Accounts

Account Private Key​

An account private key is constructed from a randomly-sampled account seed. This account seed is used to generate:

• a secret key for the account signature scheme,

• a pseudorandom function seed for transaction serial numbers, and

• a commitment randomness for the account commitment scheme.

Private Key Format​

APrivateKey1zkp4X9ApjTb7Rv8EABfZRugXBhbPzCL245GyNtYJP5GYY2k

An account private key is formatted as a Base58 string, comprised of 59 characters. The account private key is encoded with a private key prefix that reads APrivateKey1, indicating that it is a private key and should not be shared with other users.

Account View Key​

An Beo account view key is derived from an account private key and enables users to decrypt their records from the global ledger. As account view keys are able to access every record in a user's account, this key can be used by third-party auditors to verify the complete history of an account.

The account view key is comprised of:

• a secret key for the account encryption scheme.

View Key Format​

AViewKey1nKB4qr9b5gK8wQvmM5sTPEuBwshtDdkCZB1SPWppAG9Y

An account view key is formatted as a Base58 string, comprised of 53 characters. The account view key is encoded with a view key prefix that reads AViewKey1, indicating that it is a view key and should only be shared with authorized parties.

Account Address​

An Beo account address is a unique identifier that allows users to transfer value and record data to one another in transactions.

The account address is comprised of:

• a public key for the account encryption scheme.

Address Format​

Beo1dg722m22fzpz6xjdrvl9tzu5t68zmypj5p74khlqcac0gvednygqxaax0j

An account address is formatted as a Bech32 string, comprised of 63 characters. The account address is encoded with an address prefix that reads beo1.

Advanced Topics​

The descriptions of algorithms below make use of the following definitions of mathematical objects:

Prime Fields​

For a prime r, the prime field of order r is defined as the set of integers {0, 1, ..., r - 1} with addition and multiplication modulo r. In this document, we will use two prime fields:

• Fscalar, of prime order p = 2111115437357092606062206234695386632838870926408408195193685246394721360383

• Fbase, of prime order q = 8444461749428370424248824938781546531375899335154063827935233455917409239041

Prime Order Elliptic Curve Groups​

In this document, we will consider the order-p subgroup of points on an elliptic curve defined over the base field Fbase.

Elements of this subgroup consist of a coordinate pair (x, y). The group has two associated operations: point addition, and point doubling. The group also has a distinguished point, the generator G, which is a fixed point of the group.

HashToField​

For a finite field F, HashToField is a cryptographic hash function that takes as input either a sequence of bytes or a sequence of field elements and outputs a field element. The output is uniformly distributed over the field F.

HashToScalar​

An instantiation of HashToField that output elements in the scalar field Fscalar. source code

EncodeToF​

EncodeToF(x) is a function that encodes the Unicode string x into an element of Fbase.

Details of the encoding:

• x is converted to its UTF-8 sequence of bytes b.

• b is turned into an unsigned integer v that represents the little endian value of b.

• v is reduced modulo the prime that defines the field Fbase.

Account Prefixes​

	Type	Human-Readable Prefix	Prefix Bytes
Account Private Key	bytes	APrivateKey1	[ 127, 134, 189, 116, 210, 221, 210, 137, 144 ]
Account View Key	bytes	AViewKey1	[ 14, 138, 223, 204, 247, 224, 122 ]
Account Address	string	beo1	beo1

Offline Accounts​

In many instances such as enterprise settings, it is advisable to handle sensitive keys and data on isolated, offline machines. An Beo account can be created on an offline machine and available for immediate use. In conjunction with account proving keys, a user can ensure their private key remains offline even for creating transactions.

While no solution is perfect, it is advisable to create a new Beo account on a disconnected device to minimize the risk of leaking one's account private key to unintended parties.

Account Commitment Outputs​

The account commitment output is used to create an account view key, which is comprised of an encryption secret key. This encryption secret key is a scalar field element derived from the account commitment output. To ensure the validity of the account view key, the account commitment output should be representable in the scalar field.

Create an Account​

Given global instantiated Beo parameters and subroutines.

Generate a Private Key​

1. Sample a 32 byte seed from random

2. Construct private key components

   • sk_sig = HashToScalar(EncodeToF("BeoAccountSignatureSecretKey0") | seed))

   • r_sig = HashToScalar(EncodeToF("BeoAccountSignatureRandomizer0.0") | seed))

   where | denotes concatenation, and where HashToScalar denotes the Poseidon hash function.

3.private_key = (seed, (sk_sig, r_sig))

Generate a View Key​

1. (sk_sig, r_sig) = private_key

2. view_key = sk_sig + r_sig + HashToScalar(sk_sig * G | r_sig * G)

where G is the generator of the base field.

Generate an Address​

1. address = view_key * G