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zva~Z#?bUd*e;4aFvp3dfM)L|?KPJAbZ?0XV?vZKbQpLyCZ+hdV)_X1DNs#m@Cq72j z3JVqa1t&gB6|VQ@opELQ)sXcX%ica+K6~q*b(KHfn9NZP<`sRLoAT@LzxJp3ZyZ0c z2mSc`k?ZrL=SM;({bx9Q%l3239nUhK_OPpWe(si;zpo?0+syxr*Gd-S5?-VCzDd<&PpEYGg2QIYh% z{nIW(w`m@Wp;puB6C5k$3~tKD)ZLZeeEi6NhQ6?UB71%mCGN3Oj#E81*Y?ouJafCS zn-fmBq^#&!ozmQ7I4}D~eM)_k)%gSUEh`_!3;DC$I<~OhY<11HH*p#%GnG1%!WHsw z%V4yzRWgGan^$ZKmtC zZ#wL%z4~5o^>+1VUpL)-^;_Rv|KX3zN4;gcrrU;p*Y}?g=qmbw{bH*~pabgwVfo>E zck*bNKRSm+R2pC&J)?!FaKcvCkBSYCwk7lE=@X-QV1(Bf%%i7IjOKw6p9e` implementing this idea, as well as a +:ref:`new forbidden period`. + +.. _adaptive_slashing_fn: + +Adaptive Slashing Function +========================== + +.. _adaptive_slashing_informal: + +Informal presentation +--------------------- + +For a given block, we call “fraction of double-attestations” the ratio +between the total weight of attestations for which a valid +denunciation has been included and the total weight of possible +attestations in a block. + +The shape of the slashing function for double attestations is the +following: + +.. figure:: adaptive-slashing-new.jpeg + + ++------------------------------------------+----------------------------------------+ +| f: fraction of double attestations | S: slashing ratio | ++==========================================+========================================+ +| 1.00% | 0.09% | ++------------------------------------------+----------------------------------------+ +| 5.00% | 2.25% | ++------------------------------------------+----------------------------------------+ +| 10.00% | 9.00% | ++------------------------------------------+----------------------------------------+ +| 20.00% | 36.00% | ++------------------------------------------+----------------------------------------+ +| 23.57% | 50.00% | ++------------------------------------------+----------------------------------------+ +| 33.34% | 100.00% | ++------------------------------------------+----------------------------------------+ +| 100.00% | | ++------------------------------------------+----------------------------------------+ + +Instead of using a constant function as in Oxford2, we propose to use +a convex function that saturates at 100% when a critical fraction of +doubled attestations are issued. Accidental double attestations are +unlikely to cause a large amount of slashing to be applied, but +concerted attacks result in severe penalties. + +\ **Remark 1.** Even though the baker does not attest to a weight +exactly equivalent to its staked funds at each block, the slashing +function is applied to bakers’ total staked funds for simplicity. + +\ **Remark 2.** As in Oxford2, slashing happens at the end of each +cycle. Since the denunciation period for a block ranges over its cycle +and the next one, a baker can be punished for misbehaving during the +previous cycle, not only the one that has just ended. + +\ **Remark 3.** If a baker wants to get back their at-stake funds, it +takes more than 2 cycles to complete the unstaking process. This +ensures that the baker can't decrease their at-stake funds after being +denunciated and before facing penalties. + +.. _formal_adaptive_slashing: + +A formal definition of slashing function for double-attestations +---------------------------------------------------------------- + +* :math:`\mathcal{W}` denotes the maximal possible *weight* of + attestations in a block, that is, the fixed number of available + :ref:`slots` in any block. It is also known as + :ref:`CONSENSUS_COMMITTEE_SIZE`. + +* :math:`f(B)` is the *fraction of double attestations* for block + :math:`B`, that is, the ratio of the total weight of double + attestations in :math:`B`, over :math:`\mathcal{W}`. + +* :math:`T` is the *threshold* for the fraction of double attestations + to be considered critical. A typical value for :math:`T` is + :math:`{1 \over 3} \mathcal{W}`, which is the difference between + :math:`\mathcal{W}` and the + :ref:`CONSENSUS_THRESHOLD` which is set to + :math:`{2 \over 3} \mathcal{W}`. + +We define :math:`S(B)` the percentage of slashed funds for all +misbehaving bakers at the block :math:`B` as follows: + +:math:`S(B) = \text{min} (100\%, {1 \over T^2} \cdot f(B)^2 \cdot 100\%)` + +Then, the percentage of slashed funds :math:`S(b,C)` for a baker +:math:`b` at the end of the cycle :math:`C` is defined as follows: + +:math:`S(b, C) = \text{min} (100\%, \sum_{(b, B) \in C} S(B))` + +where :math:`(b, B) \in C` means that: + +* the double attestation by baker :math:`b` of block :math:`B` has + been denounced before the end of cycle :math:`C`, and + +* :math:`C` is the last cycle of the denunciation period for + :math:`B`. + +.. _new_forbidden_period: + +A new definition for the forbidden period +========================================= + +Given that slashing occurs with a delay, immediate action at +denunciation time is necessary upon clear evidence of a baker's +misbehavior to prevent further misconduct, or to protect the baker +against their own faulty setup. Any double-signing denunciation +immediately triggers the beginning of a forbidden period that lasts at +least 2 cycles, to make sure the slashing occurs before accepting new +attestations or blocks from the baker. Note that it is still possible +for one baker to commit multiple double signings, but only if they all +happen before any corresponding denunciation gets included in a block. diff --git a/docs/paris/protocol.rst b/docs/paris/protocol.rst index da493586f242..080d9f0023d5 100644 --- a/docs/paris/protocol.rst +++ b/docs/paris/protocol.rst @@ -117,6 +117,11 @@ Sapling, etc), and some details about its implementation. adaptive_issuance +.. toctree:: + :maxdepth: 2 + + adaptive_slashing + .. toctree:: :maxdepth: 2 -- GitLab