toString

  public java.lang.String toString​()

  オーバーライド:

  toString クラス内 java.lang.Object