TY - GEN
T1 - Multivariate signature scheme using quadratic forms
AU - Yasuda, Takanori
AU - Takagi, Tsuyoshi
AU - Sakurai, Kouichi
PY - 2013
Y1 - 2013
N2 - Multivariate Public Key Cryptosystems (MPKC) are candidates for post-quantum cryptography. MPKC has an advantage in that its encryption and decryption are relatively efficient. In this paper, we propose a multivariate signature scheme using quadratic forms. For a finite dimensional vector space V, it is known that there are exactly two equivalence classes of non-degenerate quadratic forms over V. We utilize the method to transform any non-degenerate quadratic form into the normal form of either of the two equivalence classes in order to construct a new signature scheme in MPKC. The signature generation of our scheme is between eight and nine times more efficient more than the multivariate signature scheme Rainbow at the level of 88-bit security. We show that the public keys of our scheme can not be represented by the public keys of other MPKC signature schemes and this means our scheme is immune to many attacks that depend on the form of the central map used by these schemes.
AB - Multivariate Public Key Cryptosystems (MPKC) are candidates for post-quantum cryptography. MPKC has an advantage in that its encryption and decryption are relatively efficient. In this paper, we propose a multivariate signature scheme using quadratic forms. For a finite dimensional vector space V, it is known that there are exactly two equivalence classes of non-degenerate quadratic forms over V. We utilize the method to transform any non-degenerate quadratic form into the normal form of either of the two equivalence classes in order to construct a new signature scheme in MPKC. The signature generation of our scheme is between eight and nine times more efficient more than the multivariate signature scheme Rainbow at the level of 88-bit security. We show that the public keys of our scheme can not be represented by the public keys of other MPKC signature schemes and this means our scheme is immune to many attacks that depend on the form of the central map used by these schemes.
UR - http://www.scopus.com/inward/record.url?scp=84884495379&partnerID=8YFLogxK
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U2 - 10.1007/978-3-642-38616-9_17
DO - 10.1007/978-3-642-38616-9_17
M3 - Conference contribution
AN - SCOPUS:84884495379
SN - 9783642386152
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 243
EP - 258
BT - Post-Quantum Cryptography - 5th International Workshop, PQCrypto 2013, Proceedings
T2 - 5th International Workshop on Post-Quantum Cryptography, PQCrypto 2013
Y2 - 4 June 2013 through 7 June 2013
ER -