module Ed25519

Extended Modules

• Ed25519

Defined in:

ed25519.cr
ed25519/point.cr

Constant Summary

BigInt255 = BigInt.new(255)

CURVE_ORDER = (Two ** (BigInt.new(252))) + (BigInt.new("27742317777372353535851937790883648493"))

D_MINUS_ONE_SQ = BigInt.new("40440834346308536858101042469323190826248399146238708352240133220865137265952")

(d-1)²

INVSQRT_A_MINUS_D = BigInt.new("54469307008909316920995813868745141605393597292927456921205312896311721017578")

1 / √(a-d)

MAX_256B = Ed25519::Two ** (BigInt.new(256))

One = BigInt.new(1)

ONE_MINUS_D_SQ = BigInt.new("1159843021668779879193775521855586647937357759715417654439879720876111806838")

1-d²

PointPrecomputes = Hash(Point, Array(ExtendedPoint)).new

Stores precomputed values for points.

SQRT_AD_MINUS_ONE = BigInt.new("25063068953384623474111414158702152701244531502492656460079210482610430750235")

√(ad - 1)

SQRT_D = BigInt.new("6853475219497561581579357271197624642482790079785650197046958215289687604742")

√d aka sqrt(-486664)

SQRT_M1 = BigInt.new("19681161376707505956807079304988542015446066515923890162744021073123829784752")

√(-1) aka √(a) aka 2^((p-1)/4)

Two = BigInt.new(2)

VERSION = "1.0.3"

Zero = BigInt.new(0)

Instance Method Summary

• #adjust_bytes_25519(bytes : Bytes) : Bytes
• #bytes_255_to_number_le(bytes : Bytes) : BigInt
• #bytes_to_hex(uint8a : Bytes) : String

  Convert between types ---------------------

• #bytes_to_number_le(uint8a : Bytes) : BigInt

  Little Endian

• #concat_bytes(*arrays) : Bytes
• #cswap(swap : BigInt, x_2 : BigInt, x_3 : BigInt) : Tuple(BigInt, BigInt)

  cswap from RFC7748

• #decode_scalar_25519(n : Hex) : BigInt
• #decode_u_coordinate(u_enc : Hex) : BigInt
• #ed_is_negative(num : BigInt)

  Little-endian check for first LE bit (last BE bit)

• #encode_u_coordinate(u : BigInt) : Bytes
• #ensure_bytes(hex : Hex, expected_length : Int32 | Nil = nil) : Bytes
• #equal_bytes(b1 : Bytes, b2 : Bytes)
• #get_extended_public_key(key : PrivKey)

  Private convenience method RFC8032 5.1.5

• #get_public_key(private_key : PrivKey) : Bytes

  ** Calculates ed25519 public key.

• #get_shared_secret(private_key : PrivKey, public_key : Hex) : Bytes

  ** Calculates X25519 DH shared secret from ed25519 private & public keys.

• #hex_to_bytes(hex : String) : Bytes
• #invert(number : BigInt, modulo : BigInt = Curve::P) : BigInt

  Note: this egcd-based invert is 50% faster than powMod-based one.

• #invert_batch(nums : Array(BigInt), p : BigInt = Curve::P) : Array(BigInt)

  ** Takes a list of numbers, efficiently inverts all of them.

• #invert_sqrt(number : BigInt)

  Calculates 1/√(number)

• #mod(a : BigInt, b : BigInt = Curve::P) : BigInt
• #montgomery_ladder(point_u : BigInt, scalar : BigInt) : BigInt

  x25519 from 4 **

• #normalize_scalar(num : Int, max : BigInt, strict = true) : BigInt

  ** Checks for num to be in range: For strict == true: 0 < num < max.

• #number_to_32_bytes_be(num : BigInt) : Bytes
• #number_to_32_bytes_le(num : BigInt) : Bytes
• #pow2(x : BigInt, power : BigInt) : BigInt

  Does x ^ (2 ^ power) mod p.

• #pow_2_252_3(x : BigInt)

  Power to (p-5)/8 aka x^(2^252-3) Used to calculate y - the square root of y².

• #sha512_modq_le(*args) : BigInt

  Little-endian SHA512 with modulo n

• #sign(message : Hex, private_key : Hex) : Bytes

  ** Signs message with private_key.

• #uv_ratio(u : BigInt, v : BigInt) : NamedTuple(is_valid: Bool, value: BigInt)

  Ratio of u to v.

• #verify(sig : SigType, message : Hex, public_key : PubKey) : Bool

  ** Verifies ed25519 signature against message and public key.

Instance Method Detail