Accounts

Twilight

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Twilight

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Twilight Spec

Relayer Spec

Perpetual Futures Guide

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Accounts

An account on the base layer is defined as a pair of pubkey and a commitment s.t.
Acci=(pki,comi)  s.t.  pki=(giri,hiri) Acc_i=(pk_i,com_i) \ \ s.t. \ \ pk_i = (g_i^{r_i},h^{r_i}_i) \ Acci​=(pki​,comi​)  s.t.  pki​=(giri​​,hiri​​) 
where g is the globally available generator point, r  is a random scalar and h is defined as
hi=giskh_i=g_i^{sk}hi​=gisk​
Note h here is not a global generator point but an elgamal public key point.  Commitment is defined as an elgamal style commitment scheme s.t.
com=(gi(ri∗ri′),gvhi(ri∗ri′))com=(g_i^{(r_i*r'_i)} ,g^vh_i^{(r_i*r'_i)})com=(gi(ri​∗ri′​)​,gvhi(ri​∗ri′​)​)
where r' is a random scalar which updates the public key points to generate a new commitment for the key and v is the secret scalar of the balance in the account s.t. 0≤bl<2320\leq bl<2^{32}0≤bl<232
 . 
Updatable Accounts
A public key is updated using scalar multiplication of a random scalar r1r_1r1​
 with the group elements. 
Update(pk,r1)=(gr1,hr1)=pk′Update(pk,r_1)= (g^{r_1},h^{r_1})=pk'Update(pk,r1​)=(gr1​,hr1​)=pk′
A commitment is updated by adding it to a new zero balance commitment, generated using (pk,r2)(pk,r_2)(pk,r2​)
.
Update(com,r2)=com⋅Commitpk(0,r2)Update(com,r_2)=com \cdot Commit_{pk}(0,r_2)Update(com,r2​)=com⋅Commitpk​(0,r2​)
Accounts are updated by updating public key pk→pk′pk→ pk'pk→pk′
, generating a zero balance commitment using (pk,r2)(pk,r_2)(pk,r2​)
and adding the previous and new commitment compk(v)⋅compk(0,r2)com_{pk}(v) \cdot com_{pk}(0,r_2)compk​(v)⋅compk​(0,r2​)
.
UpdateAcc(pk,com);r1,r2=Update(pk,r1);com⋅Commitpk(0,r2)UpdateAcc(pk, com); r_1,r_2=Update(pk,r_1);com\cdot Commit_{pk}(0,r_2)UpdateAcc(pk,com);r1​,r2​=Update(pk,r1​);com⋅Commitpk​(0,r2​)
This construction follows the Updatable Public Key primitive introduced in QuisQuis by Mieklejohn et.al. (2018). 
Updatable Public Key
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Core Concepts

Transaction

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