AGMOS: Algebraic Group Model with Oblivious

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AGMOS: Algebraic Group Model with Oblivious

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AGMOS: Algebraic Group Model with Oblivious Sampling Helger Lipmaa Roberto Parisella Janno Siim Cryptographic Groups 2 Ideal models for Cryptographic Groups GGM: generic group model Perfect unstructured group. Group elements are perfect

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AGMOS: Algebraic Group Model with Oblivious Sampling Helger Lipmaa
Roberto Parisella
Janno Siim

Cryptographic Groups 2

Ideal models for Cryptographic Groups GGM: generic group model Perfect unstructured group.
Group elements are perfect encryptions of the exponent. 3

GGM Criticisms Un-instantiability results
Does not capture group-specific algorithms
Reductions can always program group elements, with random known exponents

Ideal Models for Cryptographic Groups AGM: algebraic group model [FKL18] Adversaries provide a linear representation of their outputs, with respect to the group element they received on input 5

AGM Advantages … Capture some known group-specific algorithms
Proofs by reductions and Criticisms Un-instantiability result.
Unclear relation between GGM and AGM
Knowledge assumptions secure in AGM but not in the standard model.

Oblivious Sampling

Spurious Knowledge Assumptions: example Extractor Used by reductions

Spurious Knowledge Assumptions: KZG PLONK, Lunar: SNARKs with security proof based on this assumption

AGMOS: AGM with Oblivious Sampling Non-programmable oracle

Example: CDH AGMOS adversary

Example: CDH holds in AGMOS

Thanks for your attentionCheck the full version on e-printhttps://eprint.iacr.org/2023/1504 Questions?

And Open Problems Cryptanalysis of TOFR …

AGMOS: Algebraic Group Model with Oblivious

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