Book Chapter10.1007/978-3-030-17656-3_3
Minicrypt Primitives with Algebraic Structure and Applications
Navid Alamati,Hart Montgomery,Sikhar Patranabis,Arnab Roy +3 more
- 19 May 2019
- pp 55-82
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TL;DR: This work affirmatively answer the question: instead of building (Cryptomania) primitives from concrete assumptions, can the authors build them from simple Minicrypt primitives endowed with some additional algebraic structure?
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Abstract: Algebraic structure lies at the heart of Cryptomania as we know it. An interesting question is the following: instead of building (Cryptomania) primitives from concrete assumptions, can we build them from simple Minicrypt primitives endowed with some additional algebraic structure? In this work, we affirmatively answer this question by adding algebraic structure to the following Minicrypt primitives:
One-Way Function (OWF)
Weak Unpredictable Function (wUF)
Weak Pseudorandom Function (wPRF)
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Citations
Cryptographic Group Actions and Applications
Navid Alamati,Luca De Feo,Hart Montgomery,Sikhar Patranabis +3 more
- 07 Dec 2020
TL;DR: A new assumption over group actions called Linear Hidden Shift (LHS) assumption is introduced and it is shown that it implies symmetric KDM-secure encryption, which in turn enables many other primitives that were not previously known from isogeny-based assumptions.
New Constructions of Hinting PRGs, OWFs with Encryption, and More
Rishab Goyal,Satyanarayana Vusirikala,Brent Waters +2 more
- 17 Aug 2020
TL;DR: The primitive of one-way function with encryption (OWFE) and its relatives (chameleon encryption, one-time signatures with encryption, hinting PRGs, trapdoor hash encryption, batch encryption) have been a centerpiece in all these results.
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•Posted Content
Ring Key-Homomorphic Weak PRFs and Applications.
TL;DR: Almost all of the major known cryptosystems can be built from a weak PRF with either a group or ring homomorphism over either the input space or the key space, and the SXDH assumption plausibly holds over it.
Multiparty Noninteractive Key Exchange from Ring Key-Homomorphic Weak PRFs
Navid Alamati,Hart Montgomery,Sikhar Patranabis +2 more
- 01 Jan 2023
TL;DR: In this paper , it was shown that any ring key-homomorphic weak PRF implies multiparty noninteractive key exchange (NIKE) for an arbitrary number of parties in the standard model.
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