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Common random string model is a popular model in classi- cal cryptography. We study a quantum analogue of this model called the common Haar state (CHS) model. In this model, every party participating in the cryptographic system receives many copies of one or more i.i.d Haar random states. We study feasibility and limitations of cryptographic primitives in this model and its variants: – We present a construction of pseudorandom function-like states with security against computationally unbounded adversaries, as long as the adversaries only receive (a priori) bounded number of copies. By suitably instantiating the CHS model, we obtain a new approach to construct pseudorandom function-like states in the plain model. – We present separations between pseudorandom function-like states (with super-logarithmic length) and quantum cryptographic primitives, such as interactive key agreement and bit commitment, with classical communication. To show these separations, we prove new results on the indistinguishability of identical versus independent Haar states against LOCC (local operations, classical communication) adversaries. 

We introduce a new notion called Q-secure pseudorandom isometries (PRI). A pseudorandom isometry is an efficient quantum circuit that maps an n-qubit state to an (n+m)-qubit state in an isometric manner. In terms of security, we require that the output of a q-fold PRI on \rho, for \rho \in Q, for any polynomial q, should be computationally indistinguishable from the output of a q-fold Haar isometry on \rho. By fine-tuning Q, we recover many existing notions of pseudorandomness. We present a construction of PRIs and assuming post-quantum one-way functions, we prove the security of Q-secure pseudorandom isometries (PRI) for different interesting settings of Q. We also demonstrate many cryptographic applications of PRIs, including, length extension theorems for quantum pseudorandomness notions, message authentication schemes for quantum states, multi-copy secure public and private encryption schemes, and succinct quantum commitments. 

We report a new design of polymer phenylacetylene (PA) ligands and the ligand exchange methodology for colloidal noble metal nanoparticles (NPs). PA-terminated poly(ethylene glycol) (PEG) can bind to metal NPs through acetylide (M-CC-R) that affords a high grafting density. The ligand−metal interaction can be switched between σ bonding and extended π backbonding by changing grafting conditions. The σ bonding of PEG−PA with NPs is strong and it can compete with other capping ligands including thiols, while the π backbonding is much weaker. The σ bonding is also demonstrated to improve the catalytic performance of Pd for ethanol oxidation and prevent surface absorption of the reaction intermediates. Those unique binding characteristics will enrich the toolbox in the control of colloidal surface chemistry and their applications using polymer ligands. 

This study revisits the material properties of solid “liquid crystalline” films made from synthetic helical polypeptides and explores their structure–property relationships. Poly(γ-benzyl-l-glutamate) (PBLG) with various molecular weights and architectures (linear, comb-, and brush-like) were transformed into films through mechanical hot pressing. The resulting materials are composed of helical PBLGs arranged in a near-hexagonal lattice, similar to those formed by casting from a concentrated solution in 1,2-dichloroethane (EDC). Despite exhibiting lower apparent crystallinity, these films showed superior mechanical strength, potentially due to the promotion of more interrupted helices and their entanglements under high temperature and pressure. A pronounced chain length effect on the tensile modulus and mechanical strength was observed, aligning with the “interrupted helices” model proposed by us and others. Macromolecules with a polynorbornene (PN) backbone and PBLG side chains mirrored the mechanical and viscoelastic properties of linear PBLGs. Our findings suggest that the folding structures of polypeptide chains and the discontinuity of the folding in longer chains are more influential in determining the macroscopic mechanical properties of the resultant materials than crystallinity, packing ordering, or macromolecular architecture, emphasizing the critical role of cohesive chain network formation in achieving enhanced mechanical strength. This research also presents a versatile approach to fabricating solid-state polypeptide materials, circumventing solubility challenges associated with traditional solution-based processing methods. 

The biological significance of self-assembled protein filament networks and their unique mechanical properties have sparked interest in the development of synthetic filament networks that mimic these attributes. Building on the recent advancement of autoaccelerated ring-opening polymerization of amino acid N-carboxyanhydrides (NCAs), this study strategically explores a series of random copolymers comprising multiple amino acids, aiming to elucidate the core principles governing gelation pathways of these purpose-designed copolypeptides. Utilizing glutamate (Glu) as the primary component of copolypeptides, two targeted pathways were pursued: first, achieving a fast fibrillation rate with lower interaction potential using serine (Ser) as a comonomer, facilitating the creation of homogeneous fibril networks; and second, creating more rigid networks of fibril clusters by incorporating alanine (Ala) and valine (Val) as comonomers. The selection of amino acids played a pivotal role in steering both the morphology of fibril superstructures and their assembly kinetics, subsequently determining their potential to form sample-spanning networks. Importantly, the viscoelastic properties of the resulting supramolecular hydrogels can be tailored according to the specific copolypeptide composition through modulations in filament densities and lengths. The findings enhance our understanding of directed self-assembly in high molecular weight synthetic copolypeptides, offering valuable insights for the development of synthetic fibrous networks and biomimetic supramolecular materials with custom-designed properties. 

Polypeptides, as the synthetic analogues of natural proteins, are an important class of biopolymers that are widely studied and used in various biomedical applications. However, the preparation of polypeptide materials from the polymerization of N-carboxyanhydride (NCA) is limited by various side reactions and stringent polymerization conditions. Recently, we report the cooperative covalent polymerization (CCP) of NCA in solvents with low polarity and weak hydrogen-bonding ability (e.g., dichloromethane or chloroform). The polymerization exhibits characteristic two-stage kinetics, which is significantly accelerated compared with conventional polymerization under identical conditions. In this Account, we review our recent studies on the CCP, with the focus on the acceleration mechanism, the kinetic modeling, and the use of fast kinetics for the efficient preparation of polypeptide materials. By studying CCP with several initiating systems, we found that the polymerization rate was dependent on the secondary structure as well as the macromolecular architecture of the propagating polypeptides. The molecular interactions between the α-helical, propagating polypeptide and the monomer played an important role in the acceleration, which catalyzed the ring-opening reaction of NCA in an enzyme-mimetic, Michaelis–Menten manner. Additionally, the proximity between initiating sites further accelerated the polymerization, presumably due to the cooperative interactions of macrodipoles between neighboring helices and/or enhanced binding of monomers. A two-stage kinetic model with a reversible monomer adsorption process in the second stage was developed to describe the CCP kinetics, which highlighted the importance of cooperativity, critical chain length, binding constant, [M]0, and [M]0/[I]0. The kinetic model successfully predicted the polymerization behavior of the CCP and the molecular-weight distribution of resulting polypeptides. The remarkable rate acceleration of the CCP offers a promising strategy for the efficient synthesis of polypeptide materials, since the fast kinetics outpaces various side reactions during the polymerization process. Chain termination and chain transfer were thus minimized, which facilitated the synthesis of high-molecular-weight polypeptide materials and multiblock copolypeptides. In addition, the accelerated polymerization enabled the synthesis of polypeptides in the presence of an aqueous phase, which was otherwise challenging due to the water-induced degradation of monomers. Taking advantage of the incorporation of the aqueous phase, we reported the preparation of well-defined polypeptides from nonpurified NCAs. We believe the studies of CCP not only improve our understanding of biological catalysis, but also benefit the downstream studies in the polypeptide field by providing versatile polypeptide materials.