crypto: drbg - Export CTR DRBG DF functions

Export drbg_ctr_df() derivative function to new module df_sp80090.

Signed-off-by: Harsh Jain <h.jain@amd.com>
Signed-off-by: Herbert Xu <herbert@gondor.apana.org.au>
This commit is contained in:
Harsh Jain 2025-09-15 19:00:25 +05:30 committed by Herbert Xu
parent 3a86608788
commit 6c4fed5fee
8 changed files with 343 additions and 265 deletions

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@ -1205,8 +1205,7 @@ config CRYPTO_DRBG_HASH
config CRYPTO_DRBG_CTR
bool "CTR_DRBG"
select CRYPTO_AES
select CRYPTO_CTR
select CRYPTO_DF80090A
help
CTR_DRBG variant as defined in NIST SP800-90A.
@ -1342,6 +1341,11 @@ config CRYPTO_KDF800108_CTR
select CRYPTO_HMAC
select CRYPTO_SHA256
config CRYPTO_DF80090A
tristate
select CRYPTO_AES
select CRYPTO_CTR
endmenu
menu "Userspace interface"

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@ -209,4 +209,6 @@ obj-$(CONFIG_CRYPTO_SIMD) += crypto_simd.o
#
obj-$(CONFIG_CRYPTO_KDF800108_CTR) += kdf_sp800108.o
obj-$(CONFIG_CRYPTO_DF80090A) += df_sp80090a.o
obj-$(CONFIG_CRYPTO_KRB5) += krb5/

247
crypto/df_sp80090a.c Normal file
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@ -0,0 +1,247 @@
// SPDX-License-Identifier: GPL-2.0
/*
* NIST SP800-90A DRBG derivation function
*
* Copyright (C) 2014, Stephan Mueller <smueller@chronox.de>
*/
#include <linux/errno.h>
#include <linux/kernel.h>
#include <linux/module.h>
#include <linux/string.h>
#include <crypto/df_sp80090a.h>
#include <crypto/internal/drbg.h>
static void drbg_kcapi_symsetkey(struct crypto_cipher *tfm,
const unsigned char *key,
u8 keylen);
static int drbg_kcapi_sym(struct crypto_cipher *tfm, unsigned char *outval,
const struct drbg_string *in, u8 blocklen_bytes);
static void drbg_kcapi_symsetkey(struct crypto_cipher *tfm,
const unsigned char *key, u8 keylen)
{
crypto_cipher_setkey(tfm, key, keylen);
}
static int drbg_kcapi_sym(struct crypto_cipher *tfm, unsigned char *outval,
const struct drbg_string *in, u8 blocklen_bytes)
{
/* there is only component in *in */
BUG_ON(in->len < blocklen_bytes);
crypto_cipher_encrypt_one(tfm, outval, in->buf);
return 0;
}
/* BCC function for CTR DRBG as defined in 10.4.3 */
static int drbg_ctr_bcc(struct crypto_cipher *tfm,
unsigned char *out, const unsigned char *key,
struct list_head *in,
u8 blocklen_bytes,
u8 keylen)
{
int ret = 0;
struct drbg_string *curr = NULL;
struct drbg_string data;
short cnt = 0;
drbg_string_fill(&data, out, blocklen_bytes);
/* 10.4.3 step 2 / 4 */
drbg_kcapi_symsetkey(tfm, key, keylen);
list_for_each_entry(curr, in, list) {
const unsigned char *pos = curr->buf;
size_t len = curr->len;
/* 10.4.3 step 4.1 */
while (len) {
/* 10.4.3 step 4.2 */
if (blocklen_bytes == cnt) {
cnt = 0;
ret = drbg_kcapi_sym(tfm, out, &data, blocklen_bytes);
if (ret)
return ret;
}
out[cnt] ^= *pos;
pos++;
cnt++;
len--;
}
}
/* 10.4.3 step 4.2 for last block */
if (cnt)
ret = drbg_kcapi_sym(tfm, out, &data, blocklen_bytes);
return ret;
}
/*
* scratchpad usage: drbg_ctr_update is interlinked with crypto_drbg_ctr_df
* (and drbg_ctr_bcc, but this function does not need any temporary buffers),
* the scratchpad is used as follows:
* drbg_ctr_update:
* temp
* start: drbg->scratchpad
* length: drbg_statelen(drbg) + drbg_blocklen(drbg)
* note: the cipher writing into this variable works
* blocklen-wise. Now, when the statelen is not a multiple
* of blocklen, the generateion loop below "spills over"
* by at most blocklen. Thus, we need to give sufficient
* memory.
