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| namespace P3Q |
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| structure SettlementEvent where |
| eventId : UInt32 |
| eventType : UInt8 |
| params : Array UInt8 |
| deadline : UInt64 |
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| structure MeasurementResult where |
| eventId : UInt32 |
| status : UInt8 |
| data : Array UInt8 |
| shotsCompleted: UInt32 |
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| inductive QSimCmdType where |
| | keygen256 |
| | nonce128 |
| | groverAES4 |
| | ampEstLeakage |
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| structure QSimCommand where |
| cmdType : QSimCmdType |
| qubits : UInt16 |
| shots : UInt32 |
| params : Array UInt8 |
| eventId : UInt32 |
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| structure QSimResponse where |
| eventId : UInt32 |
| status : UInt8 |
| data : Array UInt8 |
| shotsCompleted: UInt32 |
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| inductive HandshakeState where |
| | idle |
| | translate |
| | issueCmd |
| | waitRsp |
| | formatRsp |
| | done |
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| structure HandshakeContext where |
| state : HandshakeState |
| eventId : UInt32 |
| eventType : UInt8 |
| deadline : UInt64 |
| cycleCounter : UInt64 |
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| def ValidEventType (t : UInt8) : Bool := |
| t == 0x01 || t == 0x02 || t == 0x03 || t == 0x04 |
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| def ValidQubitCount (cmdType : QSimCmdType) (qubits : UInt16) : Bool := |
| match cmdType with |
| | QSimCmdType.keygen256 => qubits == 256 |
| | QSimCmdType.nonce128 => qubits == 128 |
| | QSimCmdType.groverAES4 => qubits >= 512 |
| | QSimCmdType.ampEstLeakage => qubits >= 257 |
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| def xtime (b : UInt8) : UInt8 := |
| let shifted := b <<< 1 |
| if b &&& 0x80 != 0 then |
| shifted ^^^ 0x1B |
| else |
| shifted |
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| def mixColumn (a0 a1 a2 a3 : UInt8) : UInt8 × UInt8 × UInt8 × UInt8 := |
| let t := a0 ^^^ a1 ^^^ a2 ^^^ a3 |
| let x0 := xtime (a0 ^^^ a1) |
| let x1 := xtime (a1 ^^^ a2) |
| let x2 := xtime (a2 ^^^ a3) |
| let x3 := xtime (a3 ^^^ a0) |
| (a0 ^^^ t ^^^ x0, a1 ^^^ t ^^^ x1, a2 ^^^ t ^^^ x2, a3 ^^^ t ^^^ x3) |
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| theorem handshake_preserves_event_id |
| (ctx : HandshakeContext) (evt : SettlementEvent) |
| (h_state : ctx.state = HandshakeState.idle) |
| (h_id : ctx.eventId = evt.eventId) : |
| ctx.eventId = evt.eventId := h_id |
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| theorem xtime_bit7_clear (b : UInt8) : |
| (xtime b) &&& 0x80 = 0 := by |
| simp [xtime] |
| split |
| · next h => simp [h] |
| · next h => simp [h] |
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| theorem mixColumn_preserves_zero : |
| mixColumn 0 0 0 0 = (0, 0, 0, 0) := by |
| simp [mixColumn, xtime] |
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| theorem mixColumn_preserves_uniform (a : UInt8) : |
| mixColumn a a a a = (a, a, a, a) := by |
| simp [mixColumn, xtime, UInt8.xor_self] |
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| theorem canonical_vector_correct : |
| let (y0, y1, y2, y3) := mixColumn 0xD4 0xBF 0x5D 0x30 |
| y0 == 0x04 && y1 == 0x66 && y2 == 0x81 && y3 == 0xE5 := by |
| native_decide |
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| structure ResourceEstimate where |
| tCount : Nat |
| tDepth : Nat |
| logicalQubits : Nat |
| cnotCount : Nat |
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| def aes4_grover_iteration_resources : ResourceEstimate := |
| { tCount := 4400, tDepth := 350, logicalQubits := 1200, cnotCount := 7000 } |
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| def grover_iterations_full_key : Nat := 2^64 |
| def grover_iterations_64bit : Nat := 2^32 |
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| theorem full_key_grover_impractical : |
| aes4_grover_iteration_resources.tCount * grover_iterations_full_key > 2^100 := by |
| native_decide |
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| theorem reduced_key_grover_feasible_sim_only : |
| aes4_grover_iteration_resources.tCount * grover_iterations_64bit < 2^50 := by |
| native_decide |
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| end P3Q |
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