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Showing content from https://docs.aws.amazon.com/IAM/latest/UserGuide/reference_policies_multi-value-conditions.html below:

Conditions with multiple context keys or values

You can use the Condition element of a policy to test multiple context keys or multiple values for a single context key in a request. When you make a request to AWS, either programmatically or through the AWS Management Console, your request includes information about your principal, operation, tags, and more. You can use context keys to test the values of the matching context keys in the request, with the context keys specified in the policy condition. To learn about information and data included in a request, see The request context.

Evaluation logic for multiple context keys or values

A Condition element can contain multiple condition operators, and each condition operator can contain multiple context key-value pairs. Most context keys support using multiple values, unless otherwise specified.

If your policy statement has multiple condition operators, the condition operators are evaluated using a logical AND.
If your policy statement has multiple context keys attached to a single condition operator, the context keys are evaluated using a logical AND.
If a single condition operator includes multiple values for a context key, those values are evaluated using a logical OR.
If a single negated matching condition operator includes multiple values for a context key, those values are evaluated using a logical NOR.

All context keys in a condition element block must resolve to true to invoke the desired Allow or Deny effect. The following figure illustrates the evaluation logic for a condition with multiple condition operators and context key-value pairs.

For example, the following S3 bucket policy illustrates how the previous figure is represented in a policy. The condition block includes condition operators StringEquals and ArnLike, and context keys aws:PrincipalTag and aws:PrincipalArn. To invoke the desired Allow or Deny effect, all context keys in the condition block must resolve to true. The user making the request must have both principal tag keys, department and role, that include one of the tag key values specified in the policy. Also, the principal ARN of the user making the request must match one of the aws:PrincipalArn values specified in the policy to be evaluated as true.

JSON

{
  "Version": "2012-10-17",
  "Statement": [
    {
      "Sid": "ExamplePolicy",
      "Effect": "Allow",
      "Principal": {
        "AWS": "arn:aws:iam::222222222222:root"
      },
      "Action": "s3:ListBucket",
      "Resource": "arn:aws:s3:::amzn-s3-demo-bucket",
      "Condition": {
        "StringEquals": {
          "aws:PrincipalTag/department": [
            "finance",
            "hr",
            "legal"
          ],
          "aws:PrincipalTag/role": [
            "audit",
            "security"
          ]
        },
        "ArnLike": {
          "aws:PrincipalArn": [
            "arn:aws:iam::222222222222:user/Ana",
            "arn:aws:iam::222222222222:user/Mary"
          ]
        }
      }
    }
  ]
}

The following table shows how AWS evaluates this policy based on the condition key values in your request.

Policy Condition Request Context Result

"StringEquals": {
  "aws:PrincipalTag/department": [
    "finance",
    "hr",
    "legal"
  ],
  "aws:PrincipalTag/role": [
    "audit",
    "security"
  ]
},
"ArnLike": {
  "aws:PrincipalArn": [
      "arn:aws:iam::222222222222:user/Ana",
      "arn:aws:iam::222222222222:user/Mary"
  ]
}

aws:PrincipalTag/department: legal
aws:PrincipalTag/role: audit
aws:PrincipalArn: 
  arn:aws:iam::222222222222:user/Mary

Match

"StringEquals": {
  "aws:PrincipalTag/department": [
    "finance",
    "hr",
    "legal"
  ],
  "aws:PrincipalTag/role": [
    "audit",
    "security"
  ]
},
"ArnLike": {
  "aws:PrincipalArn": [
      "arn:aws:iam::222222222222:user/Ana",
      "arn:aws:iam::222222222222:user/Mary"
  ]
}

aws:PrincipalTag/department: hr
aws:PrincipalTag/role: audit
aws:PrincipalArn:
  arn:aws:iam::222222222222:user/Nikki

No match

"StringEquals": {
  "aws:PrincipalTag/department": [
    "finance",
    "hr",
    "legal"
  ],
  "aws:PrincipalTag/role": [
    "audit",
    "security"
  ]
},
"ArnLike": {
  "aws:PrincipalArn": [
      "arn:aws:iam::222222222222:user/Ana",
      "arn:aws:iam::222222222222:user/Mary"
  ]
}

aws:PrincipalTag/department: hr
aws:PrincipalTag/role: payroll
aws:PrincipalArn:
  arn:aws:iam::222222222222:user/Mary

No match

"StringEquals": {
  "aws:PrincipalTag/department": [
    "finance",
    "hr",
    "legal"
  ],
  "aws:PrincipalTag/role": [
    "audit",
    "security"
  ]
},
"ArnLike": {
  "aws:PrincipalArn": [
      "arn:aws:iam::222222222222:user/Ana",
      "arn:aws:iam::222222222222:user/Mary"
  ]
}

No aws:PrincipalTag/role in the request context.

aws:PrincipalTag/department: hr
aws:PrincipalArn:
  arn:aws:iam::222222222222:user/Mary

No match

"StringEquals": {
  "aws:PrincipalTag/department": [
    "finance",
    "hr",
    "legal"
  ],
  "aws:PrincipalTag/role": [
    "audit",
    "security"
  ]
},
"ArnLike": {
  "aws:PrincipalArn": [
      "arn:aws:iam::222222222222:user/Ana",
      "arn:aws:iam::222222222222:user/Mary"
  ]
}

No aws:PrincipalTag in the request context.

aws:PrincipalArn:
  arn:aws:iam::222222222222:user/Mary

No match

Evaluation logic for negated matching condition operators

Some condition operators, such as StringNotEquals or ArnNotLike, use negated matching to compare the context key-value pairs in your policy against the context key-value pairs in a request. When multiple values are specified for a single context key in a policy with negated matching condition operators, the effective permissions work like a logical NOR. In negated matching, a logical NOR or NOT OR returns true only if all values evaluate to false.

