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CRYPTO CORNER
Editors: Peter Gutmann, [email protected] | David Naccache, [email protected] | Charles C. Palmer, [email protected]
Automated Proof and
Flaw-Finding Tools in
Cryptography
Graham Steel | Cryptosense
O
ne of the few things cryptographers can agree on is
that cryptography is a complex subject—so complex that even after
expert peer review, flaws are regularly found in security proofs, APIs,
protocols, and protocol implementations. Computer scientists have
long hoped that computers could
do the work of checking hardware
and software for flaws, but this
idea—called formal analysis—has
only recently been successfully
implemented in cryptography.
Unlike conventional software
verification, cryptographic analysis requires verifiers to account
for all possible actions of a malicious intruder trying to break into
the system. To facilitate this task,
researchers have turned to algebraic modeling as a way to produce
abstract models of crypto protocols.
Dolev and Yao’s
Verification Model
In 1983, Daniel Dolev and Andrew
C. Yao proposed modeling cryptographic protocols and a hypothetical attacker in an abstract way to
allow verification of the protocols’
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March/April 2015
security.1 By modeling bitstrings as
terms in abstract algebra, cryptographic algorithms as functions of
those terms, and an intruder as a set
of deduction rules on the abstract
algebra, Dolev and Yao (DY) were
able to verify simple protocols in
their model.
Formal tools such as model
checkers and theorem provers that
matured through the 1990s all used
the DY protocol verification model.
By the early 2000s, several purposebuilt tools were capable of verifying
abstract DY models of large protocols for unbounded numbers of
protocol sessions. However, the DY
model is usually an approximation
rather than an abstraction of the protocol implementation. This means
that attacks found in a DY model
don’t always correspond to real
attacks on an implemented protocol and—more worryingly—that an
absence of attacks in the DY model
doesn’t generally imply absence of
attacks on the real protocols.
In the mid- to late 2000s, several groups worked to close the
gap between DY models and real
protocols. They were particularly
Copublished by the IEEE Computer and Reliability Societies interested in examining when DY
model proofs might imply security proofs in the more detailed
“standard model” of cryptography
wherein intruders are modeled as
arbitrary probabilistic polynomialtime Turing machines and bitstrings
are modeled as real bitstrings.
An alternative approach is to
use computers to assist with direct
proofs in the standard model. Typically, these proofs show that any
attack on the protocol can be efficiently translated into an attack on
a mathematical problem believed
to be “hard.” This means that if an
attack is found on the protocol, it
would be possible to use current
computing power to solve a problem considered “impossible.” Therefore, logically, there can’t be any
attacks on the protocol.
Formal Proofs in the
Standard Model
Proofs in the standard model can
be strong but are notoriously difficult to get right. One approach is
to formalize the proof using a proof
assistant, a piece of software that
mechanizes logical reasoning with
a very high degree of confidence of
correctness. This high confidence
comes from the fact that the trusted
code base—the part of the software
we have to believe is correct to trust
the proofs—is very small and has
been tested extensively.
Successful approaches using
this method in other fields include
using the Coq proof assistant to
verify proofs of the four-color
theorem (http://research.microso f t .co m / en -u s / u m / p eo pl e /
gonthier/4colproof.pdf)
and,
more recently, using Isabelle and
1540-7993/15/$31.00 © 2015 IEEE
HOL Light proof assistants to refinement type checker and verify algorithms rather than creating their
verify Johannes Kepler’s con- that the implementation instantiates own. These algorithms are accessed
jecture
(http://arxiv.org/ the specification. Their work shows via an API. For this reason, it’s also
abs/1501.02155). The Computer- how cryptographic security guaran- necessary to study cryptographic
Aided Cryptography group at the tees, which are typically seen only security at the API level to see
IMDEA Software Institute and for low-level primitives and proto- whether, for example, a rogue appliINRIA Sophia Antipolis developed cols, can be scaled up to a real imple- cation could extract cryptographic
the EasyCrypt proof assistant and mentation of a complex protocol.
keys from a piece of secure crypto
While completing the specifica- hardware by calling an unexpected
used it to verify security proofs
for several well-known crypto- tion and implementation of their sequence of commands.
graphic primitives (such as OAEP2) software, which requires a deep underExamples of formal analysis
and protocols (such as
being used to search for
NAXOS3). EasyCrypt
attacks on APIs date back
Although proving the security of
is technically impressive
to the early 1990s,6 but
a
protocol
specification
is
useful,
but requires significant
the subject came to promuser expertise and effort.
inence in the early 2000s
security flaws are often introduced
Although
proving
when a series of such
at the implementation level.
the security of a protoattacks was discovered
col specification is useful,
on the hardware security
security flaws are often
modules (HSMs) widely
introduced at the implementation standing of the protocol, the miTLS used in banking and other seculevel. Several research groups have team discovered several exploitable rity-critical applications.7,8 These
tackled this problem over the past flaws in the most widely used imple- attacks were discovered by manual
10 years. One idea is to take a for- mentations (www.secure-resumption analysis or ad hoc tools, so several
mally verified protocol specification .com; www.smacktls.com).
research groups wanted to see if
Other automated analysis the general API security problem
and compile it into an implementation that’s guaranteed to be secure.4 approaches focus on finding vul- could be tackled using formal tools
Another approach is to prove an nerabilities in real implementations similar to those used for DY-style
implementation’s security in a high- without looking at the source code. protocols.
level language that’s amenable to Erik Poll’s group at the Institute for
In 2010, Matteo Bortolozzo
formal verification, enabling the Computing and Information Sci- and his colleagues demonstrated
specification of rich properties that ences at Radboud University has Tookan—a tool capable of learning
translate to cryptographic security recently shown how to determine an implementation model of RSA
a protocol’s state machine from its PKCS#11, the most widely used
guarantees.
