diff --git a/staging/src/k8s.io/cluster-bootstrap/token/util/helpers.go b/staging/src/k8s.io/cluster-bootstrap/token/util/helpers.go
index f9ea35b5ee3..70abe8f1cb3 100644
--- a/staging/src/k8s.io/cluster-bootstrap/token/util/helpers.go
+++ b/staging/src/k8s.io/cluster-bootstrap/token/util/helpers.go
@@ -17,9 +17,9 @@ limitations under the License.
 package util
 
 import (
-	"bufio"
 	"crypto/rand"
 	"fmt"
+	"math/big"
 	"regexp"
 	"strings"
 
@@ -59,29 +59,21 @@ func GenerateBootstrapToken() (string, error) {
 // randBytes returns a random string consisting of the characters in
 // validBootstrapTokenChars, with the length customized by the parameter
 func randBytes(length int) (string, error) {
-	// len("0123456789abcdefghijklmnopqrstuvwxyz") = 36 which doesn't evenly divide
-	// the possible values of a byte: 256 mod 36 = 4. Discard any random bytes we
-	// read that are >= 252 so the bytes we evenly divide the character set.
-	const maxByteValue = 252
-
 	var (
-		b     byte
-		err   error
 		token = make([]byte, length)
+		max   = new(big.Int).SetUint64(uint64(len(validBootstrapTokenChars)))
 	)
 
-	reader := bufio.NewReaderSize(rand.Reader, length*2)
 	for i := range token {
-		for {
-			if b, err = reader.ReadByte(); err != nil {
-				return "", err
-			}
-			if b < maxByteValue {
-				break
-			}
+		val, err := rand.Int(rand.Reader, max)
+		if err != nil {
+			return "", fmt.Errorf("could not generate random integer: %w", err)
 		}
-
-		token[i] = validBootstrapTokenChars[int(b)%len(validBootstrapTokenChars)]
+		// Use simple operations in constant-time to obtain a byte in the a-z,0-9
+		// character range
+		x := val.Uint64()
+		res := x + 48 + (39 & ((9 - x) >> 8))
+		token[i] = byte(res)
 	}
 
 	return string(token), nil