diff --git a/pkg/air/schema.go b/pkg/air/schema.go
index e102751..6ee0b0c 100644
--- a/pkg/air/schema.go
+++ b/pkg/air/schema.go
@@ -186,8 +186,8 @@ func (p *Schema) AddComputation(c table.TraceComputation) {
 
 // AddPermutationConstraint appends a new permutation constraint which
 // ensures that one column is a permutation of another.
-func (p *Schema) AddPermutationConstraint(target string, source string) {
-	p.permutations = append(p.permutations, table.NewPermutation(target, source))
+func (p *Schema) AddPermutationConstraint(targets []string, sources []string) {
+	p.permutations = append(p.permutations, table.NewPermutation(targets, sources))
 }
 
 // AddVanishingConstraint appends a new vanishing constraint.
diff --git a/pkg/mir/schema.go b/pkg/mir/schema.go
index 43e3a47..80b0900 100644
--- a/pkg/mir/schema.go
+++ b/pkg/mir/schema.go
@@ -192,8 +192,9 @@ func lowerPermutationToAir(c Permutation, mirSchema *Schema, airSchema *air.Sche
 	// Add individual permutation constraints
 	for i := 0; i < ncols; i++ {
 		airSchema.AddColumn(c.Targets[i], true)
-		airSchema.AddPermutationConstraint(c.Targets[i], c.Sources[i])
 	}
+	//
+	airSchema.AddPermutationConstraint(c.Targets, c.Sources)
 	// Add the trace computation.
 	airSchema.AddComputation(c)
 	// Add sorting constraints + synthetic columns as necessary.
diff --git a/pkg/table/column.go b/pkg/table/column.go
index 4158f85..58c5cd6 100644
--- a/pkg/table/column.go
+++ b/pkg/table/column.go
@@ -154,15 +154,19 @@ func (c *ComputedColumn[E]) String() string {
 // Permutation declares a constraint that one column is a permutation
 // of another.
 type Permutation struct {
-	// The target column
-	Target string
+	// The target columns
+	Targets []string
 	// The so columns
-	Source string
+	Sources []string
 }
 
 // NewPermutation creates a new permutation
-func NewPermutation(target string, source string) *Permutation {
-	return &Permutation{target, source}
+func NewPermutation(targets []string, sources []string) *Permutation {
+	if len(targets) != len(sources) {
+		panic("differeng number of target / source permutation columns")
+	}
+
+	return &Permutation{targets, sources}
 }
 
 // RequiredSpillage returns the minimum amount of spillage required to ensure
@@ -174,18 +178,44 @@ func (p *Permutation) RequiredSpillage() uint {
 // Accepts checks whether a permutation holds between the source and
 // target columns.
 func (p *Permutation) Accepts(tr Trace) error {
-	// Check column in trace!
-	if !tr.HasColumn(p.Target) {
-		return fmt.Errorf("Trace missing permutation target column ({%s})", p.Target)
-	} else if !tr.HasColumn(p.Source) {
-		return fmt.Errorf("Trace missing permutation source column ({%s})", p.Source)
+	// Sanity check columns well formed.
+	if err := validPermutationColumns(p.Targets, p.Sources, tr); err != nil {
+		return err
 	}
-
-	return IsPermutationOf(p.Target, p.Source, tr)
+	// Slice out data
+	src := sliceMatchingColumns(p.Sources, tr)
+	dst := sliceMatchingColumns(p.Targets, tr)
+	// Sanity check whether column exists
+	if !util.ArePermutationOf(dst, src) {
+		msg := fmt.Sprintf("Target columns (%v) not permutation of source columns ({%v})",
+			p.Targets, p.Sources)
+		return errors.New(msg)
+	}
+	// Success
+	return nil
 }
 
 func (p *Permutation) String() string {
-	return fmt.Sprintf("(permutation %s %s)", p.Target, p.Source)
+	targets := ""
+	sources := ""
+
+	for i, s := range p.Targets {
+		if i != 0 {
+			targets += " "
+		}
+
+		targets += s
+	}
+
+	for i, s := range p.Sources {
+		if i != 0 {
+			sources += " "
+		}
+
+		sources += s
+	}
+
+	return fmt.Sprintf("(permutation (%s) (%s))", targets, sources)
 }
 