* df_data
* start: drbg->scratchpad +
* drbg_statelen(drbg) + drbg_blocklen(drbg)
* length: drbg_statelen(drbg)
*
* crypto_drbg_ctr_df:
* pad
* start: df_data + drbg_statelen(drbg)
* length: drbg_blocklen(drbg)
* iv
* start: pad + drbg_blocklen(drbg)
* length: drbg_blocklen(drbg)
* temp
* start: iv + drbg_blocklen(drbg)
* length: drbg_satelen(drbg) + drbg_blocklen(drbg)
* note: temp is the buffer that the BCC function operates
* on. BCC operates blockwise. drbg_statelen(drbg)
* is sufficient when the DRBG state length is a multiple
* of the block size. For AES192 (and maybe other ciphers)
* this is not correct and the length for temp is
* insufficient (yes, that also means for such ciphers,
* the final output of all BCC rounds are truncated).
* Therefore, add drbg_blocklen(drbg) to cover all
* possibilities.
* refer to crypto_drbg_ctr_df_datalen() to get required length
*/
/* Derivation Function for CTR DRBG as defined in 10.4.2 */
int crypto_drbg_ctr_df(struct crypto_cipher *tfm,
unsigned char *df_data, size_t bytes_to_return,
struct list_head *seedlist,
u8 blocklen_bytes,
u8 statelen)
{
int ret = -EFAULT;
unsigned char L_N[8];
/* S3 is input */
struct drbg_string S1, S2, S4, cipherin;
LIST_HEAD(bcc_list);
unsigned char *pad = df_data + statelen;
unsigned char *iv = pad + blocklen_bytes;
unsigned char *temp = iv + blocklen_bytes;
size_t padlen = 0;
unsigned int templen = 0;
/* 10.4.2 step 7 */
unsigned int i = 0;
/* 10.4.2 step 8 */
const unsigned char *K = (unsigned char *)
"\x00\x01\x02\x03\x04\x05\x06\x07"
"\x08\x09\x0a\x0b\x0c\x0d\x0e\x0f"
"\x10\x11\x12\x13\x14\x15\x16\x17"
"\x18\x19\x1a\x1b\x1c\x1d\x1e\x1f";
unsigned char *X;
size_t generated_len = 0;
size_t inputlen = 0;
struct drbg_string *seed = NULL;
u8 keylen;
memset(pad, 0, blocklen_bytes);
memset(iv, 0, blocklen_bytes);
keylen = statelen - blocklen_bytes;
/* 10.4.2 step 1 is implicit as we work byte-wise */
/* 10.4.2 step 2 */
if ((512 / 8) < bytes_to_return)
return -EINVAL;
/* 10.4.2 step 2 -- calculate the entire length of all input data */
list_for_each_entry(seed, seedlist, list)
inputlen += seed->len;
drbg_cpu_to_be32(inputlen, &L_N[0]);
/* 10.4.2 step 3 */
drbg_cpu_to_be32(bytes_to_return, &L_N[4]);
/* 10.4.2 step 5: length is L_N, input_string, one byte, padding */
padlen = (inputlen + sizeof(L_N) + 1) % (blocklen_bytes);
/* wrap the padlen appropriately */
if (padlen)
padlen = blocklen_bytes - padlen;
/*
* pad / padlen contains the 0x80 byte and the following zero bytes.
* As the calculated padlen value only covers the number of zero
* bytes, this value has to be incremented by one for the 0x80 byte.
