@@ -325,6 +325,32 @@ Return values:
325325| :------ | :--- | :------------------------------------------ |
326326| result_ | bool | True if their affine representations match. |
327327
328+ ### jNegatePoint
329+
330+ ``` solidity
331+ function jNegatePoint(
332+ EC256.Curve memory ec,
333+ EC256.JPoint memory jPoint_
334+ ) internal pure returns (EC256.JPoint memory jNegated_)
335+ ```
336+
337+ Computes the negation of a Jacobian point: -P = (X, -Y, Z).
338+
339+
340+ Parameters:
341+
342+ | Name | Type | Description |
343+ | :------ | :------------------ | :--------------------- |
344+ | ec | struct EC256.Curve | The curve parameters. |
345+ | jPoint_ | struct EC256.JPoint | The Jacobian point P. |
346+
347+
348+ Return values:
349+
350+ | Name | Type | Description |
351+ | :-------- | :------------------ | :--------------------------------- |
352+ | jNegated_ | struct EC256.JPoint | The Jacobian representation of -P. |
353+
328354### jMultShamir
329355
330356``` solidity
@@ -407,6 +433,34 @@ Parameters:
407433| jPoint2_ | struct EC256.JPoint | The second Jacobian point P2. |
408434
409435
436+ Return values:
437+
438+ | Name | Type | Description |
439+ | :------- | :------------------ | :--------------------------------------------- |
440+ | jPoint3_ | struct EC256.JPoint | The Jacobian representation of result point R. |
441+
442+ ### jSubPoint
443+
444+ ``` solidity
445+ function jSubPoint(
446+ EC256.Curve memory ec,
447+ EC256.JPoint memory jPoint1_,
448+ EC256.JPoint memory jPoint2_
449+ ) internal pure returns (EC256.JPoint memory jPoint3_)
450+ ```
451+
452+ Subtracts one Jacobian point from another: R = P1 - P2 = P1 + (-P2).
453+
454+
455+ Parameters:
456+
457+ | Name | Type | Description |
458+ | :------- | :------------------ | :----------------------------- |
459+ | ec | struct EC256.Curve | The curve parameters. |
460+ | jPoint1_ | struct EC256.JPoint | The first Jacobian point P1. |
461+ | jPoint2_ | struct EC256.JPoint | The second Jacobian point P2. |
462+
463+
410464Return values:
411465
412466| Name | Type | Description |
@@ -438,3 +492,14 @@ Return values:
438492| Name | Type | Description |
439493| :------- | :------------------ | :--------------------------------------------- |
440494| jPoint2_ | struct EC256.JPoint | The Jacobian representation of result point R. |
495+
496+ ### _ jNegate
497+
498+ ``` solidity
499+ function _jNegate(
500+ EC256.JPoint memory jPoint_,
501+ uint256 p_
502+ ) internal pure returns (EC256.JPoint memory jNegated_)
503+ ```
504+
505+ Internal Jacobian point negation.
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