An example of this approach is black-box implementation using standard for cryptographic hardthe miTLS (www.mitls.org) soft- the L* algorithm. Once a model ware—by sending a call sequence
ware for the widely used Web pro- has been created, it can be explored and observing the error responses.9
tocol SSL/TLS. Developed by with a model checker, allowing the After learning a model, Tookan
Karthikeyan Bhargavan’s team at discovery of paths leading to bugs.
queries a model checker to search
Comparing several implementa- for sequences of calls that could
INRIA in the functional programming language F#, this software tions of the same protocol has also reveal the value of a sensitive crypincludes a full implementation of proved fruitful in finding flaws. Poll’s tographic key. If such a sequence
the standard protocol including team applied this approach to chip is found, Tookan converts the
multiple cipher suites, resumption, and PIN cards and, more recently, sequence of steps in the model back
and renegotiation of sessions. The to implementations of TLS. In into a sequence of real PKCS#11
use of the memory-safe F# language doing so, they uncovered several API calls and executes the attack
guarantees an absence of the kinds anomalies and security bugs.5
on the hardware being tested. Using
of buffer-overflow bugs that led to
this methodology, Tookan was
the widely publicized Heartbleed API-Level Attacks
able to find key-recovery attacks
vulnerability discovered in 2014 When developing new enterprise on several commercially available
(http://heartbleed.com).
applications that will use cryp- PKCS#11 smart cards and HSMs.
Bhargavan’s team then used F7 tography, developers typically
Following industrial interest, a
programming language to spec- use existing software or hardware spin-off company of INRIA called
ify the security of TLS and F7’s implementations of cryptographic Cryptosense now commercializes
www.computer.org/security
3
CRYPTO CORNER
the tool under the name Cryptosense Analyzer. Many large banks
and security agencies use it to audit
cryptographic hardware and ensure
that the crypto infrastructure is
configured securely.
Side-Channel Attacks
Side-channel attacks are significant
threats to real cryptography implementations. These attacks rely on
the information leakage by power
consumption, execution timing,
electromagnetic or audio emissions,
or the error messages given by a
cryptographic application. New
side channels are continually being
discovered, and each typically has
its own specific set of countermeasures. However, the idea of automatically verifying the effectiveness
of a given side channel’s countermeasures has only recently begun to
receive attention.
One defense against attacks that
rely on variations in execution time
is to implement cryptography in
such a way that the execution time
is constant regardless of the data
or the value of the cryptographic
key. Tools that can verify whether
a piece of code will execute in constant time are beginning to emerge
(https://github.com/agl/ctgrind);
however, this analysis isn’t easy.
Code that seems to be constant
at the source code level might not
always produce constant-time
machine code. Recent work has
looked directly at machine code.10
Many open challenges remain in
verifying the absence of side-channel attacks.
C
urrent trends such as cloud
computing,
smartphones,
and the Internet of Things are creating a growing need for security
that will be provided by cryptography. As a consequence, developers are now required to implement
cryptography without necessarily
developing the expertise needed to
4
IEEE Security & Privacy
do it securely. It’s safe to say we’ll see
more automated analysis technologies for all aspects of cryptography
in the years to come.
References
1. D. Dolev and A. Yao, “On the Security of Public Key Protocols,” IEEE
Trans. Information Theory, vol. 29,
no. 2, 1983, pp. 198–208.
2. M. Bellare and P. Rogaway, “Optimal Asymmetric Encryption—
How to Encrypt with RSA,”
Advances in Cryptology—Eurocrypt
94 Proc., LNCS 950, 1995; https://
cseweb.ucsd.edu/~mihir/papers
/oae.pdf.
3. B. LaMacchia, K. Lauter, and A.
Mityagin, “Stronger Security of
Authenticated Key Exchange,”
Provable Security, LNCS 4784,
2007, pp. 1–16.
4. D. Cadé and B. Blanchet, “Proved
Generation of Implementations
from Computationally Secure
Protocol Specifications,” D. Basin
and J.C. Mitchell, eds., Principles
of Security and Trust, LNCS 7796,
Springer, 2013, pp. 63–82.
5. F. Aarts, E. Poll, and J. de Ruiter,
“Formal Models of Bank Cards for
Free,” Proc. 6th Int’l Conf. Software
Testing, Verification and Validation
Workshops (ICSTW 13), 2013, pp.
461–468.
6. D. Longley and S. Rigby, “An Automatic Search for Security Flaws in
Key Management Schemes,” Computers and Security, vol. 11, no. 1,
1992, pp. 75–89.
7. M. Bond and R. Anderson, “APILevel Attacks on Embedded Systems,” Computer, vol. 34, no. 10,
2001, pp. 67–75.
8. J. Clulow, “The Design and Analysis of Cryptographic APIs for
Security Devices,” master’s thesis,
Dept. Mathematics, Univ. of Natal,
2003; www.cl.cam.ac.uk/~mkb23
/research/Clulow-Dissertation.pdf.
9. M. Bortolozzo et al., “Attacking and
Fixing PKCS#11 Security Tokens,”
Proc. 17th ACM Conf. Computer
and Communications Security (CCS
10), 2010, pp. 260–269.
10. G. Barthe et al., “System-Level
Non-interference for ConstantTime Cryptography,” Proc. 2014
ACM SIGSAC Conf. Computer and
Communications Security (CCS 14),
2014, pp. 1267–1279.
Graham Steel is CEO and cofounder
of Cryptosense, a spin-off of
INRIA that produces software for
security analysis of cryptographic
systems. Contact him at graham.
[email protected].
Selected CS articles and columns
are also available for free at
http://ComputingNow.computer.org.
March/April 2015