*/
padlen++;
pad[0] = 0x80;
/* 10.4.2 step 4 -- first fill the linked list and then order it */
drbg_string_fill(&S1, iv, blocklen_bytes);
list_add_tail(&S1.list, &bcc_list);
drbg_string_fill(&S2, L_N, sizeof(L_N));
list_add_tail(&S2.list, &bcc_list);
list_splice_tail(seedlist, &bcc_list);
drbg_string_fill(&S4, pad, padlen);
list_add_tail(&S4.list, &bcc_list);
/* 10.4.2 step 9 */
while (templen < (keylen + (blocklen_bytes))) {
/*
* 10.4.2 step 9.1 - the padding is implicit as the buffer
* holds zeros after allocation -- even the increment of i
* is irrelevant as the increment remains within length of i
*/
drbg_cpu_to_be32(i, iv);
/* 10.4.2 step 9.2 -- BCC and concatenation with temp */
ret = drbg_ctr_bcc(tfm, temp + templen, K, &bcc_list,
blocklen_bytes, keylen);
if (ret)
goto out;
/* 10.4.2 step 9.3 */
i++;
templen += blocklen_bytes;
}
/* 10.4.2 step 11 */
X = temp + (keylen);
drbg_string_fill(&cipherin, X, blocklen_bytes);
/* 10.4.2 step 12: overwriting of outval is implemented in next step */
/* 10.4.2 step 13 */
drbg_kcapi_symsetkey(tfm, temp, keylen);
while (generated_len < bytes_to_return) {
short blocklen = 0;
/*
* 10.4.2 step 13.1: the truncation of the key length is
* implicit as the key is only drbg_blocklen in size based on
* the implementation of the cipher function callback
*/
ret = drbg_kcapi_sym(tfm, X, &cipherin, blocklen_bytes);
if (ret)
goto out;
blocklen = (blocklen_bytes <
(bytes_to_return - generated_len)) ?
blocklen_bytes :
(bytes_to_return - generated_len);
/* 10.4.2 step 13.2 and 14 */
memcpy(df_data + generated_len, X, blocklen);
generated_len += blocklen;
}
ret = 0;
out:
memset(iv, 0, blocklen_bytes);
memset(temp, 0, statelen + blocklen_bytes);
memset(pad, 0, blocklen_bytes);
return ret;
}
EXPORT_SYMBOL_GPL(crypto_drbg_ctr_df);
MODULE_IMPORT_NS("CRYPTO_INTERNAL");
MODULE_LICENSE("GPL v2");
MODULE_AUTHOR("Stephan Mueller <smueller@chronox.de>");
MODULE_DESCRIPTION("Derivation Function conformant to SP800-90A");

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@ -98,6 +98,7 @@
*/
#include <crypto/drbg.h>
#include <crypto/df_sp80090a.h>
#include <crypto/internal/cipher.h>
#include <linux/kernel.h>
#include <linux/jiffies.h>
@ -261,26 +262,6 @@ static int drbg_fips_continuous_test(struct drbg_state *drbg,
return 0;
}
/*
* Convert an integer into a byte representation of this integer.
* The byte representation is big-endian
*
* @val value to be converted
* @buf buffer holding the converted integer -- caller must ensure that
* buffer size is at least 32 bit
*/
#if (defined(CONFIG_CRYPTO_DRBG_HASH) || defined(CONFIG_CRYPTO_DRBG_CTR))
static inline void drbg_cpu_to_be32(__u32 val, unsigned char *buf)
{
struct s {
__be32 conv;
};
struct s *conversion = (struct s *) buf;
conversion->conv = cpu_to_be32(val);
}
#endif /* defined(CONFIG_CRYPTO_DRBG_HASH) || defined(CONFIG_CRYPTO_DRBG_CTR) */
/******************************************************************
* CTR DRBG callback functions
******************************************************************/
@ -294,10 +275,6 @@ MODULE_ALIAS_CRYPTO("drbg_nopr_ctr_aes192");
MODULE_ALIAS_CRYPTO("drbg_pr_ctr_aes128");
MODULE_ALIAS_CRYPTO("drbg_nopr_ctr_aes128");
static void drbg_kcapi_symsetkey(struct drbg_state *drbg,
const unsigned char *key);
static int drbg_kcapi_sym(struct drbg_state *drbg, unsigned char *outval,
const struct drbg_string *in);
static int drbg_init_sym_kernel(struct drbg_state *drbg);
static int drbg_fini_sym_kernel(struct drbg_state *drbg);
static int drbg_kcapi_sym_ctr(struct drbg_state *drbg,
@ -305,202 +282,12 @@ static int drbg_kcapi_sym_ctr(struct drbg_state *drbg,
u8 *outbuf, u32 outlen);
#define DRBG_OUTSCRATCHLEN 256