The following figure illustrates the evaluation logic for a condition with multiple condition operators and context key-value pairs. The figure includes a negated matching condition operator for context key 3.

For example, the following S3 bucket policy illustrates how the previous figure is represented in a policy. The condition block includes condition operators StringEquals and ArnNotLike, and context keys aws:PrincipalTag and aws:PrincipalArn. To invoke the desired Allow or Deny effect, all context keys in the condition block must resolve to true. The user making the request must have both principal tag keys, department and role, that include one of the tag key values specified in the policy. Since the ArnNotLike condition operator uses negated matching, the principal ARN of the user making the request must not match any of the aws:PrincipalArn values specified in the policy to be evaluated as true.

JSON

{
  "Version": "2012-10-17",
  "Statement": [
    {
      "Sid": "ExamplePolicy",
      "Effect": "Allow",
      "Principal": {
        "AWS": "arn:aws:iam::222222222222:root"
      },
      "Action": "s3:ListBucket",
      "Resource": "arn:aws:s3:::amzn-s3-demo-bucket",
      "Condition": {
        "StringEquals": {
          "aws:PrincipalTag/department": [
            "finance",
            "hr",
            "legal"
          ],
          "aws:PrincipalTag/role": [
            "audit",
            "security"
          ]
        },
        "ArnNotLike": {
          "aws:PrincipalArn": [
            "arn:aws:iam::222222222222:user/Ana",
            "arn:aws:iam::222222222222:user/Mary"
          ]
        }
      }
    }
  ]
}

The following table shows how AWS evaluates this policy based on the condition key values in your request.

Policy Condition Request Context Result

"StringEquals": {
  "aws:PrincipalTag/department": [
    "finance",
    "hr",
    "legal"
  ],
  "aws:PrincipalTag/role": [
    "audit",
    "security"
  ]
},
"ArnNotLike": {
  "aws:PrincipalArn": [
      "arn:aws:iam::222222222222:user/Ana",
      "arn:aws:iam::222222222222:user/Mary"
  ]
}

aws:PrincipalTag/department: legal
aws:PrincipalTag/role: audit
aws:PrincipalArn:
  arn:aws:iam::222222222222:user/Nikki

Match

"StringEquals": {
  "aws:PrincipalTag/department": [
    "finance",
    "hr",
    "legal"
  ],
  "aws:PrincipalTag/role": [
    "audit",
    "security"
  ]
},
"ArnNotLike": {
  "aws:PrincipalArn": [
      "arn:aws:iam::222222222222:user/Ana",
      "arn:aws:iam::222222222222:user/Mary"
  ]
}

aws:PrincipalTag/department: hr
aws:PrincipalTag/role: audit
aws:PrincipalArn:
  arn:aws:iam::222222222222:user/Mary

No match

"StringEquals": {
  "aws:PrincipalTag/department": [
    "finance",
    "hr",
    "legal"
  ],
  "aws:PrincipalTag/role": [
    "audit",
    "security"
  ]
},
"ArnNotLike": {
  "aws:PrincipalArn": [
      "arn:aws:iam::222222222222:user/Ana",
      "arn:aws:iam::222222222222:user/Mary"
  ]
}

aws:PrincipalTag/department: hr
aws:PrincipalTag/role: payroll
aws:PrincipalArn:
  arn:aws:iam::222222222222:user/Nikki

No match

"StringEquals": {
  "aws:PrincipalTag/department": [
    "finance",
    "hr",
    "legal"
  ],
  "aws:PrincipalTag/role": [
    "audit",
    "security"
  ]
},
"ArnNotLike": {
  "aws:PrincipalArn": [
      "arn:aws:iam::222222222222:user/Ana",
      "arn:aws:iam::222222222222:user/Mary"
  ]
}

No aws:PrincipalTag/role in the request context.

aws:PrincipalTag/department: hr
aws:PrincipalArn:
  arn:aws:iam::222222222222:user/Nikki

No match

"StringEquals": {
  "aws:PrincipalTag/department": [
    "finance",
    "hr",
    "legal"
  ],
  "aws:PrincipalTag/role": [
    "audit",
    "security"
  ]
},
"ArnNotLike": {
  "aws:PrincipalArn": [
      "arn:aws:iam::222222222222:user/Ana",
      "arn:aws:iam::222222222222:user/Mary"
  ]
}

No aws:PrincipalTag in the request context.

aws:PrincipalArn:
  arn:aws:iam::222222222222:user/Nikki

No match

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