A “pure” scheme implementation (R5RS) of SHA256?

Question

I can use SHA256 in Scheme using external libraries (Java, C or system dependent) or using a specific Scheme implementation (like Chicken e.g.), but I wonder if there is a "pure" scheme implementation.

Answer 1

I wrote an implementation today. Alas, R5RS has neither bytevectors nor binary I/O, so this uses the R7RS APIs for bytevectors and binary I/O. It should be easy to bridge those APIs to your Scheme implementation's native APIs (for example, I actually tested my implementation on Racket and Guile).

A few notes:

• This code assumes case-sensitivity. This is the default for R7RS, but not R5RS, so if you're using an R5RS implementation, beware.
• It requires SRFIs 1, 26, 43, and 60.
• I emphasise elegance and clarity over speed. In fact, the code is quite slow.
• Contrary to what my profile says, I'm only licensing this code under the Apache Licence 2.0 (in addition to the standard Stack Overflow licence of CC BY-SA 3.0), and not under CC0 or anything resembling public domain.

Anyway, without further ado, here it is (also available as a Gist):

;;; Auxiliary definitions to avoid having to use giant tables of constants.

(define primes80 '(2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73
                   79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157
                   163 167 173 179 181 191 193 197 199 211 223 227 229 233 239
                   241 251 257 263 269 271 277 281 283 293 307 311 313 317 331
                   337 347 349 353 359 367 373 379 383 389 397 401 409))

(define (sqrt x)
  (fold (lambda (_ y) (/ (+ (/ x y) y) 2)) 4 (iota 7)))

(define (cbrt x)
  (fold (lambda (_ y) (/ (+ (/ x y y) y y) 3)) 4 (iota 8)))

(define (frac x scale base)
  (bitwise-and (floor (* x (arithmetic-shift 1 scale)))
               (- (arithmetic-shift 1 base) 1)))

;;; The actual initialisation and constant values.

(define sha1-init '(#x67452301 #xefcdab89 #x98badcfe #x10325476 #xc3d2e1f0))
(define sha2-init (map (lambda (x) (frac (sqrt x) 64 64)) (take primes80 16)))
(define-values (sha512-init sha384-init) (split-at sha2-init 8))
(define sha256-init (map (cut arithmetic-shift <> -32) sha512-init))
(define sha224-init (map (cut frac <> 0 32) sha384-init))

(define sha1-const (map (lambda (x) (frac (sqrt x) 30 32)) '(2 3 5 10)))
(define sha512-const (map (lambda (x) (frac (cbrt x) 64 64)) primes80))
(define sha256-const (map (cut arithmetic-shift <> -32) (take sha512-const 64)))

;;; Utility functions used by the compression and driver functions.

(define (u32+ . xs) (bitwise-and (apply + xs) #xffffffff))
(define (u64+ . xs) (bitwise-and (apply + xs) #xffffffffffffffff))
(define (bitwise-majority x y z)
  (bitwise-xor (bitwise-and x y) (bitwise-and x z) (bitwise-and y z)))

(define (bytevector-be-ref bv base n)
  (let loop ((res 0) (i 0))
    (if (< i n)
        (loop (+ (arithmetic-shift res 8) (bytevector-u8-ref bv (+ base i)))
              (+ i 1))
        res)))
(define (bytevector-u64-ref bv i)
  (bytevector-be-ref bv (arithmetic-shift i 3) 8))
(define (bytevector-u32-ref bv i)
  (bytevector-be-ref bv (arithmetic-shift i 2) 4))

(define (bytevector-be-set! bv base n val)
  (let loop ((i n) (val val))
    (when (positive? i)
      (bytevector-u8-set! bv (+ base i -1) (bitwise-and val 255))
      (loop (- i 1) (arithmetic-shift val -8)))))

(define (md-pad! bv offset count counter-size)
  (define block-size (bytevector-length bv))
  (unless (negative? offset)
    (bytevector-u8-set! bv offset #x80))
  (let loop ((i (+ offset 1)))
    (when (< i block-size)
      (bytevector-u8-set! bv i 0)
      (loop (+ i 1))))
  (when count
    (bytevector-be-set! bv (- block-size counter-size) counter-size
                        (arithmetic-shift count 3))))

(define (hash-state->bytevector hs trunc word-size)
  (define result (make-bytevector (* trunc word-size)))
  (for-each (lambda (h i)
              (bytevector-be-set! result i word-size h))
            hs (iota trunc 0 word-size))
  result)

;;; The compression functions.

