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fix: alignment fix comment and \inst use in titles
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‎hub/instruction_handling/call/precompiles/ecadd_ecmul_ecpairing_bls_pverify/_inputs.tex‎

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\subsubsubsection{Dealing with empty call data \lispNone{}} \label{hub: instruction handling: call: precompiles: ecadd ecmul ecpairing bls and pverify: empty} \input{instruction_handling/call/precompiles/ecadd_ecmul_ecpairing_bls_pverify/empty}
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\subsubsubsection{\inst{ECADD/MUL/PAIRING}, \inst{BLS} and \inst{PVERIFY} shorthands \lispDone{}} \label{hub: instruction handling: call: precompiles: ecadd ecmul ecpairing bls and pverify: shorthands} \input{instruction_handling/call/precompiles/ecadd_ecmul_ecpairing_bls_pverify/shorthands}
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\subsubsubsection{\inst{ECADD/MUL/PAIRING}, \inst{BLS} and \inst{PVERIFY} representation \lispNone{}} \label{hub: instruction handling: call: precompiles: ecadd ecmul ecpairing bls and pverify: representation} \input{instruction_handling/call/precompiles/ecadd_ecmul_ecpairing_bls_pverify/representation}
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\subsubsubsection{\inst{ECADD/MUL/PAIRING}, \inst{BLS} and \inst{PVERIFY} the \scenPrcFailureKnownToRam{} case \lispDone{}} \label{hub: instruction handling: call: precompiles: ecadd ecmul ecpairing bls and pverify: failure KTR} \input{instruction_handling/call/precompiles/ecadd_ecmul_ecpairing_bls_pverify/failure_KTR}
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\subsubsubsection{\inst{ECADD/MUL/PAIRING}, \inst{BLS} and \inst{PVERIFY} the \scenPrcSuccess{} case \lispDone{}} \label{hub: instruction handling: call: precompiles: ecadd ecmul ecpairing bls and pverify: success} \input{instruction_handling/call/precompiles/ecadd_ecmul_ecpairing_bls_pverify/success}
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\subsubsubsection{\instEcadd{}, \instEcmul{}, \instEcpairing{}, \inst{BLS}-precompiles and \instPVerify{} shorthands \lispDone{}} \label{hub: instruction handling: call: precompiles: ecadd ecmul ecpairing bls and pverify: shorthands} \input{instruction_handling/call/precompiles/ecadd_ecmul_ecpairing_bls_pverify/shorthands}
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\subsubsubsection{\instEcadd{}, \instEcmul{}, \instEcpairing{}, \inst{BLS}-precompiles and \instPVerify{} representation \lispNone{}} \label{hub: instruction handling: call: precompiles: ecadd ecmul ecpairing bls and pverify: representation} \input{instruction_handling/call/precompiles/ecadd_ecmul_ecpairing_bls_pverify/representation}
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\subsubsubsection{\instEcadd{}, \instEcmul{}, \instEcpairing{}, \inst{BLS}-precompiles and \instPVerify{}the \scenPrcFailureKnownToRam{} case \lispDone{}} \label{hub: instruction handling: call: precompiles: ecadd ecmul ecpairing bls and pverify: failure KTR} \input{instruction_handling/call/precompiles/ecadd_ecmul_ecpairing_bls_pverify/failure_KTR}
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\subsubsubsection{\instEcadd{}, \instEcmul{}, \instEcpairing{}, \inst{BLS}-precompiles and \instPVerify{} the \scenPrcSuccess{} case \lispDone{}} \label{hub: instruction handling: call: precompiles: ecadd ecmul ecpairing bls and pverify: success} \input{instruction_handling/call/precompiles/ecadd_ecmul_ecpairing_bls_pverify/success}

