# Side Channels¶

Many cryptographic systems can be easily broken by side channels. This document notes side channel protections which are currently implemented, as well as areas of the code which are known to be vulnerable to side channels. The latter are obviously all open for future improvement.

The following text assumes the reader is already familiar with cryptographic implementations, side channel attacks, and common countermeasures.

## Modular Exponentiation¶

Modular exponentiation uses a fixed window algorithm with Montgomery representation. A side channel silent table lookup is used to access the precomputed powers. The caller provides the maximum possible bit length of the exponent, and the exponent is zero-padded as required. For example, in a DSA signature with 256-bit q, the caller will specify a maximum length of exponent of 256 bits, even if the k that was generated was 250 bits. This avoids leaking the length of the exponent through the number of loop iterations. See monty_exp.cpp and monty.cpp

Karatsuba multiplication algorithm avoids any conditional branches; in cases where different operations must be performed it instead uses masked operations. See mp_karat.cpp for details.

The Montgomery reduction is written to run in constant time. The final reduction is handled with a masked subtraction. See mp_monty.cpp.

## Barrett Reduction¶

The Barrett reduction code is written to avoid input dependent branches. The Barrett algorithm only works for inputs up to a certain size, and larger values fall back on a different (slower) division algorithm. This secondary algorithm is also const time, but the branch allows detecting when a value larger than 2^{2k} was reduced, where k is the word length of the modulus. This leaks only the size of the two values, and not anything else about their value.

## RSA¶

Blinding is always used to protect private key operations (there is no way to turn it off). Both base blinding and exponent blinding are used.

For base blinding, as an optimization, instead of choosing a new random mask and inverse with each decryption, both the mask and its inverse are simply squared to choose the next blinding factor. This is much faster than computing a fresh value each time, and the additional relation is thought to provide only minimal useful information for an attacker. Every BOTAN_BLINDING_REINIT_INTERVAL (default 64) operations, a new starting point is chosen.

Exponent blinding uses new values for each signature, with 64 bit masks.

RSA signing uses the CRT optimization, which is much faster but vulnerable to trivial fault attacks [RsaFault] which can result in the key being entirely compromised. To protect against this (or any other computational error which would have the same effect as a fault attack in this case), after every private key operation the result is checked for consistency with the public key. This introduces only slight additional overhead and blocks most fault attacks; it is possible to use a second fault attack to bypass this verification, but such a double fault attack requires significantly more control on the part of an attacker than a BellCore style attack, which is possible if any error at all occurs during either modular exponentiation involved in the RSA signature operation.

RSA key generation is also prone to side channel vulnerabilities due to the need
to calculate the CRT parameters. The GCD computation, LCM computations, modulo,
and inversion of `q`

modulo `p`

are all done via constant time algorithms.
An additional inversion, of `e`

modulo `phi(n)`

, is also required. This one
is somewhat more complicated because `phi(n)`

is even and the primary constant
time algorithm for inversions only works for odd moduli. This is worked around
by a technique based on the CRT - `phi(n)`

is factored to `2**e * z`

for
some `e`

> 1 and some odd `z`

. Then `e`

is inverted modulo `2**e`

and
also modulo `z`

. The inversion modulo `2**e`

is done via a specialized
constant-time algoirthm which only works for powers of 2. Then the two
inversions are combined using the CRT. This process does leak the value of
`e`

; to avoid problems `p`

and `q`

are chosen so that `e`

is always 1.

See blinding.cpp and rsa.cpp.

## Decryption of PKCS #1 v1.5 Ciphertexts¶

This padding scheme is used with RSA, and is very vulnerable to errors. In a scenario where an attacker can repeatedly present RSA ciphertexts, and a legitimate key holder will attempt to decrypt each ciphertext and simply indicates to the attacker if the PKCS padding was valid or not (without revealing any additional information), the attacker can use this behavior as an oracle to perform iterative decryption of arbitrary RSA ciphertexts encrypted under that key. This is the famous million message attack [MillionMsg]. A side channel such as a difference in time taken to handle valid and invalid RSA ciphertexts is enough to mount the attack [MillionMsgTiming].

As a first step, the PKCS v1.5 decoding operation runs without any conditional jumps or indexes, with the only variance in runtime being based on the length of the public modulus, which is public information.

Preventing the attack in full requires some application level changes. In protocols which know the expected length of the encrypted key, PK_Decryptor provides the function decrypt_or_random which first generates a random fake key, then decrypts the presented ciphertext, then in constant time either copies out the random key or the decrypted plaintext depending on if the ciphertext was valid or not (valid padding and expected plaintext length). Then in the case of an attack, the protocol will carry on with a randomly chosen key, which will presumably cause total failure in a way that does not allow an attacker to distinguish (via any timing or other side channel, nor any error messages specific to the one situation vs the other) if the RSA padding was valid or invalid.