(define (sha2-compress K Σ0 Σ1 σ0 σ1 mod+ getter hs)
  (define W (vector->list (apply vector-unfold
                                 (lambda (_ a b c d e f g h i j k l m n o p)
                                   (values a b c d e f g h i j k l m n o p
                                           (mod+ a (σ0 b) j (σ1 o))))
                                 (length K)
                                 (list-tabulate 16 getter))))
  (define (loop k w a b c d e f g h)
    (if (null? k)
        (map mod+ hs (list a b c d e f g h))
        (let ((T1 (mod+ h (Σ1 e) (bitwise-if e f g) (car k) (car w)))
              (T2 (mod+ (Σ0 a) (bitwise-majority a b c))))
          (loop (cdr k) (cdr w) (mod+ T1 T2) a b c (mod+ d T1) e f g))))
  (apply loop K W hs))

(define (sha512-compress bv hs)
  (define (rotr x y) (rotate-bit-field x (- y) 0 64))
  (define (shr x y) (arithmetic-shift x (- y)))
  (sha2-compress sha512-const
                 (lambda (x) (bitwise-xor (rotr x 28) (rotr x 34) (rotr x 39)))
                 (lambda (x) (bitwise-xor (rotr x 14) (rotr x 18) (rotr x 41)))
                 (lambda (x) (bitwise-xor (rotr x 1) (rotr x 8) (shr x 7)))
                 (lambda (x) (bitwise-xor (rotr x 19) (rotr x 61) (shr x 6)))
                 u64+ (cut bytevector-u64-ref bv <>) hs))

(define (sha256-compress bv hs)
  (define (rotr x y) (rotate-bit-field x (- y) 0 32))
  (define (shr x y) (arithmetic-shift x (- y)))
  (sha2-compress sha256-const
                 (lambda (x) (bitwise-xor (rotr x 2) (rotr x 13) (rotr x 22)))
                 (lambda (x) (bitwise-xor (rotr x 6) (rotr x 11) (rotr x 25)))
                 (lambda (x) (bitwise-xor (rotr x 7) (rotr x 18) (shr x 3)))
                 (lambda (x) (bitwise-xor (rotr x 17) (rotr x 19) (shr x 10)))
                 u32+ (cut bytevector-u32-ref bv <>) hs))

(define (sha1-compress bv hs)
  (define (getter x) (bytevector-u32-ref bv x))
  (define (rotl x y) (rotate-bit-field x y 0 32))
  (define W (vector->list (apply vector-unfold
                                 (lambda (_ a b c d e f g h i j k l m n o p)
                                   (values a b c d e f g h i j k l m n o p
                                           (rotl (bitwise-xor a c i n) 1)))
                                 80
                                 (list-tabulate 16 getter))))
  (define (outer f k w a b c d e)
    (if (null? k)
        (map u32+ hs (list a b c d e))
        (let inner ((i 0) (w w) (a a) (b b) (c c) (d d) (e e))
          (if (< i 20)
              (let ((T (u32+ (rotl a 5) ((car f) b c d) e (car k) (car w))))
                (inner (+ i 1) (cdr w) T a (rotl b 30) c d))
              (outer (cdr f) (cdr k) w a b c d e)))))
  (apply outer (list bitwise-if bitwise-xor bitwise-majority bitwise-xor)
               sha1-const W hs))

;;; The Merkle-Damgård "driver" function.

