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IACR Transactions on Cryptographic Hardware and Embedded Systems

Improving the Performance of the Picnic Signature Scheme

Daniel Kales, Greg Zaverucha

Published Aug 26, 2020• 44 citations
Publisher

Abstract

Picnic is a digital signature algorithm designed to provide security against attacks by quantum computers. The design uses only symmetric-key primitives, and is an efficient instantiation of the MPC-in-the-head paradigm. In this work, we explore the Picnic design in great detail. We investigate and benchmark different parameter choices and show that there exist better parameter choices than those in the current specification. We also present improvements to the MPC protocol that shorten signatures and reduce signing time. The proposed MPC changes tailor the protocol to the circuit of interest in Picnic, but may also be of independent interest. Taken together, these changes give a new instantiation of Picnic that signs messages 7.9 to 13.9 times faster, and verifies signatures 4.5 to 5.5 times faster than the existing “Picnic2” design, while having nearly the same signature sizes.

DOI
10.46586/tches.v2020.i4.154-188

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When powerful quantum computers are built, they will break most of the public key cryptography schemes due to Shor’s quantum algorithm. Therefore, public key cryptography algorithm schemes that is secure against classical and quantum computers are needed. In this thesis, we study Picnic algorithm, a post-quantum digital signature scheme. Picnic digital signature algorithm has the security of symmetric-key primitives that is considered to be secure against quantum attacks. In Picnic algorithm, zero knowledge proof systems and circuits to compute their protocol are used.

•Jan 1, 2019•0 citations

Compact Post-Quantum Signatures from Proofs of Knowledge leveraging Structure for the PKP, SD and RSD Problems

Loïc Bidoux, Philippe Gaborit

The MPC-in-the-head introduced in [IKOS07] has established itself as an important paradigm to design efficient digital signatures. It has been leveraged in the Picnic scheme [CDG+ 20] that reached the third round of the NIST PQC Standardization process. It has also been used in [Beu20] to introduce the Proof of Knowledge (PoK) with Helper paradigm. This construction permits to design shorter signatures but induces a non negligible performance overhead as it uses cut-and-choose. In this paper, we introduce the PoK leveraging structure paradigm along with its associated challenge space amplification technique. Our new approach to design PoK brings some improvements over the PoK with Helper one. Indeed, we show how one can substitute the Helper in these constructions by leveraging the underlying structure of the considered problem. This approach does not suffer from the performance overhead inherent to the PoK with Helper paradigm hence offers different trade-offs between security, signature sizes and performances. We also present four new post-quantum signature schemes. The first one is based on a new PoK with Helper for the Syndrome Decoding problem. It relies on ideas from [BGKM22] and [FJR21] and improve the latter using a new technique that can be seen as performing some cut-and-choose with a meet in the middle approach. The three other signatures are based on our new PoK leveraging structure approach and as such illustrate its versatility. We provide new PoK related to the Permuted Kernel Problem (PKP), Syndrome Decoding (SD) problem and Rank Syndrome Decoding (RSD) problem. In practice, these PoK lead to comparable or shorter signatures than existing ones. Indeed, considering (public key + signature), we get sizes below 9kB for our signature related to the PKP problem, below 15kB for our signature related to the SD problem and below 7kB for our signature related to the RSD problem.

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Since 2016’s NIST call for standardization of post-quantum cryptographic primitives, developing efficient post-quantum secure digital signature schemes has become a highly active area of research. The difficulty in constructing such schemes is evidenced by NIST reopening the call in 2022 for digital signature schemes, because of missing diversity in existing proposals. In this work, we introduce the new postquantum digital signature scheme MiRitH. As direct successor of a scheme recently developed by Adj, Rivera-Zamarripa and Verbel (Africacrypt ’23), it is based on the hardness of the MinRank problem and follows the MPC-in-the-Head paradigm. We revisit the initial proposal, incorporate design-level improvements and provide more efficient parameter sets. We also provide the missing justification for the quantum security of all parameter sets following NIST metrics. In this context we design a novel Grover-amplified quantum search algorithm for solving the MinRank problem that outperforms a naive quantum brute-force search for the solution.MiRitH obtains signatures of size 5.7 kB for NIST category I security and therefore competes for the smallest signatures among any post-quantum signature following the MPCitH paradigm.At the same time MiRitH offers competitive signing and verification timings compared to the state of the art. To substantiate those claims we provide extensive implementations. This includes a reference implementation as well as optimized constant-time implementations for Intel processors (AVX2), and for the ARM (NEON) architecture. The speedup of our optimized AVX2 implementation relies mostly on a redesign of the finite field arithmetic, improving over existing implementations as well as an improved memory management.