/* BCC function for CTR DRBG as defined in 10.4.3 */
static int drbg_ctr_bcc(struct drbg_state *drbg,
unsigned char *out, const unsigned char *key,
struct list_head *in)
{
int ret = 0;
struct drbg_string *curr = NULL;
struct drbg_string data;
short cnt = 0;
drbg_string_fill(&data, out, drbg_blocklen(drbg));
/* 10.4.3 step 2 / 4 */
drbg_kcapi_symsetkey(drbg, key);
list_for_each_entry(curr, in, list) {
const unsigned char *pos = curr->buf;
size_t len = curr->len;
/* 10.4.3 step 4.1 */
while (len) {
/* 10.4.3 step 4.2 */
if (drbg_blocklen(drbg) == cnt) {
cnt = 0;
ret = drbg_kcapi_sym(drbg, out, &data);
if (ret)
return ret;
}
out[cnt] ^= *pos;
pos++;
cnt++;
len--;
}
}
/* 10.4.3 step 4.2 for last block */
if (cnt)
ret = drbg_kcapi_sym(drbg, out, &data);
return ret;
}
/*
* scratchpad usage: drbg_ctr_update is interlinked with drbg_ctr_df
* (and drbg_ctr_bcc, but this function does not need any temporary buffers),
* the scratchpad is used as follows:
* drbg_ctr_update:
* temp
* start: drbg->scratchpad
* length: drbg_statelen(drbg) + drbg_blocklen(drbg)
* note: the cipher writing into this variable works
* blocklen-wise. Now, when the statelen is not a multiple
* of blocklen, the generateion loop below "spills over"
* by at most blocklen. Thus, we need to give sufficient
* memory.
* df_data
* start: drbg->scratchpad +
* drbg_statelen(drbg) + drbg_blocklen(drbg)
* length: drbg_statelen(drbg)
*
* drbg_ctr_df:
* pad
* start: df_data + drbg_statelen(drbg)
* length: drbg_blocklen(drbg)
* iv
* start: pad + drbg_blocklen(drbg)
* length: drbg_blocklen(drbg)
* temp
* start: iv + drbg_blocklen(drbg)
* length: drbg_satelen(drbg) + drbg_blocklen(drbg)
* note: temp is the buffer that the BCC function operates
* on. BCC operates blockwise. drbg_statelen(drbg)
* is sufficient when the DRBG state length is a multiple
* of the block size. For AES192 (and maybe other ciphers)
* this is not correct and the length for temp is
* insufficient (yes, that also means for such ciphers,
* the final output of all BCC rounds are truncated).
* Therefore, add drbg_blocklen(drbg) to cover all
* possibilities.
*/
/* Derivation Function for CTR DRBG as defined in 10.4.2 */
static int drbg_ctr_df(struct drbg_state *drbg,
unsigned char *df_data, size_t bytes_to_return,
struct list_head *seedlist)
{
int ret = -EFAULT;
unsigned char L_N[8];
/* S3 is input */
struct drbg_string S1, S2, S4, cipherin;
LIST_HEAD(bcc_list);
unsigned char *pad = df_data + drbg_statelen(drbg);
unsigned char *iv = pad + drbg_blocklen(drbg);
unsigned char *temp = iv + drbg_blocklen(drbg);
size_t padlen = 0;
unsigned int templen = 0;
/* 10.4.2 step 7 */
unsigned int i = 0;
/* 10.4.2 step 8 */
const unsigned char *K = (unsigned char *)
"\x00\x01\x02\x03\x04\x05\x06\x07"
"\x08\x09\x0a\x0b\x0c\x0d\x0e\x0f"
"\x10\x11\x12\x13\x14\x15\x16\x17"
"\x18\x19\x1a\x1b\x1c\x1d\x1e\x1f";
unsigned char *X;
size_t generated_len = 0;
size_t inputlen = 0;
struct drbg_string *seed = NULL;
memset(pad, 0, drbg_blocklen(drbg));
memset(iv, 0, drbg_blocklen(drbg));
/* 10.4.2 step 1 is implicit as we work byte-wise */
/* 10.4.2 step 2 */
if ((512/8) < bytes_to_return)
return -EINVAL;
/* 10.4.2 step 2 -- calculate the entire length of all input data */
list_for_each_entry(seed, seedlist, list)
inputlen += seed->len;
drbg_cpu_to_be32(inputlen, &L_N[0]);
/* 10.4.2 step 3 */
drbg_cpu_to_be32(bytes_to_return, &L_N[4]);
/* 10.4.2 step 5: length is L_N, input_string, one byte, padding */
padlen = (inputlen + sizeof(L_N) + 1) % (drbg_blocklen(drbg));
/* wrap the padlen appropriately */
if (padlen)
padlen = drbg_blocklen(drbg) - padlen;
/*
* pad / padlen contains the 0x80 byte and the following zero bytes.
