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# math/big: ModInverse with modulus zero is undefined#47606

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opened this issue Aug 9, 2021 · 5 comments
Open

# math/big: ModInverse with modulus zero is undefined #47606

opened this issue Aug 9, 2021 · 5 comments
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NeedsFix The path to resolution is known, but the work has not been done.
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### FiloSottile commented Aug 9, 2021 • edited

 ModInverse is defined for all values of g, and for positive and negative values n, but not for a zero n. ModInverse sets z to the multiplicative inverse of g in the ring ℤ/nℤ and returns z. If g and n are not relatively prime, g has no multiplicative inverse in the ring ℤ/nℤ. In this case, z is unchanged and the return value is nil. The ring of numbers modulo zero does not exist, and being coprime with zero is meaningless, so the current docs don't cover it. Arguably, ModInverse should always panic when the modulo is zero, but currently it returns nil for g > 1, returns 1 for g = 1, returns nil for g = 0, and panics for g < 0. Turning a non-panic into a panic for the sake of consistency is asking for trouble, so we should just make it return nil consistently for n = 0. This could break programs that try to dereference the return value of ModInverse(1, 0), but that feels like a specific enough condition that programs won't have come to rely on it #famouslastwords. The text was updated successfully, but these errors were encountered:
added the NeedsFix The path to resolution is known, but the work has not been done. label Aug 9, 2021
added this to the Go1.18 milestone Aug 9, 2021

### gunadhya commented Aug 10, 2021

 Hi @FiloSottile, I'd like to work on this issue.

mentioned this issue Aug 15, 2021

### gopherbot commented Aug 15, 2021

 Change https://golang.org/cl/342211 mentions this issue: `big/int: Explicit checks in ModInverse for g modulo n=0`

### odeke-em commented Dec 20, 2021

 Thank you for filing this issue @FiloSottile, and thank you @ok-john for sending the CL https://go-review.googlesource.com/c/go/+/342211/ This issue is marked for Go1.18, but the CL was marked with "Wait-Release". Shall we roll this over to Go1.19 or should we make the breaking change to return nil if the modulus is zero. Now one reservation here is that the internal code has a comment that its internal implementation of GCD expects the parameters to be > 0. Should we perhaps instead document this issue or just wait until Go1.19. What do you think @griesemer @ianlancetaylor?

### odeke-em commented Jan 6, 2022

 Alright, I shall make the call to move this to the Go1.19 milestone as per the CL labelling and given that it is quite late in the cycle for a breakiing change.

modified the milestones: Go1.18, Go1.19 Jan 6, 2022

### ianlancetaylor commented Jun 24, 2022

 CC @golang/security Looks like this didn't make 1.19. Moving to backlog. Please recategorize as appropriate.

modified the milestones: Go1.19, Backlog Jun 24, 2022
modified the milestones: Backlog, Go1.20 Jul 18, 2022
modified the milestones: Go1.20, Go1.21 Feb 1, 2023
modified the milestones: Go1.21, Go1.22 Aug 8, 2023
modified the milestones: Go1.22, Go1.23 Feb 5, 2024