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Sphinx-in-the-Head: Group Signatures from Symmetric Primitives

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Group signatures and their variants have been widely used in privacy-sensitive scenarios such as anonymous authentication and attestation. In this paper, we present a new post-quantum group signature scheme from symmetric primitives. Using only symmetric primitives makes the scheme less prone to unknown attacks than basing the design on newly proposed hard problems whose security is less well-understood. However, symmetric primitives do not have rich algebraic properties, and this makes it extremely challenging to design a group signature scheme on top of them. It is even more challenging if we want a group signature scheme suitable for real-world applications, one that can support large groups and require few trust assumptions. Our scheme is based on MPC-in-the-head non-interactive zero-knowledge proofs, and we specifically design a novel hash-based group credential scheme, which is rooted in the SPHINCS+ signature scheme but with various modifications to make it MPC (multi-party computation) friendly. The security of the scheme has been proved under the fully dynamic group signature model. We provide an implementation of the scheme and demonstrate the feasibility of handling a group size as large as 2 60 . This is the first group signature scheme from symmetric primitives that supports such a large group size and meets all the security requirements.

ACM Transactions on Privacy and Security•Dec 27, 2023•12 citations
Picnic is a digital signature algorithm designed to provide security against attacks by quantum computers. The design uses only symmetric-key primitives, and is an efficient instantiation of the MPC-in-the-head paradigm. In this work, we explore the Picnic design in great detail. We investigate and benchmark different parameter choices and show that there exist better parameter choices than those in the current specification. We also present improvements to the MPC protocol that shorten signatures and reduce signing time. The proposed MPC changes tailor the protocol to the circuit of interest in Picnic, but may also be of independent interest. Taken together, these changes give a new instantiation of Picnic that signs messages 7.9 to 13.9 times faster, and verifies signatures 4.5 to 5.5 times faster than the existing “Picnic2” design, while having nearly the same signature sizes.
When powerful quantum computers are built, they will break most of the public key cryptography schemes due to Shor’s quantum algorithm. Therefore, public key cryptography algorithm schemes that is secure against classical and quantum computers are needed. In this thesis, we study Picnic algorithm, a post-quantum digital signature scheme. Picnic digital signature algorithm has the security of symmetric-key primitives that is considered to be secure against quantum attacks. In Picnic algorithm, zero knowledge proof systems and circuits to compute their protocol are used.
The MPC-in-the-head introduced in [IKOS07] has established itself as an important paradigm to design efficient digital signatures. It has been leveraged in the Picnic scheme [CDG+ 20] that reached the third round of the NIST PQC Standardization process. It has also been used in [Beu20] to introduce the Proof of Knowledge (PoK) with Helper paradigm. This construction permits to design shorter signatures but induces a non negligible performance overhead as it uses cut-and-choose. In this paper, we introduce the PoK leveraging structure paradigm along with its associated challenge space amplification technique. Our new approach to design PoK brings some improvements over the PoK with Helper one. Indeed, we show how one can substitute the Helper in these constructions by leveraging the underlying structure of the considered problem. This approach does not suffer from the performance overhead inherent to the PoK with Helper paradigm hence offers different trade-offs between security, signature sizes and performances. We also present four new post-quantum signature schemes. The first one is based on a new PoK with Helper for the Syndrome Decoding problem. It relies on ideas from [BGKM22] and [FJR21] and improve the latter using a new technique that can be seen as performing some cut-and-choose with a meet in the middle approach. The three other signatures are based on our new PoK leveraging structure approach and as such illustrate its versatility. We provide new PoK related to the Permuted Kernel Problem (PKP), Syndrome Decoding (SD) problem and Rank Syndrome Decoding (RSD) problem. In practice, these PoK lead to comparable or shorter signatures than existing ones. Indeed, considering (public key + signature), we get sizes below 9kB for our signature related to the PKP problem, below 15kB for our signature related to the SD problem and below 7kB for our signature related to the RSD problem.