(define (md-loop init compress block-size trunc word-size counter-size in)
  (define leftover (- block-size counter-size))
  (define bv (make-bytevector block-size))
  (define pad! (cut md-pad! bv <> <> counter-size))
  (define hs->bv (cut hash-state->bytevector <> trunc word-size))

  (let loop ((count 0) (hs init))
    (define read-size (read-bytevector! bv in))
    (cond ((eof-object? read-size)
           (pad! 0 count)
           (hs->bv (compress bv hs)))
          ((= read-size block-size)
           (loop (+ count read-size) (compress bv hs)))
          ((< read-size leftover)
           (pad! read-size (+ count read-size))
           (hs->bv (compress bv hs)))
          (else
           (pad! read-size #f)
           (let ((pen (compress bv hs)))
             (pad! -1 (+ count read-size))
             (hs->bv (compress bv pen)))))))

;;; SHA-512/t stuff.

(define sha512/t-init (map (cut bitwise-xor <> #xa5a5a5a5a5a5a5a5) sha512-init))
(define (make-sha512/t-init t)
  (define key (string->utf8 (string-append "SHA-512/" (number->string t))))
  (define size (bytevector-length key))
  (define bv (make-bytevector 128))
  (bytevector-copy! bv 0 key)
  (md-pad! bv size size 16)
  (sha512-compress bv sha512/t-init))

(define (make-sha512/t t)
  (define init (make-sha512/t-init t))
  (define words (arithmetic-shift t -6))
  (if (zero? (bitwise-and t 63))
      (cut md-loop init sha512-compress 128 words 8 16 <>)
      (lambda (in)
        (bytevector-copy
         (md-loop init sha512-compress 128 (ceiling words) 8 16 in)
         0 (arithmetic-shift t -3)))))

;;; Public entry points.

(define sha1 (cut md-loop sha1-init sha1-compress 64 5 4 8 <>))
(define sha224 (cut md-loop sha224-init sha256-compress 64 7 4 8 <>))
(define sha256 (cut md-loop sha256-init sha256-compress 64 8 4 8 <>))
(define sha384 (cut md-loop sha384-init sha512-compress 128 6 8 16 <>))
(define sha512 (cut md-loop sha512-init sha512-compress 128 8 8 16 <>))
(define sha512/256 (make-sha512/t 256))
(define sha512/224 (make-sha512/t 224))

I implemented all the algorithms in FIPS 180-4, but you can strip out whatever you don't need.

---

As mentioned before, I tested this on Racket; the definitions I added to bridge to Racket's APIs are as follows:

#lang racket
(require (only-in srfi/1 iota)
         (only-in srfi/26 cut)
         (only-in srfi/43 vector-unfold)
         (only-in srfi/60 bitwise-if rotate-bit-field)
         (rename-in racket/base [build-list list-tabulate]
                                [bytes-copy! bytevector-copy!]
                                [bytes-length bytevector-length]
                                [bytes-ref bytevector-u8-ref]
                                [bytes-set! bytevector-u8-set!]
                                [foldl fold]
                                [make-bytes make-bytevector]
                                [read-bytes! read-bytevector!]
                                [string->bytes/utf-8 string->utf8]
                                [subbytes bytevector-copy]))

And here are the definitions for Guile (requires version 2.0.11 or above):

(use-modules (srfi srfi-1) (srfi srfi-26) (srfi srfi-43) (srfi srfi-60)
             (rnrs bytevectors) (ice-9 binary-ports))

(define* (bytevector-copy bv #:optional (start 0) (end (bytevector-length bv)))
  (define copy (make-bytevector (- end start)))
  (bytevector-copy! copy 0 bv start end)
  copy)
(define* (bytevector-copy! to at from #:optional (start 0)
                                                 (end (bytevector-length from)))
  ((@ (rnrs bytevectors) bytevector-copy!) from start to at (- end start)))
(define* (read-bytevector! bv #:optional (port (current-input-port)) (start 0)
                                         (end (bytevector-length bv)))
  (get-bytevector-n! port bv start (- end start)))

It should be easy to make something similar for your chosen implementation.

---

I also have a function that prints out the output as a hex string, for ready comparison with various command-line SHA-1 and SHA-2 utilities (e.g., sha1sum, sha256sum, sha512sum, etc.):

(define (hex bv)
  (define out (open-output-string))
  (do ((i 0 (+ i 1)))
      ((>= i (bytevector-length bv)) (get-output-string out))
    (let-values (((q r) (truncate/ (bytevector-u8-ref bv i) 16)))
      (display (number->string q 16) out)
      (display (number->string r 16) out))))