CryptoNote Elements

Loki uses the Monero source code because of the high level of privacy it affords to transactions. Monero is an evolution on the CryptoNote protocol, which uses ring signatures, stealth addresses, and RingCT, giving users the ability to sign transactions and obfuscate amounts while maintaining plausible deniability.

Ring Signatures

Ring signatures work by constructing a ring of possible signers to a transaction where only one of the signers is the actual sender. Loki makes use of ring signatures to obfuscate the true history of transaction outputs. Ring signatures will be mandatory for all Loki transactions (excluding block reward transactions), and uniquely, a fixed ring-size of ten is enforced on the Loki blockchain. This means that each input will spend from one of ten possible outputs, including the true output.

Ring Signature Size

The size of a ring signature refers to how many mixins are used to construct the ring. Monero currently has an enforced minimum ring signature size of seven, with six mixins used alongside the real unspent output in a transaction.

The effect of larger ring-sizes has been sparsely studied, however, in paper 0001 (published by the Monero Research Lab), the effect of differing ring-sizes was analysed versus an attacker who owned a large number of outputs on the blockchain . It was found that higher ring-sizes reduce the timeframe in which a malicious attacker who owned a large number of unspent outputs would be able to perform effective analysis of transactions. Mandating larger ring-sizes also protects against a theoretical attack known as an EABE/Knacc attack, where a third-party (i.e. an exchange) can perform limited temporal analysis on transactions between two users.

Additionally, Monero has no maximum ring-size enforced by network consensus rules. Many wallets like the Monero GUI wallet cap the ring-size at 26. However, a user is free to manually create a transaction with whatever ring-size they wish, as long as it is above a ring-size of seven. This is problematic since most wallets have a default ring-size of seven. Increasing a transactions ring-size above seven makes it stand out. Further, if an individuals transactions were to always use a non-standard ring-size in Monero (ten for example), a passive third-party could analyse the blockchain and infer patterns using temporal analysis.

transaction hash ring size tx size[kB]
3feaff3f48de0bc4c92ec027236165337b64df404aca098e212c1215e9456697 7 13.47
39d484f7c0a2e8f3823a514056d7cb0bf269171cb4582e05955d4c5ee995cad0 7 13.47
e08f5a937e725011bedd44075334ae98dcca32749da231c56da1278d49c0a231 7 13.50
ab35e69d9cca39219c90df8b2b7aab4a54c82127fb1fbaae65d76357f8f76387 7 13.5
6d8ccd56dc2d3eb7de03ba767f0dbf4d5f42ae91e67f4c28f16d6f8b0229c272 10 13.87

Loki Static Ring Size

Loki improves on both of these problems by statically enforcing ring-sizes, and setting the ring-size to ten. Statically setting the maximum ring-size protects users who construct rings with more than nine mixins and setting the ring-size minimum to ten more effectively prevents an attacker who owns a large number of outputs from discerning the true outputs spent in a ring signature. Larger ring-sizes also increase the default churning effectiveness non-linearly, becoming more effective as ring-sizes grow.

In the current transaction scheme, increasing the ring-size to 10 would lead to a 2.6% increase in the size of the transaction. However, when Bulletproofs are implemented it will account for about a 8 - 13% increase in the size of a transaction. This is because of the overall reduction in transaction size caused by Bulletproofs. Increasing the minimum ring-size may present a problem on a network that lacks architecture to support larger sized transactions, due to the increased overhead. With Loki however, this burden can be carried by Service Nodes that are incentivised to operate and provide sufficient bandwidth.

Stealth Addresses

Loki makes use of stealth addresses to ensure that the true public key of the receiver is never linked to their transaction. Every time a Loki transaction is sent, a one-time stealth address is created and the funds are sent to this address. Using a Diffie-Hellman key exchange, the receiver of the transaction is able to calculate a private spend key for this stealth address, thereby taking ownership of the funds without having to reveal their true public address. Stealth addresses provide protection to receivers of transactions and are a core privacy feature in Loki.

RingCT

RingCT was first proposed by the Monero Research Lab as a way to obfuscate transaction amounts. Current deployments of RingCT use range proofs, which leverage Pedersen commitments to prove that the amount of a transaction being sent is between 0 and 264. This range ensures that only non-negative amounts of currency are sent, without revealing the actual amount sent in the transaction. Recently a number of cryptocurrencies have proposed implementing bulletproofs as a replacement to traditional range proofs in RingCT because of the significant reduction in transaction size. Loki will utilise bulletproofs, reducing the information that nodes are required to store and relay, thereby improving scalability.