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Algorand Specifications

A player is uniquely identified by a 256-bit string II called an address.

Each player owns exactly one participation keypair. A participation keypair consists of a public key pkpk and a secret key sksk.

A keypair is defined in the specification of participation keys in Algorand. Each participation keypair is valid for a range of protocol rounds [rfirst,rlast].

Let mm, m′ be arbitrary sequences of bits.

Let Bk, B¯ be 64-bit integers representing balances in μALGO with rewards applied.

Let τ, τ¯ be 32-bit integers, and QQ be a 256-bit string.

Let (pkk, skk) be some valid keypair.

A secret key supports a signing procedure

y := Sign(m, m′, skk, Bk, B¯, Q, τ, τ¯)

Where y is opaque and cryptographically resistant to tampering, where defined.

Signing is not defined on many inputs: for any given input, signing may fail to produce an output.

The following functions are defined on y:

• Verifying: Verify(y, m, m′, pkk, Bk, B¯, Q, τ, τ¯) = w where w is a 64-bit integer called the weight of y. w ≠ 0 if and only if y was produced by signing by skk (up to cryptographic security). w is uniquely determined given fixed values of m′, pkk, Bk, B¯, Q, τ, τ¯.

• Comparing: Fixing the inputs m′, B¯, Q, τ, τ¯ to a signing operation, there exists a total ordering on the outputs y. In other words, if f(sk, B) = Sign(m, m′, sk, B, B¯, Q, τ, τ¯) = y, and S = {(sk0, B0), (sk1, B1), …, (skn, Bn)}, then {f(x) | x ∈ S} is a totally ordered set. We write that y1 < y2 if y1 comes before y2 in this ordering.

• Generating Randomness: Let y be a valid output of a signing operation with skk. Then R = Rand(y, pkk) is defined to be a pseudorandom 256-bit integer (up to cryptographic security). R is uniquely determined given fixed values of m′, pkk, Bk, B¯, Q, τ, τ¯.

The signing procedure is allowed to produce a nondeterministic output, but the functions above must be well-defined with respect to a given input to the signing procedure (e.g., a procedure that implements Verify(Sign(…)) always returns the same value).