One very important user of PKCS #1 v1.5 encryption is the TLS protocol. In TLS, some extra versioning information is embedded in the plaintext message, along with the key. It turns out that this version information must be treated in an identical (constant-time) way with the PKCS padding, or again the system is broken. [VersionOracle]. This is supported by a special version of PK_Decryptor::decrypt_or_random that additionally allows verifying one or more content bytes, in addition to the PKCS padding.

See eme_pkcs.cpp and pubkey.cpp.

## Verification of PKCS #1 v1.5 Signatures¶

One way of verifying PKCS #1 v1.5 signature padding is to decode it with an ASN.1 BER parser. However such a design commonly leads to accepting signatures besides the (single) valid RSA PKCS #1 v1.5 signature for any given message, because often the BER parser accepts variations of the encoding which are actually invalid. It also needlessly exposes the BER parser to untrusted inputs.

It is safer and simpler to instead re-encode the hash value we are expecting using the PKCS #1 v1.5 encoding rules, and const time compare our expected encoding with the output of the RSA operation. So that is what Botan does.

See emsa_pkcs.cpp.

## OAEP¶

RSA OAEP is (PKCS#1 v2) is the recommended version of RSA encoding standard, because it is not directly vulnerable to Bleichenbacher attack. However, if implemented incorrectly, a side channel can be presented to an attacker and create an oracle for decrypting RSA ciphertexts [OaepTiming].

This attack is avoided in Botan by making the OAEP decoding operation run without any conditional jumps or indexes, with the only variance in runtime coming from the length of the RSA key (which is public information).

See eme_oaep.cpp.

## ECC point decoding¶

The API function OS2ECP, which is used to convert byte strings to ECC points, verifies that all points satisfy the ECC curve equation. Points that do not satisfy the equation are invalid, and can sometimes be used to break protocols ([InvalidCurve] [InvalidCurveTLS]). See ec_point.cpp.

## ECC scalar multiply¶

There are several different implementations of ECC scalar multiplications which
depend on the API invoked. This include `EC_Point::operator*`

,
`EC_Group::blinded_base_point_multiply`

and
`EC_Group::blinded_var_point_multiply`

.

The `EC_Point::operator*`

implementation uses the Montgomery ladder, which is
fairly resistant to side channels. However it leaks the size of the scalar,
because the loop iterations are bounded by the scalar size. It should not be
used in cases when the scalar is a secret.

Both `blinded_base_point_multiply`

and `blinded_var_point_multiply`

apply
side channel countermeasures. The scalar is masked by a multiple of the group
order (this is commonly called Coron’s first countermeasure [CoronDpa]),
currently the mask is scaled to be half the bit length of the order of the group.

Botan stores all ECC points in Jacobian representation. This form allows faster computation by representing points (x,y) as (X,Y,Z) where x=X/Z^2 and y=Y/Z^3. As the representation is redundant, for any randomly chosen non-zero r, (X*r^2,Y*r^3,Z*r) is an equivalent point. Changing the point values prevents an attacker from mounting attacks based on the input point remaining unchanged over multiple executions. This is commonly called Coron’s third countermeasure, see again [CoronDpa].

The base point multiplication algorithm is a comb-like technique which
precomputes `P^i,(2*P)^i,(3*P)^i`

for all `i`

in the range of valid scalars.
This means the scalar multiplication involves only point additions and no
doublings, which may help against attacks which rely on distinguishing between
point doublings and point additions. The elements of the table are accessed by
masked lookups, so as not to leak information about bits of the scalar via a
cache side channel. However, whenever 3 sequential bits of the (masked) scalar
are all 0, no operation is performed in that iteration of the loop. This exposes
the scalar multiply to a cache-based side channel attack; scalar blinding is
necessary to prevent this attack from leaking information about the scalar.

The variable point multiplication algorithm uses a fixed-window algorithm. Since this is normally invoked using untrusted points (eg during ECDH key exchange) it randomizes all inputs to prevent attacks which are based on chosen input points. The table of precomputed multiples is accessed using a masked lookup which should not leak information about the secret scalar to an attacker who can mount a cache-based side channel attack.

See ec_point.cpp and point_mul.cpp in src/lib/pubkey/ec_group

## ECDH¶

ECDH verifies (through its use of OS2ECP) that all input points received from the other party satisfy the curve equation. This prevents twist attacks. The same check is performed on the output point, which helps prevent fault attacks.

## ECDSA¶

Inversion of the ECDSA nonce k must be done in constant time, as any leak of even a single bit of the nonce can be sufficient to allow recovering the private key. In Botan all inverses modulo an odd number are performed using a constant time algorithm due to Niels Möller.

