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Nonsecure RSA public exponent

Context used in key generation is associated with low exponent value

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Description

This defect occurs when you attempt RSA key generation by using a context object that is associated with a low public exponent.

For instance, you set a public exponent of 3 in the context object, and then use it for key generation.

/* Set public exponent */
ret = BN_dec2bn(&pubexp, "3");

/* Initialize context */
ctx = EVP_PKEY_CTX_new_id(EVP_PKEY_RSA, NULL); 
pkey = EVP_PKEY_new();
ret = EVP_PKEY_keygen_init(kctx);

/* Set public exponent in context */
ret = EVP_PKEY_CTX_set_rsa_keygen_pubexp(ctx, pubexp);

/* Generate key */
ret = EVP_PKEY_keygen(kctx, &pkey);

Risk

A low RSA public exponent makes certain kinds of attacks more damaging, especially when a weak padding scheme is used or padding is not used at all.

Fix

It is recommended to use a public exponent of 65537. Using a higher public exponent can make the operations slower.

Examples

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#include <stddef.h>
#include <openssl/rsa.h>
#include <openssl/evp.h>

#define fatal_error() exit(-1)

int ret;
int func(EVP_PKEY *pkey){
  BIGNUM* pubexp;
  EVP_PKEY_CTX* ctx;

  pubexp = BN_new();
  if (pubexp == NULL) fatal_error();
  ret = BN_set_word(pubexp, 3);
  if (ret <= 0) fatal_error();

  ctx = EVP_PKEY_CTX_new_id(EVP_PKEY_RSA, NULL);
  if (ctx == NULL) fatal_error();

  ret = EVP_PKEY_keygen_init(ctx);
  if (ret <= 0) fatal_error();
  ret = EVP_PKEY_CTX_set_rsa_keygen_bits(ctx, 2048);
  if (ret <= 0) fatal_error();
  ret = EVP_PKEY_CTX_set_rsa_keygen_pubexp(ctx, pubexp);
  if (ret <= 0) fatal_error();
  return EVP_PKEY_keygen(ctx, &pkey);
}

In this example, an RSA public exponent of 3 is associated with the context object ctx. The low exponent makes operations that use the generated key vulnerable to certain attacks.

Correction — Use Public Exponent of 65537

One possible correction is to use the recommended public exponent 65537.

#include <stddef.h>
#include <openssl/rsa.h>
#include <openssl/evp.h>

#define fatal_error() exit(-1)

int ret;
int func(EVP_PKEY *pkey){
  BIGNUM* pubexp;
  EVP_PKEY_CTX* ctx;

  pubexp = BN_new();
  if (pubexp == NULL) fatal_error();
  ret = BN_set_word(pubexp, 65537);
  if (ret <= 0) fatal_error();

  ctx = EVP_PKEY_CTX_new_id(EVP_PKEY_RSA, NULL);
  if (ctx == NULL) fatal_error();

  ret = EVP_PKEY_keygen_init(ctx);
  if (ret <= 0) fatal_error();
  ret = EVP_PKEY_CTX_set_rsa_keygen_bits(ctx, 2048);
  if (ret <= 0) fatal_error();
  ret = EVP_PKEY_CTX_set_rsa_keygen_pubexp(ctx, pubexp);
  if (ret <= 0) fatal_error();
  return EVP_PKEY_keygen(ctx, &pkey);
}

Result Information

Group: Cryptography
Language: C | C++
Default: Off
Command-Line Syntax: CRYPTO_RSA_LOW_EXPONENT
Impact: Medium

Version History

Introduced in R2018a

See Also

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