* As the calculated padlen value only covers the number of zero
* bytes, this value has to be incremented by one for the 0x80 byte.
*/
padlen++;
pad[0] = 0x80;
/* 10.4.2 step 4 -- first fill the linked list and then order it */
drbg_string_fill(&S1, iv, drbg_blocklen(drbg));
list_add_tail(&S1.list, &bcc_list);
drbg_string_fill(&S2, L_N, sizeof(L_N));
list_add_tail(&S2.list, &bcc_list);
list_splice_tail(seedlist, &bcc_list);
drbg_string_fill(&S4, pad, padlen);
list_add_tail(&S4.list, &bcc_list);
/* 10.4.2 step 9 */
while (templen < (drbg_keylen(drbg) + (drbg_blocklen(drbg)))) {
/*
* 10.4.2 step 9.1 - the padding is implicit as the buffer
* holds zeros after allocation -- even the increment of i
* is irrelevant as the increment remains within length of i
*/
drbg_cpu_to_be32(i, iv);
/* 10.4.2 step 9.2 -- BCC and concatenation with temp */
ret = drbg_ctr_bcc(drbg, temp + templen, K, &bcc_list);
if (ret)
goto out;
/* 10.4.2 step 9.3 */
i++;
templen += drbg_blocklen(drbg);
}
/* 10.4.2 step 11 */
X = temp + (drbg_keylen(drbg));
drbg_string_fill(&cipherin, X, drbg_blocklen(drbg));
/* 10.4.2 step 12: overwriting of outval is implemented in next step */
/* 10.4.2 step 13 */
drbg_kcapi_symsetkey(drbg, temp);
while (generated_len < bytes_to_return) {
short blocklen = 0;
/*
* 10.4.2 step 13.1: the truncation of the key length is
* implicit as the key is only drbg_blocklen in size based on
* the implementation of the cipher function callback
*/
ret = drbg_kcapi_sym(drbg, X, &cipherin);
if (ret)
goto out;
blocklen = (drbg_blocklen(drbg) <
(bytes_to_return - generated_len)) ?
drbg_blocklen(drbg) :
(bytes_to_return - generated_len);
/* 10.4.2 step 13.2 and 14 */
memcpy(df_data + generated_len, X, blocklen);
generated_len += blocklen;
}
ret = 0;
out:
memset(iv, 0, drbg_blocklen(drbg));
memset(temp, 0, drbg_statelen(drbg) + drbg_blocklen(drbg));
memset(pad, 0, drbg_blocklen(drbg));
return ret;
return crypto_drbg_ctr_df(drbg->priv_data, df_data, drbg_statelen(drbg),
seedlist, drbg_blocklen(drbg), drbg_statelen(drbg));
}
/*
@ -1310,10 +1097,8 @@ static inline int drbg_alloc_state(struct drbg_state *drbg)
sb_size = 0;
else if (drbg->core->flags & DRBG_CTR)
sb_size = drbg_statelen(drbg) + drbg_blocklen(drbg) + /* temp */
drbg_statelen(drbg) + /* df_data */
drbg_blocklen(drbg) + /* pad */
drbg_blocklen(drbg) + /* iv */
drbg_statelen(drbg) + drbg_blocklen(drbg); /* temp */
crypto_drbg_ctr_df_datalen(drbg_statelen(drbg),
drbg_blocklen(drbg));
else
sb_size = drbg_statelen(drbg) + drbg_blocklen(drbg);
@ -1800,25 +1585,6 @@ static int drbg_init_sym_kernel(struct drbg_state *drbg)
return alignmask;
}
static void drbg_kcapi_symsetkey(struct drbg_state *drbg,
const unsigned char *key)
{
struct crypto_cipher *tfm = drbg->priv_data;
crypto_cipher_setkey(tfm, key, (drbg_keylen(drbg)));
}
static int drbg_kcapi_sym(struct drbg_state *drbg, unsigned char *outval,
const struct drbg_string *in)
{
struct crypto_cipher *tfm = drbg->priv_data;
/* there is only component in *in */
BUG_ON(in->len < drbg_blocklen(drbg));
crypto_cipher_encrypt_one(tfm, outval, in->buf);
return 0;
}
static int drbg_kcapi_sym_ctr(struct drbg_state *drbg,
u8 *inbuf, u32 inlen,
u8 *outbuf, u32 outlen)

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@ -728,6 +728,7 @@ config CRYPTO_DEV_TEGRA
config CRYPTO_DEV_XILINX_TRNG
tristate "Support for Xilinx True Random Generator"