## x25519¶

The x25519 code is independent of the main Weierstrass form ECC code, instead based on curve25519-donna-c64.c by Adam Langley. The code seems immune to cache based side channels. It does make use of integer multiplications; on some old CPUs these multiplications take variable time and might allow a side channel attack. This is not considered a problem on modern processors.

## TLS CBC ciphersuites¶

The original TLS v1.0 CBC Mac-then-Encrypt mode is vulnerable to an oracle attack. If an attacker can distinguish padding errors through different error messages [TlsCbcOracle] or via a side channel attack like [Lucky13], they can abuse the server as a decryption oracle.

The side channel protection for Lucky13 follows the approach proposed in the Lucky13 paper. It is not perfectly constant time, but does hide the padding oracle in practice. Tools to test TLS CBC decoding are included in the timing tests. See https://github.com/randombit/botan/pull/675 for more information.

The Encrypt-then-MAC extension, which completely avoids the side channel, is implemented and used by default for CBC ciphersuites.

## CBC mode padding¶

In theory, any good protocol protects CBC ciphertexts with a MAC. But in practice, some protocols are not good and cannot be fixed immediately. To avoid making a bad problem worse, the code to handle decoding CBC ciphertext padding bytes runs in constant time, depending only on the block size of the cipher.

## base64 decoding¶

Base64 (and related encodings base32, base58 and hex) are sometimes used to encode or decode secret data. To avoid possible side channels which might leak key material during the encoding or decoding process, these functions avoid any input-dependent table lookups.

## AES¶

Some x86, ARMv8 and POWER processors support AES instructions which are fast and are thought to be side channel silent. These instructions are used when available.

On CPUs which do not have hardware AES instructions but do support SIMD vectors with a byte shuffle (including x86’s SSSE3, ARM’s NEON and PowerPC AltiVec), a version of AES is implemented which is side channel silent. This implementation is based on code by Mike Hamburg [VectorAes], see aes_vperm.cpp.

On all other processors, a constant time bitsliced implementation is used. This is typically slower than the vector permute implementation, and additionally for best performance multiple blocks must be processed in parellel. So modes such as CTR, GCM or XTS are relatively fast, but others such as CBC encryption suffer.

## GCM¶

On platforms that support a carryless multiply instruction (ARMv8 and recent x86), GCM is fast and constant time.

On all other platforms, GCM uses an algorithm based on precomputing all powers of H from 1 to 128. Then for every bit of the input a mask is formed which allows conditionally adding that power without leaking information via a cache side channel. There is also an SSSE3 variant of this algorithm which is somewhat faster on processors which have SSSE3 but no AES-NI instructions.

## OCB¶

It is straightforward to implement OCB mode in a efficient way that does not depend on any secret branches or lookups. See ocb.cpp for the implementation.

## Poly1305¶

The Poly1305 implementation does not have any secret lookups or conditionals. The code is based on the public domain version by Andrew Moon.

## DES/3DES¶

The DES implementation relies on table lookups but they are limited to tables which are exactly 64 bytes in size. On systems with 64 byte (or larger) cache lines, these should not leak information. It may still be vulnerable to side channels on processors which leak cache line access offsets via cache bank conflicts; vulnerable hardware includes Sandy Bridge processors, but not later Intel or AMD CPUs.

## Twofish¶

This algorithm uses table lookups with secret sboxes. No cache-based side channel attack on Twofish has ever been published, but it is possible nobody sufficiently skilled has ever tried.

## ChaCha20, Serpent, Threefish, …¶

Some algorithms including ChaCha, Salsa, Serpent and Threefish are ‘naturally’ silent to cache and timing side channels on all recent processors.

## IDEA¶

IDEA encryption, decryption, and key schedule are implemented to take constant time regardless of their inputs.

## Hash Functions¶

Most hash functions included in Botan such as MD5, SHA-1, SHA-2, SHA-3, Skein, and BLAKE2 do not require any input-dependent memory lookups, and so seem to not be affected by common CPU side channels. However the implementations of Whirlpool and Streebog use table lookups and probably can be attacked by side channels.

## Memory comparisons¶

The function same_mem in header mem_ops.h provides a constant-time comparison function. It is used when comparing MACs or other secret values. It is also exposed for application use.

## Memory zeroizing¶

There is no way in portable C/C++ to zero out an array before freeing it, in such a way that it is guaranteed that the compiler will not elide the ‘additional’ (seemingly unnecessary) writes to zero out the memory.

The function secure_scrub_memory (in mem_ops.cpp) uses some system specific
trick to zero out an array. If possible an OS provided routine (such as
`RtlSecureZeroMemory`

or `explicit_bzero`

) is used.

