Protecting obfuscation against arithmetic attacks

Obfuscation, the task of compiling circuits or programs to make the internal computation unintelligible while preserving input/output functionality, has become an object of central focus in the cryptographic community. A work of Garg et al. [FOCS 2013] gave the first candidate obfuscator for general polynomial-size circuits, and led to several other works constructing candidate obfuscators. Each of these constructions is built upon another cryptographic primitive called a multilinear map, or alternatively a graded encoding scheme. Several of these candidates have been shown to achieve the strongest notion of security (virtual black-box, or VBB) against purely algebraic attacks in a model that we call the fully-restricted graded encoding model. In this model, each operation performed by an adversary is required to obey the algebraic restrictions of the graded encoding scheme. These restrictions essentially impose strong forms of homogeneity and multilinearity on the allowed polynomials. While important, the scope of the security proofs is limited by the stringency of these restrictions. We propose and analyze another variant of the Garg et al. obfuscator in a setting that imposes fewer restrictions on the adversary, which we call the arithmetic setting. This setting captures a broader class of attacks than considered in previous works. We also explore connections between notions of obfuscation security and longstanding questions in arithmetic circuit complexity. Our results include the following. (1) In the arithmetic setting where the adversary is limited to creating multilinear, but not necessarily homogenous polynomials, we obtain an unconditional proof of VBB security. This requires a substantially different analysis than previous security proofs. (2) In the arithmetic setting where the adversary can create polynomials of arbitrary degree, we show that a proof of VBB security for any currently available candidate obfuscator would imply VP != VNP. To complement this, we show that a weaker notion of security (indistinguishability obfuscation) can be achieved unconditionally in this setting, and that VBB security can be achieved under a complexity-theoretic assumption related to the Exponential Time Hypothesis

Runtime protection via dataflow flattening

Software running on an open architecture, such as the PC, is vulnerable to inspection and modification. Since software may process valuable or sensitive information, many defenses against data analysis and modification have been proposed. This paper complements existing work and focuses on hiding data location throughout program execution. To achieve this, we combine three techniques: (i) periodic reordering of the heap, (ii) migrating local variables from the stack to the heap and (iii) pointer scrambling. By essentialy flattening the dataflow graph of the program, the techniques serve to complicate static dataflow analysis and dynamic data tracking. Our methodology can be viewed as a data-oriented analogue of control-flow flattening techniques. Dataflow flattening is useful in practical scenarios like DRM, information-flow protection, and exploit resistance. Our prototype implementation compiles C programs into a binary for which every access to the heap is redirected through a memory management unit. Stack-based variables may be migrated to the heap, while pointer accesses and arithmetic may be scrambled and redirected. We evaluate our approach experimentally on the SPEC CPU2006 benchmark suit

Chaotic Compilation for Encrypted Computing: Obfuscation but Not in Name

An `obfuscation' for encrypted computing is quantified exactly here, leading to an argument that security against polynomial-time attacks has been achieved for user data via the deliberately `chaotic' compilation required for security properties in that environment. Encrypted computing is the emerging science and technology of processors that take encrypted inputs to encrypted outputs via encrypted intermediate values (at nearly conventional speeds). The aim is to make user data in general-purpose computing secure against the operator and operating system as potential adversaries. A stumbling block has always been that memory addresses are data and good encryption means the encrypted value varies randomly, and that makes hitting any target in memory problematic without address decryption, yet decryption anywhere on the memory path would open up many easily exploitable vulnerabilities. This paper `solves (chaotic) compilation' for processors without address decryption, covering all of ANSI C while satisfying the required security properties and opening up the field for the standard software tool-chain and infrastructure. That produces the argument referred to above, which may also hold without encryption.Comment: 31 pages. Version update adds "Chaotic" in title and throughout paper, and recasts abstract and Intro and other sections of the text for better access by cryptologists. To the same end it introduces the polynomial time defense argument explicitly in the final section, having now set that denouement out in the abstract and intr

Affine Determinant Programs: A Framework for Obfuscation and Witness Encryption

An affine determinant program ADP: {0,1}^n → {0,1} is specified by a tuple (A,B_1,...,B_n) of square matrices over F_q and a function Eval: F_q → {0,1}, and evaluated on x \in {0,1}^n by computing Eval(det(A + sum_{i \in [n]} x_i B_i)). In this work, we suggest ADPs as a new framework for building general-purpose obfuscation and witness encryption. We provide evidence to suggest that constructions following our ADP-based framework may one day yield secure, practically feasible obfuscation. As a proof-of-concept, we give a candidate ADP-based construction of indistinguishability obfuscation (iO) for all circuits along with a simple witness encryption candidate. We provide cryptanalysis demonstrating that our schemes resist several potential attacks, and leave further cryptanalysis to future work. Lastly, we explore practically feasible applications of our witness encryption candidate, such as public-key encryption with near-optimal key generation