TY - GEN
T1 - Linear-time encodable codes meeting the gilbert-varshamov bound and their cryptographic applications
AU - Druk, Erez
AU - Ishai, Yuval
PY - 2014
Y1 - 2014
N2 - A random linear code has good minimal distance with high probability. The conjectured intractability of decoding random linear codes has recently found many applications in cryptography. One disadvantage of random linear codes is that their encoding complexity grows quadratically with the message length. Motivated by this disadvantage, we present a randomized construction of linear error-correcting codes which can be encoded in linear time and yet enjoy several useful features of random linear codes. Our construction is based on a linear-time computable hash function due to Ishai, Kushilevitz, Ostrovsky and Sahai [25]. We demonstrate the usefulness of these new codes by presenting several applications in coding theory and cryptography. These include the first family of linear-time encodable codes meeting the Gilbert-Varshamov bound, the first nontrivial linear-time secret sharing schemes, and plausible candidates for symmetric encryption and identification schemes which can be conjectured to achieve better asymptotic efficiency/security tradeoffs than all current candidates.
AB - A random linear code has good minimal distance with high probability. The conjectured intractability of decoding random linear codes has recently found many applications in cryptography. One disadvantage of random linear codes is that their encoding complexity grows quadratically with the message length. Motivated by this disadvantage, we present a randomized construction of linear error-correcting codes which can be encoded in linear time and yet enjoy several useful features of random linear codes. Our construction is based on a linear-time computable hash function due to Ishai, Kushilevitz, Ostrovsky and Sahai [25]. We demonstrate the usefulness of these new codes by presenting several applications in coding theory and cryptography. These include the first family of linear-time encodable codes meeting the Gilbert-Varshamov bound, the first nontrivial linear-time secret sharing schemes, and plausible candidates for symmetric encryption and identification schemes which can be conjectured to achieve better asymptotic efficiency/security tradeoffs than all current candidates.
KW - Cryptography
KW - Error-correcting codes
KW - Gilbert-Varshamov bound
KW - Lineartime encodable codes
UR - http://www.scopus.com/inward/record.url?scp=84893242693&partnerID=8YFLogxK
U2 - 10.1145/2554797.2554815
DO - 10.1145/2554797.2554815
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AN - SCOPUS:84893242693
SN - 9781450322430
T3 - ITCS 2014 - Proceedings of the 2014 Conference on Innovations in Theoretical Computer Science
SP - 169
EP - 182
BT - ITCS 2014 - Proceedings of the 2014 Conference on Innovations in Theoretical Computer Science
T2 - 2014 5th Conference on Innovations in Theoretical Computer Science, ITCS 2014
Y2 - 12 January 2014 through 14 January 2014
ER -