Since 2016’s NIST call for standardization of post-quantum cryptographic primitives, developing efficient post-quantum secure digital signature schemes has become a highly active area of research. The difficulty in constructing such schemes is evidenced by NIST reopening the call in 2022 for digital signature schemes, because of missing diversity in existing proposals. In this work, we introduce the new postquantum digital signature scheme MiRitH. As direct successor of a scheme recently developed by Adj, Rivera-Zamarripa and Verbel (Africacrypt ’23), it is based on the hardness of the MinRank problem and follows the MPC-in-the-Head paradigm. We revisit the initial proposal, incorporate design-level improvements and provide more efficient parameter sets. We also provide the missing justification for the quantum security of all parameter sets following NIST metrics. In this context we design a novel Grover-amplified quantum search algorithm for solving the MinRank problem that outperforms a naive quantum brute-force search for the solution.MiRitH obtains signatures of size 5.7 kB for NIST category I security and therefore competes for the smallest signatures among any post-quantum signature following the MPCitH paradigm.At the same time MiRitH offers competitive signing and verification timings compared to the state of the art. To substantiate those claims we provide extensive implementations. This includes a reference implementation as well as optimized constant-time implementations for Intel processors (AVX2), and for the ARM (NEON) architecture. The speedup of our optimized AVX2 implementation relies mostly on a redesign of the finite field arithmetic, improving over existing implementations as well as an improved memory management.
We provide a pre-obfuscation circuit-level implementation of an efficient one shot signature scheme, which has known applications to delegated signatures, secure token transfer, and publicly verifiable randomness. The algorithm consists of two stages: a key generation stage where a classical public key/quantum secret key pair is produced, and a signing stage where the quantum secret key is processed with a message string to produce a classical signature. There is no algorithmic error in the construction and the signed message can be efficiently checked by a classical verifier. Our scheme works by preparing a superposition over elements of a random affine coset determined by the output of a puncturable pseudorandom function, together with a circuit that tests coset membership. The logical qubit number scales like Θ(κlog⁡(r)+n+l)Θ( κ\log(r) + n + l)Θ(κlog(r)+n+l) and the gate complexity scales like Θ(n3+nl)Θ(n^3 + nl)Θ(n3+nl), where rrr is the public key size, n+ln+ln+l is the signature size, lll is the message size, and κ=Ω(n)κ= Ω(n)κ=Ω(n) is the cryptographic security parameter. We provide explicit qubit and gate counts before obfuscation. A secure instantiation additionally requires modified key generation and a security proof for the resulting obfuscated construction.
Multiparty Computation (hereafter MPC) is a technique for allowing a set ofparticipants to run a secure computation with the assurance that the output is (1) correct, and (2) that a malicious party did not learn anything about the inputs of the honest parties besides what it can glean from the output. Impor- tantly much of cryptography is based on the assumption that an honest party has a private and secret input, and if the adversary learns this input the security of the scheme is broken. Then naturally the techniques of MPC can be applied to create threshold protocols for these cryptographic schemes to ensure that the secret inputs are not leaked and moreover that no group of parties smaller than the threshold know the input at all. While we have known how to generically evaluate MPC for any function since the 80s the question of efficiency still drives progress to this day. This thesis looks at two approaches for making secure com- putation more practical to deploy: developing specialized protocols for appli- cations such as distributed key generation and signing with RSA and ECDSA; and improving the state of the art of maliciously secure generic boolean-circuit MPC. We first look at work that produced a distributed key generation protocol for RSA that utilizes a novel candidate sampling mechanism to reduce waste in primality testing. The second work builds a threshold scheme for symmetric cryptographic primitives such as AES and SHA where there is limited algebraic structure to exploit by efficiently converting a generic n-of-n MPC protocol into a threshold t-of-n MPC protocol. Future directions in this thesis are in combin- ing techniques from the prior works to create a blind signature scheme for the Elliptic Curve Digital Signature Algorithm (ECDSA) that requires both alge- braic operations over elliptic curves and additionally symmetric evaluations of the SHA2 hash function.--Author's abstract
Group signatures and their variants have been widely used in privacy-sensitive scenarios such as anonymous authentication and attestation. In this paper, we present a new post-quantum group signature scheme from symmetric primitives. Using only symmetric primitives makes the scheme less prone to unknown attacks than basing the design on newly proposed hard problems whose security is less well-understood. However, symmetric primitives do not have rich algebraic properties, and this makes it extremely challenging to design a group signature scheme on top of them. It is even more challenging if we want a group signature scheme suitable for real-world applications, one that can support large groups and require few trust assumptions. Our scheme is based on MPC-in-the-head non-interactive zero-knowledge proofs, and we specifically design a novel hash-based group credential scheme, which is rooted in the SPHINCS+ signature scheme but with various modifications to make it MPC (multi-party computation) friendly. The security of the scheme has been proved under the fully dynamic group signature model. We provide an implementation of the scheme and demonstrate the feasibility of handling a group size as large as 2 60 . This is the first group signature scheme from symmetric primitives that supports such a large group size and meets all the security requirements.