Add new proof

contracts/HistoricalSPVGateway.sol

@@ -14,14 +14,14 @@ import {SPVGateway} from "./SPVGateway.sol";
 
 contract HistoricalSPVGateway is IHistoricalSPVGateway, SPVGateway {
     using BlockHeader for bytes;
-    using TargetsHelper for bytes32;
     using EndianConverter for bytes32;
     using BlockHistory for bytes32[];
 
     bytes32 public constant HISTORICAL_SPV_GATEWAY_STORAGE_SLOT =
         keccak256("spv.gateway.historical.spv.gateway.storage");
 
     struct HistoricalSPVGatewayStorage {
+        uint32 lastHistoryEpochStartTime;
         uint256 historyBlocksCount;
         bytes32 historyBlocksTreeRoot;
     }
@@ -41,6 +41,7 @@ contract HistoricalSPVGateway is IHistoricalSPVGateway, SPVGateway {
     function __HistoricalSPVGateway_init(
         bytes calldata blockHeaderRaw_,
         uint64 blockHeight_,
+        uint32 lastHistoryEpochStartTime_,
         uint256 cumulativeWork_,
         bytes32 historyBlocksTreeRoot_,
         BlockHistory.HistoryProofData calldata proofData_
@@ -53,12 +54,14 @@ contract HistoricalSPVGateway is IHistoricalSPVGateway, SPVGateway {
             historyBlocksTreeRoot_,
             blockHash_,
             blockHeight_,
+            lastHistoryEpochStartTime_,
             cumulativeWork_,
             proofData_
         );
 
         _initialize(blockHeader_, blockHash_, blockHeight_, cumulativeWork_);
 
+        _getHistoricalSPVGatewayStorage().lastHistoryEpochStartTime = lastHistoryEpochStartTime_;
         _getHistoricalSPVGatewayStorage().historyBlocksCount = blockHeight_;
         _getHistoricalSPVGatewayStorage().historyBlocksTreeRoot = historyBlocksTreeRoot_;
     }
@@ -107,6 +110,11 @@ contract HistoricalSPVGateway is IHistoricalSPVGateway, SPVGateway {
             );
     }
 
+    /// @inheritdoc IHistoricalSPVGateway
+    function getLastHistoryEpochStartTime() public view returns (uint32) {
+        return _getHistoricalSPVGatewayStorage().lastHistoryEpochStartTime;
+    }
+
     /// @inheritdoc IHistoricalSPVGateway
     function getHistoryBlocksCount() public view returns (uint256) {
         return _getHistoricalSPVGatewayStorage().historyBlocksCount;
@@ -116,4 +124,17 @@ contract HistoricalSPVGateway is IHistoricalSPVGateway, SPVGateway {
     function getHistoryBlocksTreeRoot() public view returns (bytes32) {
         return _getHistoricalSPVGatewayStorage().historyBlocksTreeRoot;
     }
+
+    function _getEpochPassedTime(uint64 blockHeight_) internal view override returns (uint32) {
+        uint64 startEpochBlockHeight_ = blockHeight_ -
+            TargetsHelper.DIFFICULTY_ADJUSTMENT_INTERVAL;
+
+        if (startEpochBlockHeight_ > getHistoryBlocksCount()) {
+            return super._getEpochPassedTime(blockHeight_);
+        }
+
+        uint32 epochEndTime_ = _getBlockHeaderTime(getBlockHash(blockHeight_ - 1));
+
+        return epochEndTime_ - getLastHistoryEpochStartTime();
+    }
 }

contracts/SPVGateway.sol

@@ -335,13 +335,10 @@ contract SPVGateway is ISPVGateway, Initializable {
         if (TargetsHelper.isTargetAdjustmentBlock(blockHeight_)) {
             $.lastEpochCumulativeWork += TargetsHelper.countEpochCumulativeWork(currentTarget_);
 
-            uint32 epochStartTime_ = _getBlockHeaderTime(
-                getBlockHash(blockHeight_ - TargetsHelper.DIFFICULTY_ADJUSTMENT_INTERVAL)
+            currentTarget_ = TargetsHelper.countNewRoundedTarget(
+                currentTarget_,
+                _getEpochPassedTime(blockHeight_)
             );
-            uint32 epochEndTime_ = _getBlockHeaderTime(getBlockHash(blockHeight_ - 1));
-            uint32 passedTime_ = epochEndTime_ - epochStartTime_;
-
-            currentTarget_ = TargetsHelper.countNewRoundedTarget(currentTarget_, passedTime_);
         }
 
         return currentTarget_;
@@ -439,6 +436,15 @@ contract SPVGateway is ISPVGateway, Initializable {
         return _getMedianTime(blocksTime_, needsSort_);
     }
 
