module

Ed25519

Constants

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 = "1.1.0"
Zero = BigInt.new(0)

Instance methods

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

Convert between types

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bytes_to_number_le(uint8a : Bytes) : BigInt

Little Endian

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

cswap from RFC7748

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

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

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

Private convenience method RFC8032 5.1.5

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get_public_key(private_key : PrivKey) : Bytes

** Calculates ed25519 public key.

  1. private key is hashed with sha512, then first 32 bytes are taken from the hash
  2. 3 least significant bits of the first byte are cleared RFC8032 5.1.5 /
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get_shared_secret(private_key : PrivKey, public_key : Hex) : Bytes

** Calculates X25519 DH shared secret from ed25519 private & public keys. Curve25519 used in X25519 consumes private keys as-is, while ed25519 hashes them with sha512. Which means we will need to normalize ed25519 seeds to "hashed repr". @param private_key ed25519 private key @param public_key ed25519 public key @returns X25519 shared key /

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

Note: this egcd-based invert is 50% faster than powMod-based one. Inverses number over modulo

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

** Takes a list of numbers, efficiently inverts all of them. @param nums list of BigInts @param p modulo @returns list of inverted BigInts @example Ed25519.invert_batch([1n, 2n, 4n], 21n)

=> [1n, 11n, 16n]

/

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invert_sqrt(number : BigInt)

Calculates 1/√(number)

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

x25519 from 4 **

@param point_u u coordinate (x) on Montgomery Curve 25519 @param scalar by which the point would be multiplied @returns new Point on Montgomery curve /

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

** Checks for num to be in range: For strict == true: 0 < num < max. For strict == false: 0 <= num < max. Converts non-float safe numbers to BigInts. /

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

Does x ^ (2 ^ power) mod p. pow2(30, 4) == 30 ^ (2 ^ 4)

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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. Exponentiates it to very big number. We are unwrapping the loop because it's 2x faster. (2n**252n-3n).to_string(2) would produce bits [250x 1, 0, 1] We are multiplying it bit-by-bit

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sha512_modq_le(*args) : BigInt

Little-endian SHA512 with modulo n

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

** Signs message with private_key. RFC8032 5.1.6 /

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

Ratio of u to v. Allows us to combine inversion and square root. Uses algo from RFC8032 5.1.3. Constant-time prettier-ignore

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

** Verifies ed25519 signature against message and public key. An extended group equation is checked. RFC8032 5.1.7 Compliant with ZIP215: 0 <= sig.R/public_key < 2**256 (can be >= curve.P) 0 <= sig.s < l Not compliant with RFC8032: it's not possible to comply to both ZIP & RFC at the same time. /

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Nested types