depends on ZYNQMP_FIRMWARE || COMPILE_TEST
select CRYPTO_DF80090A
select CRYPTO_RNG
select HW_RANDOM
help

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@ -0,0 +1,27 @@
/* SPDX-License-Identifier: GPL-2.0 */
/*
* Copyright Stephan Mueller <smueller@chronox.de>, 2014
*/
#ifndef _CRYPTO_DF80090A_H
#define _CRYPTO_DF80090A_H
#include <crypto/internal/cipher.h>
static inline int crypto_drbg_ctr_df_datalen(u8 statelen, u8 blocklen)
{
return statelen + /* df_data */
blocklen + /* pad */
blocklen + /* iv */
statelen + blocklen; /* temp */
}
int crypto_drbg_ctr_df(struct crypto_cipher *tfm,
unsigned char *df_data,
size_t bytes_to_return,
struct list_head *seedlist,
u8 blocklen_bytes,
u8 statelen);
#endif /* _CRYPTO_DF80090A_H */

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@ -47,6 +47,7 @@
#include <linux/module.h>
#include <linux/crypto.h>
#include <linux/slab.h>
#include <crypto/internal/drbg.h>
#include <crypto/internal/rng.h>
#include <crypto/rng.h>
#include <linux/fips.h>
@ -54,30 +55,6 @@
#include <linux/list.h>
#include <linux/workqueue.h>
/*
* Concatenation Helper and string operation helper
*
* SP800-90A requires the concatenation of different data. To avoid copying
* buffers around or allocate additional memory, the following data structure
* is used to point to the original memory with its size. In addition, it
* is used to build a linked list. The linked list defines the concatenation
* of individual buffers. The order of memory block referenced in that
* linked list determines the order of concatenation.
*/
struct drbg_string {
const unsigned char *buf;
size_t len;
struct list_head list;
};
static inline void drbg_string_fill(struct drbg_string *string,
const unsigned char *buf, size_t len)
{
string->buf = buf;
string->len = len;
INIT_LIST_HEAD(&string->list);
}
struct drbg_state;
typedef uint32_t drbg_flag_t;

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@ -0,0 +1,54 @@
/* SPDX-License-Identifier: GPL-2.0 */
/*
* NIST SP800-90A DRBG derivation function
*
* Copyright (C) 2014, Stephan Mueller <smueller@chronox.de>
*/
#ifndef _INTERNAL_DRBG_H
#define _INTERNAL_DRBG_H
/*
* Convert an integer into a byte representation of this integer.
* The byte representation is big-endian
*
* @val value to be converted
* @buf buffer holding the converted integer -- caller must ensure that
* buffer size is at least 32 bit
*/
static inline void drbg_cpu_to_be32(__u32 val, unsigned char *buf)
{
struct s {
__be32 conv;
};
struct s *conversion = (struct s *)buf;
conversion->conv = cpu_to_be32(val);
}
/*
* Concatenation Helper and string operation helper
*
* SP800-90A requires the concatenation of different data. To avoid copying
* buffers around or allocate additional memory, the following data structure
* is used to point to the original memory with its size. In addition, it
* is used to build a linked list. The linked list defines the concatenation
* of individual buffers. The order of memory block referenced in that
* linked list determines the order of concatenation.
*/
struct drbg_string {
const unsigned char *buf;
size_t len;
struct list_head list;
};
static inline void drbg_string_fill(struct drbg_string *string,
const unsigned char *buf, size_t len)
{
string->buf = buf;
string->len = len;
INIT_LIST_HEAD(&string->list);
}
#endif //_INTERNAL_DRBG_H