Abstract. The Cut-and-choose paradigm gives by far the most popular and efficient secure two-party computation protocols in the standard malicious model, able to offer s bits of security with only s copies of garbled circuits in the one-time execution scenario [33]. Nielsen, Orlandi et al. [48,13] have even proposed the seminal idea of LEGO-style cut-and-choose to further reduce the number of circuit copies to less than s while still keep constant round complexity. However, a substantial gap still exists between the theoretical idea of LEGO cut-and-choose and a practical implementation, e.g., [48] is not compatible with free-XOR and uses expensive asymmetric key operations for soldering, while [13] leaves the important building-block of soldering unspecified. In this work, we introduce XOR-Homomorphic Interactive Hash and propose an efficient implemen-tation of this primitive by combining Reed-Solomon encoding and k-out-of-n oblivious transfers. We show how to apply this primitive to solve the performance-critical wire-soldering problem and propose a new LEGO-style cut-and-choose protocol. Comparing to previous LEGO-style protocols, ours only requires a single (as opposed to “a majority of”) correctly garbled gate in each bucket to guarantee security against malicious adversaries. Plus, through integrating Half-Gates garbling, we double the chance a “bad ” gate being detected in the check stage (compared to MiniLEGO [13]). Our constructionAbstract. The Cut-and-choose paradigm gives by far the most popular and efficient secure two-party computation protocols in the standard malicious model, able to offer s bits of security with only s copies of garbled circuits in the one-time execution scenario [33]. Nielsen, Orlandi et al. [48,13] have even proposed the seminal idea of LEGO-style cut-and-choose to further reduce the number of circuit copies to less than s while still keep constant round complexity. However, a substantial gap still exists between the theoretical idea of LEGO cut-and-choose and a practical implementation, e.g., [48] is not compatible with free-XOR and uses expensive asymmetric key operations for soldering, while [13] leaves the important building-block of soldering unspecified. In this work, we introduce XOR-Homomorphic Interactive Hash and propose an efficient implemen-tation of this primitive by combining Reed-Solomon encoding and k-out-of-n oblivious transfers. We show how to apply this primitive to solve the performance-critical wire-soldering problem and propose a new LEGO-style cut-and-choose protocol. Comparing to previous LEGO-style protocols, ours only requires a single (as opposed to “a majority of”) correctly garbled gate in each bucket to guarantee security against malicious adversaries. Plus, through integrating Half-Gates garbling, we double the chance a “bad ” gate being detected in the check stage (compared to MiniLEGO [13]). Our construction

Jan 1, 20152 citations

Quantum collision finding for homomorphic hash functions

Juan Carlos García-Escartín, Vicent Gimeno, Julio José Moyano‐Fernández

Hash functions are a basic cryptographic primitive. Certain hash functions try to prove security against collision and preimage attacks by reductions to known hard problems. These hash functions usually have some additional properties that allow for that reduction. Hash functions which are additive or multiplicative are vulnerable to a quantum attack using the hidden subgroup problem algorithm for quantum computers. Using a quantum oracle to the hash, we can reconstruct the kernel of the hash function, which is enough to find collisions and second preimages. When the hash functions are additive with respect to the group operation in an Abelian group, there is always an efficient implementation of this attack. We present concrete attack examples to provable hash functions, including a preimage attack to $\oplus$ -linear hash functions and for certain multiplicative homomorphic hash schemes.Hash functions are a basic cryptographic primitive. Certain hash functions try to prove security against collision and preimage attacks by reductions to known hard problems. These hash functions usually have some additional properties that allow for that reduction. Hash functions which are additive or multiplicative are vulnerable to a quantum attack using the hidden subgroup problem algorithm for quantum computers. Using a quantum oracle to the hash, we can reconstruct the kernel of the hash function, which is enough to find collisions and second preimages. When the hash functions are additive with respect to the group operation in an Abelian group, there is always an efficient implementation of this attack. We present concrete attack examples to provable hash functions, including a preimage attack to $\oplus$-linear hash functions and for certain multiplicative homomorphic hash schemes.

arXiv:2108.00100Jul 30, 20211 citation

TinyLEGO: An Interactive Garbling Scheme for Maliciously Secure Two-party Computation.

Tore Kasper Frederiksen, Thomas Pelle Jakobsen, Jesper Buus Nielsen +1 more

This paper reports on a number of conceptual and technical contributions to the currently very lively field of two-party computation (2PC) based on garbled circuits. Our main contributions are as follows: 1. We propose the notion of an interactive garbling scheme, where the garbled circuit is generated through an interactive protocol between the garbler and the evaluator. The garbled circuit is correct and privacy preserving even if one of the two parties was acting maliciously during garbling. The security notion is game based. 2. We show that an interactive garbling scheme combined with a Universally Composable (UC) secure oblivious transfer protocol can be used in a black-box manner to implement two-party computation (2PC) UC securely against any probabilistic polynomial time static and malicious adversary. The protocol abstracts many recent protocols for implementing 2PC from garbled circuits and will allow future designers of interactive garbling schemes to prove security with the simple game based definitions, as opposed to directly proving UC security for each new scheme. 3. We propose an instantiation of interactive garbling by designing a new protocol in the LEGO family of protocols for efficient garbling against a malicious adversary. The new protocol is based on several new technical contributions and optimizations, for example making it possible to get distinct output to both parties with minimal overhead. The scheme makes black-box usage of a XOR-homomorphic commitment scheme, an authentic, private and oblivious garbling scheme and a 2-correlation-robust and collision-resistant hash function. When comparing our resulting 2PC protocol to previous works in the same setting we see a noticeable reduction in the communication that directly depends on the size of the circuit (e.g. 33% for circuits larger than 501,271 AND gates).This paper reports on a number of conceptual and technical contributions to the currently very lively field of two-party computation (2PC) based on garbled circuits. Our main contributions are as follows: 1. We propose the notion of an interactive garbling scheme, where the garbled circuit is generated through an interactive protocol between the garbler and the evaluator. The garbled circuit is correct and privacy preserving even if one of the two parties was acting maliciously during garbling. The security notion is game based. 2. We show that an interactive garbling scheme combined with a Universally Composable (UC) secure oblivious transfer protocol can be used in a black-box manner to implement two-party computation (2PC) UC securely against any probabilistic polynomial time static and malicious adversary. The protocol abstracts many recent protocols for implementing 2PC from garbled circuits and will allow future designers of interactive garbling schemes to prove security with the simple game based definitions, as opposed to directly proving UC security for each new scheme. 3. We propose an instantiation of interactive garbling by designing a new protocol in the LEGO family of protocols for efficient garbling against a malicious adversary. The new protocol is based on several new technical contributions and optimizations, for example making it possible to get distinct output to both parties with minimal overhead. The scheme makes black-box usage of a XOR-homomorphic commitment scheme, an authentic, private and oblivious garbling scheme and a 2-correlation-robust and collision-resistant hash function. When comparing our resulting 2PC protocol to previous works in the same setting we see a noticeable reduction in the communication that directly depends on the size of the circuit (e.g. 33% for circuits larger than 501,271 AND gates).

Jan 1, 201522 citations

\oplus

-linear hash functions and for certain multiplicative homomorphic hash schemes.