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SUMMARY:Anthony Fraga. RAID - Compact PKE bridging RQC and LRPC cryptosyst
 em paradigm
DTSTART:20260630T120000Z
DTEND:20260630T130000Z
DTSTAMP:20260710T025500Z
UID:indico-event-16866@indico.math.cnrs.fr
DESCRIPTION:Abstract: We introduce Rank Additive Ideal Decoding (RAID)\, a
  new rank-based encryption framework that bridges the design of the RQC an
 d LRPC cryptosystems. In contrast to RQC\, whose ciphertext has two compon
 ents\, RAID produces a single-component ciphertext by adding an LRPC error
  directly to an encoded message. The decryption procedure requires to mult
 iply the ciphertext by the secret key and leverages an encoding of the mes
 sage compatible with this multiplication. The security of the scheme relie
 s on the hardness of the Blockwise Ideal Rank Support Learning (BIRSL) pro
 blem and on the Blockwise Ideal indistinguishability of LRPC (BILRPC) code
 s. Under these assumptions\, we prove INDCPA security for the PKE and obta
 in an INDCCA KEM via the Fujisaki-Okamoto transform.\nTo instantiate this 
 framework\, we introduce Gabidulin-LowRank codes\, a new family of codes d
 efined as a direct sum of an augmented Gabidulin code and a code with low 
 rank weight rows in its generator matrix. These codes are specifically des
 igned to be compatible with the multiplication by the secret key. We ident
 ify and bound three sources of decoding failure\, which we use to derive c
 oncrete parameters.\nOur KEM achieves a sum of public key and ciphertext s
 izes that outperform ML-KEM at all three NIST security levels\, first time
 s happening for a code-based KEM to the best of our knowledge. In addition
 \, it significantly improves existing rank-based schemes\, including the m
 ost recent optimized variants of RQC and LRPC schemes.\n \nThis is a join
 t work with Nicolas Aragon\, Loïc Bidoux\, Philippe Gaborit and Ilaria Za
 ppatore.\n\nhttps://indico.math.cnrs.fr/event/16866/
URL:https://indico.math.cnrs.fr/event/16866/
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