Invoke-WebRequest SSL fails?

This can be permanently changed as well

# set strong cryptography on 32 bit .Net Framework (version 4 and above)
Set-ItemProperty -Path 'HKLM:\SOFTWARE\Wow6432Node\Microsoft\.NetFramework\v4.0.30319' -Name 'SchUseStrongCrypto' -Value '1' -Type DWord
# set strong cryptography on 64 bit .Net Framework (version 4 and above)
Set-ItemProperty -Path 'HKLM:\SOFTWARE\Microsoft\.NetFramework\v4.0.30319' -Name 'SchUseStrongCrypto' -Value '1' -Type DWord 

As BaconBits notes, .NET version > 4.5 uses SSLv3 and TLS 1.0 by default.

You can change this behavior by setting the SecurityProtocol policy with the ServicePointManager class:

PS C:\> $AllProtocols = [System.Net.SecurityProtocolType]'Ssl3,Tls,Tls11,Tls12'
PS C:\> [System.Net.ServicePointManager]::SecurityProtocol = $AllProtocols
PS C:\> (Invoke-WebRequest -Uri "https://idp.safenames.com/").StatusCode
200

This will apply to all requests in the AppDomain (so it only applies to the current instance of the host application).

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There's a module on GitHub and in PSGallery that can manage these settings now:

Install-Module BetterTls -Scope CurrentUser
Import-Module BetterTls
Enable-Tls -Tls11 -Tls12