Notional Protocol V2.1

1 Executive Summary

This report documents our first engagement with Notional, in which we started to familiarize ourselves with their protocol for fixed-rate, fixed-term crypto asset lending and borrowing. From January 31 to March 4, 2022, we invested 7 person-weeks.

The Notional team is interested in a long-term security partnership with ConsenSys Diligence. As their codebase is very large, complex, and involved, we agreed on the following procedure and goals for this engagement:

  1. Gain initial knowledge of and familiarity with the system within the Diligence team.

  2. To direct these efforts, focus on a set of three changes to the existing system that Notional will provide together with an accompanying document. These changes will be reviewed by Diligence, but given the size and complexity of the system on the one hand and the limited time available on the other, this review is strictly on a best-effort basis.

The changes can be briefly summarized as follows:
A. Allow nTokens to be redeemed in the presence of idiosyncratic fCash residuals.
B. Improve the existing incentivization calculation, and migrate existing liquidity providers to the new algorithm.
C. Add support for Aave aTokens.
We investigated the code at commit hash 582dc370e30ccae5e29110d2fd6f6c52c56d5b0e (private repository).

As mentioned above, while the focus was on developing an understanding of (some parts of) the system, any potential issues we discovered were, of course, discussed with the client. As we found the code exceptionally well-written and -documented, only one issue and two minor points were discovered. These are briefly described in the next section.

2 Findings

Each issue has an assigned severity:

  • Minor issues are subjective in nature. They are typically suggestions around best practices or readability. Code maintainers should use their own judgment as to whether to address such issues.
  • Medium issues are objective in nature but are not security vulnerabilities. These should be addressed unless there is a clear reason not to.
  • Major issues are security vulnerabilities that may not be directly exploitable or may require certain conditions in order to be exploited. All major issues should be addressed.
  • Critical issues are directly exploitable security vulnerabilities that need to be fixed.

2.1 Accounts that claim incentives immediately before the migration will be stuck Medium


For accounts that existed before the migration to the new incentive calculation, the following happens when they claim incentives for the first time after the migration: First, the incentives that are still owed from before the migration are computed according to the old formula; the incentives since the migration are calculated according to the new logic, and the two values are added together. The first part – calculating the pre-migration incentives according to the old formula – happens in function MigrateIncentives.migrateAccountFromPreviousCalculation; the following lines are of particular interest in the current context:


uint256 timeSinceMigration = finalMigrationTime - lastClaimTime;

// (timeSinceMigration * INTERNAL_TOKEN_PRECISION * finalEmissionRatePerYear) / YEAR
uint256 incentiveRate =
        // Migration emission rate is stored as is, denominated in whole tokens

// Returns the average supply using the integral of the total supply.
uint256 avgTotalSupply = finalTotalIntegralSupply.sub(lastClaimIntegralSupply).div(timeSinceMigration);

The division in the last line will throw if finalMigrationTime and lastClaimTime are equal. This will happen if an account claims incentives immediately before the migration happens – where “immediately” means in the same block. In such a case, the account will be stuck as any attempt to claim incentives will revert.


The function should return 0 if finalMigrationTime and lastClaimTime are equal. Moreover, the variable name timeSinceMigration is misleading, as the variable doesn’t store the time since the migration but the time between the last incentive claim and the migration.

2.2 type(T).max is inclusive Minor


Throughout the codebase, there are checks whether a number can be represented by a certain type.



require(accumulatedNOTEPerNToken < type(uint128).max); // dev: accumulated NOTE overflow


require(blockTime < type(uint32).max); // dev: block time overflow


require(totalSupply <= type(uint96).max);
require(blockTime <= type(uint32).max);

Sometimes these checks use <=, sometimes they use <.


type(T).max is inclusive, i.e., it is the greatest number that can be represented with type T. Strictly speaking, it can and should therefore be used consistently with <= instead of <.

2.3 Minor mathematical mistake in comment Minor


In nTokenSupply.sol, there is a comment explaining why 18 decimal places for the accumulation precision is a good choice. There is a minor mistake in the calculation. It does not invalidate the reasoning, but as it is confusing for a reader, we recommend correcting it.


// If we use 18 decimal places as the accumulation precision then we will overflow uint128 when
// a single nToken has accumulated 3.4 x 10^20 NOTE tokens. This isn't possible since the max
// NOTE that can accumulate is 10^17 (100 million NOTE in 1e8 precision) so we should be safe
// using 18 decimal places and uint128 storage slot

100 million NOTE in 1e8 precision is 10^16.

Appendix 1 - Disclosure

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