‎hub/scenario/shorthands/precompile.tex‎

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\[
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\scenPrecompileWeightedSum _{i}
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\define
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\left[ \begin{array}{l}
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+ \; \mathtt{0x\,01} \phantom{0} \cdot \scenEcrecover _{i} \\
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+ \; \mathtt{0x\,02} \phantom{0} \cdot \scenShaTwo _{i} \\
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+ \; \mathtt{0x\,03} \phantom{0} \cdot \scenRipemd _{i} \\
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+ \; \mathtt{0x\,04} \phantom{0} \cdot \scenIdentity _{i} \\
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+ \; \mathtt{0x\,05} \phantom{0} \cdot \scenModexp _{i} \\
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+ \; \mathtt{0x\,06} \phantom{0} \cdot \scenEcadd _{i} \\
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+ \; \mathtt{0x\,07} \phantom{0} \cdot \scenEcmul _{i} \\
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+ \; \mathtt{0x\,08} \phantom{0} \cdot \scenEcpairing _{i} \\
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+ \; \mathtt{0x\,09} \phantom{0} \cdot \scenBlake _{i} \\
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+ \; \mathtt{0x\,0a} \phantom{0} \cdot \scenPointEvaluation _{i} \\
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+ \; \mathtt{0x\,0b} \phantom{0} \cdot \scenBlsGOneAdd _{i} \\
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+ \; \mathtt{0x\,0c} \phantom{0} \cdot \scenBlsGOneMsm _{i} \\
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+ \; \mathtt{0x\,0d} \phantom{0} \cdot \scenBlsGTwoAdd _{i} \\
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+ \; \mathtt{0x\,0e} \phantom{0} \cdot \scenBlsGTwoMsm _{i} \\
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+ \; \mathtt{0x\,0f} \phantom{0} \cdot \scenBlsPairingCheck _{i} \\
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+ \; \mathtt{0x\,10} \phantom{0} \cdot \scenBlsMapFpToGOne _{i} \\
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+ \; \mathtt{0x\,11} \phantom{0} \cdot \scenBlsMapFpTwoToGTwo _{i} \\
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+ \; \mathtt{0x\,100} \cdot \scenPVerify _{i} \\
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\left[ \begin{array}{rcl}
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+ \; \mathtt{0x\,01} & \cdot & \scenEcrecover _{i} \\
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+ \; \mathtt{0x\,02} & \cdot & \scenShaTwo _{i} \\
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+ \; \mathtt{0x\,03} & \cdot & \scenRipemd _{i} \\
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+ \; \mathtt{0x\,04} & \cdot & \scenIdentity _{i} \\
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+ \; \mathtt{0x\,05} & \cdot & \scenModexp _{i} \\
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+ \; \mathtt{0x\,06} & \cdot & \scenEcadd _{i} \\
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+ \; \mathtt{0x\,07} & \cdot & \scenEcmul _{i} \\
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+ \; \mathtt{0x\,08} & \cdot & \scenEcpairing _{i} \\
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+ \; \mathtt{0x\,09} & \cdot & \scenBlake _{i} \\
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+ \; \mathtt{0x\,0a} & \cdot & \scenPointEvaluation _{i} \\
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+ \; \mathtt{0x\,0b} & \cdot & \scenBlsGOneAdd _{i} \\
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+ \; \mathtt{0x\,0c} & \cdot & \scenBlsGOneMsm _{i} \\
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+ \; \mathtt{0x\,0d} & \cdot & \scenBlsGTwoAdd _{i} \\
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+ \; \mathtt{0x\,0e} & \cdot & \scenBlsGTwoMsm _{i} \\
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+ \; \mathtt{0x\,0f} & \cdot & \scenBlsPairingCheck _{i} \\
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+ \; \mathtt{0x\,10} & \cdot & \scenBlsMapFpToGOne _{i} \\
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+ \; \mathtt{0x\,11} & \cdot & \scenBlsMapFpTwoToGTwo _{i} \\
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+ \; \mathtt{0x\,100} & \cdot & \scenPVerify _{i} \\
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\end{array} \right]
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\]
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We also define the following

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