Generating RSA key pairs in DER format

keys.lisp

(in-package :cl-user)

(ql:quickload '(:ironclad :asn1))

(defun generate-rsa-key-pair (num-bits)
  "Same as (ironclad:generate-key-pair :rsa :num-bits num-bits) except returning in DER format."
  (check-type num-bits integer)
  (let ((l (floor num-bits 2)))
    (multiple-value-bind (p q n)
        (loop for a = (ironclad:generate-prime (- num-bits l))
              for b = (ironclad:generate-prime l)
              for c = (* a b)
              until (and (/= a b) (= num-bits (ironclad::integer-length c)))
              finally (return (values a b c)))
      (let* ((phi (* (1- p) (1- q)))
             (e (loop for e = (+ 2 (ironclad:strong-random (- phi 2)))
                      until (= 1 (ironclad::gcd e phi))
                      finally (return e)))
             (d (ironclad::modular-inverse-with-blinding e phi)))
        (values (asn1:encode
                 `((:sequence
                    . ((:integer . 0)
                       (:integer . ,n)
                       (:integer . ,e)
                       (:integer . ,d)
                       (:integer . ,p)
                       (:integer . ,q)
                       (:integer . ,(mod d (1- p)))
                       (:integer . ,(mod d (1- q)))
                       (:integer . ,(ironclad::expt-mod q (- p 2) p))))))
                (asn1:encode
                 `((:sequence
                    . ((:sequence . ((:object-identifier . #(1 2 840 113549 1 1 1))
                                     (:null)))
                       (:bit-string . ,(asn1:encode
                                        `((:sequence . ((:integer . ,n)
                                                        (:integer . ,e)))))))))))))))