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Increase rounds of Miller-Rabin testing in DH_check #8593

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commented Mar 27, 2019

DH_check is used to test the validity of Diffie-Hellman parameter sets (p, q, g). Among the tests performed are primality tests on p and q, for this BN_is_prime_ex is called with the rounds of Miller-Rabin set as default. This will therefore use the average case error estimates derived from the function BN_prime_checks_for_size based on the bit size of the number tested.

However, these bounds are only accurate on testing random input. Within this testing scenario, where we are checking the validity of a DH parameter set, we can not assert that these parameters are randomly generated. Thus we must treat them as if they are adversarial in nature and increase the rounds of Miller-Rabin performed.

Generally, each round of Miller-Rabin can declare a composite number prime with probability at most (1/4), thus 64 rounds is sufficient in thwarting known generation techniques of malicious parameter sets that have small probabilities of being accepted by DH_check (even in safe prime settings - see https://eprint.iacr.org/2019/032 for full analysis). The choice of 64 rounds is also consistent with SRP_NUMBER_ITERATIONS_FOR_PRIME 64 as used in srp_Verify_N_and_g in openssl/apps/s_client.c.

(Discussed with Kurt Roeckx via email)

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  • documentation is added or updated
  • tests are added or updated
Increase rounds of Miller-Rabin testing DH_check
DH_check is used to test the validity of Diffie-Hellman parameter sets (p, q, g). Among the tests performed are primality tests on p and q, for this BN_is_prime_ex is called with the rounds of Miller-Rabin set as default. This will therefore use the average case error estimates derived from the function BN_prime_checks_for_size based on the bit size of the number tested.

However, these bounds are only accurate on testing random input. Within this testing scenario, where we are checking the validity of a DH parameter set, we can not assert that these parameters are randomly generated. Thus we must treat them as if they are adversarial in nature and increase the rounds of Miller-Rabin performed.

Generally, each round of Miller-Rabin can declare a composite number prime with probability at most (1/4), thus 64 rounds is sufficient in thwarting known generation techniques (even in safe prime settings - see https://eprint.iacr.org/2019/032 for full analysis). The choice of 64 rounds is also consistent with SRP_NUMBER_ITERATIONS_FOR_PRIME 64 as used in srp_Verify_N_and_g in openssl/apps/s_client.c.
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Some very interesting results in the paper.

The missing CLA will need to be addressed. See the CLA policy page. Alternatively add CLA: trivial to the commit message. For the record, I consider the changes to be trivial. The reasoning behind them is anything but.

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I agree this is trivial

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commented Mar 27, 2019

Thanks! I will sort the CLA immediately, happy to do so!

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commented Mar 27, 2019

Close/reopen to kick CLA bot.

@mattcaswell mattcaswell reopened this Mar 27, 2019

levitte pushed a commit that referenced this pull request Mar 27, 2019
Increase rounds of Miller-Rabin testing DH_check
DH_check is used to test the validity of Diffie-Hellman parameter sets (p, q, g). Among the tests performed are primality tests on p and q, for this BN_is_prime_ex is called with the rounds of Miller-Rabin set as default. This will therefore use the average case error estimates derived from the function BN_prime_checks_for_size based on the bit size of the number tested.

However, these bounds are only accurate on testing random input. Within this testing scenario, where we are checking the validity of a DH parameter set, we can not assert that these parameters are randomly generated. Thus we must treat them as if they are adversarial in nature and increase the rounds of Miller-Rabin performed.

Generally, each round of Miller-Rabin can declare a composite number prime with probability at most (1/4), thus 64 rounds is sufficient in thwarting known generation techniques (even in safe prime settings - see https://eprint.iacr.org/2019/032 for full analysis). The choice of 64 rounds is also consistent with SRP_NUMBER_ITERATIONS_FOR_PRIME 64 as used in srp_Verify_N_and_g in openssl/apps/s_client.c.

Reviewed-by: Paul Dale <paul.dale@oracle.com>
Reviewed-by: Matt Caswell <matt@openssl.org>
(Merged from #8593)

(cherry picked from commit 2500c09)
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commented Mar 27, 2019

Pushed. Thanks.

levitte pushed a commit that referenced this pull request Mar 27, 2019
Increase rounds of Miller-Rabin testing DH_check
DH_check is used to test the validity of Diffie-Hellman parameter sets (p, q, g). Among the tests performed are primality tests on p and q, for this BN_is_prime_ex is called with the rounds of Miller-Rabin set as default. This will therefore use the average case error estimates derived from the function BN_prime_checks_for_size based on the bit size of the number tested.

However, these bounds are only accurate on testing random input. Within this testing scenario, where we are checking the validity of a DH parameter set, we can not assert that these parameters are randomly generated. Thus we must treat them as if they are adversarial in nature and increase the rounds of Miller-Rabin performed.

Generally, each round of Miller-Rabin can declare a composite number prime with probability at most (1/4), thus 64 rounds is sufficient in thwarting known generation techniques (even in safe prime settings - see https://eprint.iacr.org/2019/032 for full analysis). The choice of 64 rounds is also consistent with SRP_NUMBER_ITERATIONS_FOR_PRIME 64 as used in srp_Verify_N_and_g in openssl/apps/s_client.c.

Reviewed-by: Paul Dale <paul.dale@oracle.com>
Reviewed-by: Matt Caswell <matt@openssl.org>
(Merged from #8593)
beldmit added a commit to beldmit/openssl that referenced this pull request May 31, 2019
Increase rounds of Miller-Rabin testing DH_check
DH_check is used to test the validity of Diffie-Hellman parameter sets (p, q, g). Among the tests performed are primality tests on p and q, for this BN_is_prime_ex is called with the rounds of Miller-Rabin set as default. This will therefore use the average case error estimates derived from the function BN_prime_checks_for_size based on the bit size of the number tested.

However, these bounds are only accurate on testing random input. Within this testing scenario, where we are checking the validity of a DH parameter set, we can not assert that these parameters are randomly generated. Thus we must treat them as if they are adversarial in nature and increase the rounds of Miller-Rabin performed.

Generally, each round of Miller-Rabin can declare a composite number prime with probability at most (1/4), thus 64 rounds is sufficient in thwarting known generation techniques (even in safe prime settings - see https://eprint.iacr.org/2019/032 for full analysis). The choice of 64 rounds is also consistent with SRP_NUMBER_ITERATIONS_FOR_PRIME 64 as used in srp_Verify_N_and_g in openssl/apps/s_client.c.

Reviewed-by: Paul Dale <paul.dale@oracle.com>
Reviewed-by: Matt Caswell <matt@openssl.org>
(Merged from openssl#8593)
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