 // ===================================================================
@@ -221,41 +251,26 @@ func (p *SortedPermutation) RequiredSpillage() uint {
 // Accepts checks whether a sorted permutation holds between the
 // source and target columns.
 func (p *SortedPermutation) Accepts(tr Trace) error {
-	ncols := len(p.Sources)
-	cols := make([][]*fr.Element, ncols)
-	// Check required columns in trace
-	for _, n := range p.Targets {
-		if !tr.HasColumn(n) {
-			return fmt.Errorf("Trace missing permutation target column ({%s})", n)
-		}
+	// Sanity check columns well formed.
+	if err := validPermutationColumns(p.Targets, p.Sources, tr); err != nil {
+		return err
 	}
-
-	for _, n := range p.Sources {
-		if !tr.HasColumn(n) {
-			return fmt.Errorf("Trace missing permutation source ({%s})", n)
-		}
-	}
-	// Check that target and source columns exist and are permutations of source
-	// columns.
-	for i := 0; i < ncols; i++ {
-		dstName := p.Targets[i]
-		srcName := p.Sources[i]
-		// Access column data based on column name.
-		err := IsPermutationOf(dstName, srcName, tr)
-		if err != nil {
-			return err
-		}
-
-		cols[i] = tr.ColumnByName(dstName).Data()
+	// Slice out data
+	src := sliceMatchingColumns(p.Sources, tr)
+	dst := sliceMatchingColumns(p.Targets, tr)
+	// Sanity check whether column exists
+	if !util.ArePermutationOf(dst, src) {
+		msg := fmt.Sprintf("Target columns (%v) not permutation of source columns ({%v})",
+			p.Targets, p.Sources)
+		return errors.New(msg)
 	}
-
 	// Check that target columns are sorted lexicographically.
-	if util.AreLexicographicallySorted(cols, p.Signs) {
+	if util.AreLexicographicallySorted(dst, p.Signs) {
 		return nil
 	}
-
+	// Error case
 	msg := fmt.Sprintf("Permutation columns not lexicographically sorted ({%s})", p.Targets)
-
+	// Done
 	return errors.New(msg)
 }
 
@@ -321,23 +336,32 @@ func (p *SortedPermutation) String() string {
 	return fmt.Sprintf("(permute (%s) (%s))", targets, sources)
 }
 
-// IsPermutationOf checks whether (or not) one column is a permutation
-// of another in given trace.  The order in which columns are given is
-// not important.
-func IsPermutationOf(target string, source string, tr Trace) error {
-	dst := tr.ColumnByName(target).Data()
-	src := tr.ColumnByName(source).Data()
-	// Sanity check whether column exists
-	if dst == nil {
-		msg := fmt.Sprintf("Invalid target column for permutation ({%s})", target)
-		return errors.New(msg)
-	} else if src == nil {
-		msg := fmt.Sprintf("Invalid source column for permutation ({%s})", source)
-		return errors.New(msg)
-	} else if !util.IsPermutationOf(dst, src) {
-		msg := fmt.Sprintf("Target column (%s) not permutation of source ({%s})", target, source)
-		return errors.New(msg)
+func validPermutationColumns(targets []string, sources []string, tr Trace) error {
+	ncols := len(targets)
+	// Sanity check matching length
+	if len(sources) != ncols {
+		return fmt.Errorf("Number of source and target columns differs")
 	}
-
+	// Check required columns in trace
+	for i := 0; i < ncols; i++ {
+		if !tr.HasColumn(targets[i]) {
+			return fmt.Errorf("Trace missing permutation target column ({%s})", targets[i])
+		} else if !tr.HasColumn(sources[i]) {
+			return fmt.Errorf("Trace missing permutation source ({%s})", sources[i])
+		}
+	}
+	//
 	return nil
 }
+
+func sliceMatchingColumns(names []string, tr Trace) [][]*fr.Element {
+	// Allocate return array
+	cols := make([][]*fr.Element, len(names))
+	// Slice out the data
+	for i, n := range names {
+		nth := tr.ColumnByName(n)
+		cols[i] = nth.Data()
+	}
+	// Done
+	return cols
+}
diff --git a/pkg/util/arrays.go b/pkg/util/arrays.go
index 7e9c702..f46cb7f 100644
--- a/pkg/util/arrays.go
+++ b/pkg/util/arrays.go
@@ -1,5 +1,31 @@
 package util
 