+    function _getEpochPassedTime(uint64 blockHeight_) internal view virtual returns (uint32) {
+        uint32 epochStartTime_ = _getBlockHeaderTime(
+            getBlockHash(blockHeight_ - TargetsHelper.DIFFICULTY_ADJUSTMENT_INTERVAL)
+        );
+        uint32 epochEndTime_ = _getBlockHeaderTime(getBlockHash(blockHeight_ - 1));
+
+        return epochEndTime_ - epochStartTime_;
+    }
+
     function _getBlockCumulativeWork(
         uint64 blockHeight_,
         bytes32 blockHash_

contracts/interfaces/IHistoricalSPVGateway.sol

@@ -64,6 +64,12 @@ interface IHistoricalSPVGateway is ISPVGateway {
         HistoryBlockInclusionProofData calldata inclusionProofData_
     ) external view returns (bool);
 
+    /**
+     * @notice Gets the last history epoch start time.
+     * @return Returns the start time of the last history epoch.
+     */
+    function getLastHistoryEpochStartTime() external view returns (uint32);
+
     /**
      * @notice Gets the total number of historical blocks stored.
      * @return Returns the number of historical blocks.

contracts/libs/BlockHistory.sol

@@ -39,8 +39,9 @@ library BlockHistory {
     error InvalidProofBlockHash();
     error InvalidProofBlockHeight();
     error InvalidProofCumulativeWork();
-    error InvalidProof();
+    error InvalidProofEpochStartTime();
     error InvalidHistoryBlocksTreeRoot();
+    error InvalidProof();
 
     /**
      * @notice Verifies a ZK-SNARK proof for the Bitcoin history.
@@ -55,6 +56,7 @@ library BlockHistory {
         bytes32 historyBlocksTreeRoot_,
         bytes32 blockHash_,
         uint64 blockHeight_,
+        uint32 currentEpochStartTime_,
         uint256 cumulativeWork_,
         HistoryProofData calldata proofData_
     ) internal view returns (bool) {
@@ -64,6 +66,10 @@ library BlockHistory {
             cumulativeWork_ == getProofCumulativeWork(proofData_),
             InvalidProofCumulativeWork()
         );
+        require(
+            currentEpochStartTime_ == getProofEpochStartTime(blockHeight_ + 1, proofData_),
+            InvalidProofEpochStartTime()
+        );
         require(
             historyBlocksTreeRoot_ == getHistoryBlocksTreeRoot(blockHeight_ + 1, proofData_),
             InvalidHistoryBlocksTreeRoot()
@@ -180,11 +186,9 @@ library BlockHistory {
         uint64 provedBlocksCount_,
         HistoryProofData calldata proofData_
     ) internal pure returns (bytes32 parsedBlocksTreeRoot_) {
-        uint256 frontierLength_ = Math.log2(provedBlocksCount_ / CHUNK_SIZE) + 1;
-
-        bool isPowOf2_ = provedBlocksCount_ & (provedBlocksCount_ - 1) == 0;
+        uint256 frontierLength_ = _countFrontierLength(provedBlocksCount_);
 
-        if (isPowOf2_) {
+        if (LibBit.isPo2(provedBlocksCount_)) {
             parsedBlocksTreeRoot_ = _getBytes32FromInputs(
                 proofData_,
                 PROOF_FRONTIER_OFFSET + 32 * (frontierLength_ - 1)
@@ -227,6 +231,26 @@ library BlockHistory {
         return uint256(proofData_.publicInputs[PROOF_CUMULATIVE_WORK_OFFSET]);
     }
 
+    /**
+     * @notice Retrieves the last proved epoch start time from the ZK proof's public inputs.
+     * @param provedBlocksCount_ The total number of blocks included in the proof.
+     * @param proofData_ The struct containing the proof and public inputs.
+     * @return The epoch start time.
+     */
+    function getProofEpochStartTime(
+        uint64 provedBlocksCount_,
+        HistoryProofData calldata proofData_
+    ) internal pure returns (uint32) {
+        return
+            uint32(
+                uint256(
+                    proofData_.publicInputs[
+                        PROOF_FRONTIER_OFFSET + 32 * _countFrontierLength(provedBlocksCount_)
+                    ]
+                )
+            );
+    }
+
     /**
      * @notice Calculates the chunk number for a given block height.
      * @param blockHeight_ The height of the block.
@@ -322,7 +346,7 @@ library BlockHistory {
         uint256 frontierLength_,
         HistoryProofData calldata proofData_
     ) internal pure returns (bytes32 computedRoot_) {
-        for (uint256 i = 0; i < frontierLength_; ++i) {
+        for (uint256 i = 0; i < frontierLength_ - 1; ++i) {
             bytes32 currentNode_ = _getBytes32FromInputs(
                 proofData_,
                 PROOF_FRONTIER_OFFSET + 32 * i
@@ -348,6 +372,10 @@ library BlockHistory {
         }
     }
 
+    function _countFrontierLength(uint64 provedBlocksCount_) private pure returns (uint256) {
+        return Math.log2(provedBlocksCount_ / CHUNK_SIZE, Math.Rounding.Ceil) + 1;
+    }
+
     function _processProof(
         bytes32[] calldata merkleProof_,
         bytes32 value_,