On other platforms, by default the trick of referencing memset through a volatile function pointer is used. This approach is not guaranteed to work on all platforms, and currently there is no systematic check of the resulting binary function that it is compiled as expected. But, it is the best approach currently known and has been verified to work as expected on common platforms.

If BOTAN_USE_VOLATILE_MEMSET_FOR_ZERO is set to 0 in build.h (not the default) a byte at a time loop through a volatile pointer is used to overwrite the array.

## Memory allocation¶

Botan’s secure_vector type is a std::vector with a custom allocator. The allocator calls secure_scrub_memory before freeing memory.

Some operating systems support an API call to lock a range of pages
into memory, such that they will never be swapped out (`mlock`

on POSIX,
`VirtualLock`

on Windows). On many POSIX systems `mlock`

is only usable by
root, but on Linux, FreeBSD and possibly other systems a small amount
of memory can be locked by processes without extra credentials.

If available, Botan uses such a region for storing key material. A page-aligned block of memory is allocated and locked, then the memory is scrubbed before freeing. This memory pool is used by secure_vector when available. It can be disabled at runtime setting the environment variable BOTAN_MLOCK_POOL_SIZE to 0.

## Automated Analysis¶

Currently the main tool used by the Botan developers for testing for side channels at runtime is valgrind; valgrind’s runtime API is used to taint memory values, and any jumps or indexes using data derived from these values will cause a valgrind warning. This technique was first used by Adam Langley in ctgrind. See header ct_utils.h.

To check, install valgrind, configure the build with –with-valgrind, and run the tests.

There is also a test utility built into the command line util, timing_test, which runs an operation on several different inputs many times in order to detect simple timing differences. The output can be processed using the Mona timing report library (https://github.com/seecurity/mona-timing-report). To run a timing report (here for example pow_mod):

```
$ ./botan timing_test pow_mod > pow_mod.raw
```

This must be run from a checkout of the source, or otherwise `--test-data-dir=`

must be used to point to the expected input files.

Build and run the Mona report as:

```
$ git clone https://github.com/seecurity/mona-timing-report.git
$ cd mona-timing-report
$ ant
$ java -jar ReportingTool.jar --lowerBound=0.4 --upperBound=0.5 --inputFile=pow_mod.raw --name=PowMod
```

This will produce plots and an HTML file in subdirectory starting with
`reports_`

followed by a representation of the current date and time.

## References¶

[Aes256Sc] Neve, Tiri “On the complexity of side-channel attacks on AES-256” (https://eprint.iacr.org/2007/318.pdf)

[AesCacheColl] Bonneau, Mironov “Cache-Collision Timing Attacks Against AES” (http://www.jbonneau.com/doc/BM06-CHES-aes_cache_timing.pdf)

[CoronDpa] Coron, “Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems” (https://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.1.5695)

[InvalidCurve] Biehl, Meyer, Müller: Differential fault attacks on elliptic curve cryptosystems (https://www.iacr.org/archive/crypto2000/18800131/18800131.pdf)

[InvalidCurveTLS] Jager, Schwenk, Somorovsky: Practical Invalid Curve Attacks on TLS-ECDH (https://www.nds.rub.de/research/publications/ESORICS15/)

[SafeCurves] Bernstein, Lange: SafeCurves: choosing safe curves for elliptic-curve cryptography. (https://safecurves.cr.yp.to)

[Lucky13] AlFardan, Paterson “Lucky Thirteen: Breaking the TLS and DTLS Record Protocols” (http://www.isg.rhul.ac.uk/tls/TLStiming.pdf)

[MillionMsg] Bleichenbacher “Chosen Ciphertext Attacks Against Protocols Based on the RSA Encryption Standard PKCS1” (https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.19.8543)

[MillionMsgTiming] Meyer, Somorovsky, Weiss, Schwenk, Schinzel, Tews: Revisiting SSL/TLS Implementations: New Bleichenbacher Side Channels and Attacks (https://www.nds.rub.de/research/publications/mswsst2014-bleichenbacher-usenix14/)

[OaepTiming] Manger, “A Chosen Ciphertext Attack on RSA Optimal Asymmetric Encryption Padding (OAEP) as Standardized in PKCS #1 v2.0” (http://archiv.infsec.ethz.ch/education/fs08/secsem/Manger01.pdf)

[RsaFault] Boneh, Demillo, Lipton “On the importance of checking cryptographic protocols for faults” (https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.9764)

[RandomMonty] Le, Tan, Tunstall “Randomizing the Montgomery Powering Ladder” (https://eprint.iacr.org/2015/657)

[VectorAes] Hamburg, “Accelerating AES with Vector Permute Instructions” https://shiftleft.org/papers/vector_aes/vector_aes.pdf

[VersionOracle] Klíma, Pokorný, Rosa “Attacking RSA-based Sessions in SSL/TLS” (https://eprint.iacr.org/2003/052)