+import "github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
+
+// Equals2d returns true if two 2D arrays are equal.
+func Equals2d(lhs [][]*fr.Element, rhs [][]*fr.Element) bool {
+	if len(lhs) != len(rhs) {
+		return false
+	}
+
+	for i := 0; i < len(lhs); i++ {
+		lhs_i := lhs[i]
+		rhs_i := rhs[i]
+		// Check lengths match
+		if len(lhs_i) != len(rhs_i) {
+			return false
+		}
+		// Check elements match
+		for j := 0; j < len(lhs_i); j++ {
+			if lhs_i[j].Cmp(rhs_i[j]) != 0 {
+				return false
+			}
+		}
+	}
+	//
+	return true
+}
+
 // FlatArrayIndexOf_2 returns the ith element of the flattened form of a 2d
 // array. Consider the array "[[0,7],[4]]".  Then its flattened form is
 // "[0,7,4]" and, for example, the element at index 1 is "7".
diff --git a/pkg/util/permutation.go b/pkg/util/permutation.go
index c5f5f27..73474f2 100644
--- a/pkg/util/permutation.go
+++ b/pkg/util/permutation.go
@@ -8,33 +8,43 @@ import (
 	"github.com/consensys/gnark-crypto/ecc/bls12-377/fr"
 )
 
-// IsPermutationOf checks whether or not a given destination column is a valid
-// permutation of a given source column.  This function does not modify either
-// column (though it does allocate an intermediate array).
+// ArePermutationOf checks whether or not a set of given destination columns are
+// a valid permutation of a given set of source columns.  The number of source
+// and target columns must match.  Likewise, they are expected to have the same
+// height. This function does not modify any columns (though it does allocate
+// intermediate arrays).
 //
-// This function operators by cloning both arrays, sorting them and checking
-// they are the same.
-func IsPermutationOf(dst []*fr.Element, src []*fr.Element) bool {
+// This function operators by cloning the arrays, sorting them and checking they
+// are the same.
+func ArePermutationOf(dst [][]*fr.Element, src [][]*fr.Element) bool {
 	if len(dst) != len(src) {
 		return false
 	}
-	// Copy arrays
-	dstCopy := make([]*fr.Element, len(dst))
-	srcCopy := make([]*fr.Element, len(src))
+	// Determine geometry
+	ncols := len(dst)
+	nrows := len(dst[0])
+	// Rotate input arrays
+	dstCopy := rotate(dst, ncols, nrows)
+	srcCopy := rotate(src, ncols, nrows)
+	// Sort rotated arrays
+	slices.SortFunc(dstCopy, permutationFunc)
+	slices.SortFunc(srcCopy, permutationFunc)
+	// Check rotated arrays match
+	return Equals2d(dstCopy, srcCopy)
+}
 
-	copy(dstCopy, dst)
-	copy(srcCopy, src)
-	// Sort arrays
-	slices.SortFunc(dstCopy, func(l *fr.Element, r *fr.Element) int { return l.Cmp(r) })
-	slices.SortFunc(srcCopy, func(l *fr.Element, r *fr.Element) int { return l.Cmp(r) })
-	// Check they are equal
-	for i := 0; i < len(dst); i++ {
-		if dstCopy[i].Cmp(srcCopy[i]) != 0 {
-			return false
+func permutationFunc(lhs []*fr.Element, rhs []*fr.Element) int {
+	for i := 0; i < len(lhs); i++ {
+		// Compare ith elements
+		c := lhs[i].Cmp(rhs[i])
+		// Check whether same
+		if c != 0 {
+			// Positive
+			return c
 		}
 	}
-	// Match
-	return true
+	// Identical
+	return 0
 }
 
 // PermutationSort sorts an array of columns in row-wise fashion.  For
@@ -54,17 +64,8 @@ func IsPermutationOf(dst []*fr.Element, src []*fr.Element) bool {
 func PermutationSort(cols [][]*fr.Element, signs []bool) {
 	n := len(cols[0])
 	m := len(cols)
-	//
-	rows := make([][]*fr.Element, n)
-	// project into row-wise form
-	for i := 0; i < n; i++ {
-		row := make([]*fr.Element, m)
-		for j := 0; j < m; j++ {
-			row[j] = cols[j][i]
-		}
-
-		rows[i] = row
-	}
+	// Rotate input matrix
+	rows := rotate(cols, m, n)
 	// Perform the permutation sort
 	slices.SortFunc(rows, func(l []*fr.Element, r []*fr.Element) int {
 		return permutationSortFunc(l, r, signs)
@@ -120,3 +121,20 @@ func permutationSortFunc(lhs []*fr.Element, rhs []*fr.Element, signs []bool) int
 	// Identical
 	return 0
 }
+
+// Clone and rotate a 2-dimensional array assuming a given geometry.
+func rotate(src [][]*fr.Element, ncols int, nrows int) [][]*fr.Element {
+	// Copy outer arrays
+	dst := make([][]*fr.Element, nrows)
+	// Copy inner arrays
+	for i := 0; i < nrows; i++ {
+		row := make([]*fr.Element, ncols)
+		for j := 0; j < ncols; j++ {
+			row[j] = src[j][i]
+		}
+
+		dst[i] = row
+	}
+	//
+	return dst
+}