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19 results on '"Adj, Gora"'

1. Faulty isogenies: a new kind of leakage

Author

Adj, Gora, Chi-Domínguez, Jesús-Javier, Mateu, Víctor, and Rodríguez-Henríquez, Francisco

Subjects
Mathematics - Number Theory, Computer Science - Cryptography and Security
Abstract

In SIDH and SIKE protocols, public keys are defined over quadratic extensions of prime fields. We present in this work a projective invariant property characterizing affine Montgomery curves defined over prime fields. We then force a secret 3-isogeny chain to repeatedly pass through a curve defined over a prime field in order to exploit the new property and inject zeros in the A-coefficient of an intermediate curve to successfully recover the isogeny chain one step at a time. Our results introduce a new kind of fault attacks applicable to SIDH and SIKE., Comment: Update: extended countermeasures

Published
2022

2. MinRank in the Head : Short Signatures from Zero-Knowledge Proofs

Author

Adj, Gora, Rivera-Zamarripa, Luis, Verbel, Javier, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, El Mrabet, Nadia, editor, De Feo, Luca, editor, and Duquesne, Sylvain, editor

Published
2023
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5. On the Cost of Computing Isogenies Between Supersingular Elliptic Curves

Author

Adj, Gora, Cervantes-Vázquez, Daniel, Chi-Domínguez, Jesús-Javier, Menezes, Alfred, Rodríguez-Henríquez, Francisco, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Cid, Carlos, editor, and Jacobson Jr., Michael J., editor

Published
2019
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6. Computing Discrete Logarithms in Using Magma

Author

Adj, Gora, Menezes, Alfred, Oliveira, Thomaz, Rodríguez-Henríquez, Francisco, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Koç, Çetin Kaya, editor, Mesnager, Sihem, editor, and Savaş, Erkay, editor

Published
2015
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8. Weakness of for Discrete Logarithm Cryptography

Author

Adj, Gora, Menezes, Alfred, Oliveira, Thomaz, Rodríguez-Henríquez, Francisco, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Cao, Zhenfu, editor, and Zhang, Fangguo, editor

Published
2014
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12. Karatsuba-based square-root Vélu’s formulas applied to two isogeny-based protocols

Author

Adj, Gora, Chi-Domínguez, Jesús-Javier, and Rodríguez-Henríquez, Francisco

Abstract

At a combined computational cost of about 6ℓfield operations, Vélu’s formulas are used to construct and evaluate degree-ℓisogenies in the vast majority of isogeny-based cryptographic schemes. By adapting to Vélu’s formulas a baby-step giant-step approach, Bernstein, De Feo, Leroux, and Smith presented a procedure that can compute isogeny operations at a reduced cost of just O~(ℓ)field operations. In this paper, we present a concrete computational analysis of these novel procedures along with several algorithmic tricks that helped us to further decrease its computational cost. We also report an optimized Python3-code implementation of several instantiations of two isogeny-based key-exchange protocols, namely, CSIDH and B-SIDH. Our software library uses a combination of the modified Vélu’s formulas and an adaptation of the optimal strategies commonly used in the SIDH/SIKE protocols to produce significant speedups. Compared to a traditional Vélu constant-time implementation of CSIDH, our experimental results report a saving of 5.357%, 13.68% and 25.938% base field operations for CSIDH-512, CSIDH-1024, and CSIDH-1792, respectively. Additionally, we present the first optimized implementation of B-SIDH ever reported in the open literature.

Published
2022
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19. Weakness of [formula omitted] and [formula omitted] for discrete logarithm cryptography.

Author

Adj, Gora, Menezes, Alfred, Oliveira, Thomaz, and Rodríguez-Henríquez, Francisco

Subjects
*CRYPTOGRAPHY, *LOGARITHMS, *ALGORITHMS, *FINITE fields, *CYBERTERRORISM, *DATA security
Abstract

In the past two years, there have been several dramatic improvements in algorithms for computing discrete logarithms in small-characteristic finite fields. In this paper, we examine the effectiveness of these new algorithms for computing discrete logarithms in F 3 6 ⋅ 1429 and F 2 4 ⋅ 3041 . The intractability of the discrete logarithm problem in these fields is necessary for the security of bilinear pairings derived from supersingular curves with embedding degree 6 and 4 defined, respectively, over F 3 1429 and F 2 3041 ; these curves were believed to enjoy a security level of 192 bits against attacks by Coppersmith's algorithm. Our analysis shows that these pairings offer security levels of at most 96 and 129 bits, respectively, leading us to conclude that they are dead for pairing-based cryptography. [ABSTRACT FROM AUTHOR]

Published
2015
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