Implementing Pairings at the 192-bit Security Level Diego F. Aranha1 , Laura Fuentes-Casta˜ neda2 , Edward Knapp3 , Alfred 3 Menezes , and Francisco Rodr´ıguez-Henr´ıquez2

Source URL: eprint.iacr.org

• Algebra
• Abstract algebra
• Pairing-based cryptography
• Mathematics
• Group theory
• Linear algebra
• Module theory
• Pairing
• Weil pairing
• Elliptic curve
• Proofs of quadratic reciprocity
• Basic hypergeometric series

COMPUTING DISCRETE LOGARITHMS IN F36·137 AND F36·163 USING MAGMA GORA ADJ, ALFRED MENEZES, THOMAZ OLIVEIRA, AND FRANCISCO RODR´IGUEZ-HENR´IQUEZ Abstract. We show that a Magma implementation of Joux’s new L[1/4] alg

Source URL: delta.cs.cinvestav.mx

The Brave New World of Bodacious Assumptions in Cryptography Neal Koblitz and Alfred Menezes T

Source URL: www.ams.org

Francisco Rodr´ıguez-Henr´ıquez Associate Professor CINVESTAV 3-C CINVESTAV-IPN Av. Instituto Polit´ecnico Nacional No. 2508, 07360, M´exico City, M´exico Tel: (3800 Ext. 6570

Source URL: delta.cs.cinvestav.mx

• Finite fields
• Elliptic curve cryptography
• Public-key cryptography
• Alfred Menezes
• Cryptography
• Elliptic curve
• CINVESTAV

THE RANDOM ORACLE MODEL: A TWENTY-YEAR RETROSPECTIVE NEAL KOBLITZ AND ALFRED J. MENEZES Abstract. It has been roughly two decades since the random oracle model for reductionist security arguments was introduced and one d

Source URL: cacr.uwaterloo.ca

• Diffie–Hellman problem
• Full Domain Hash
• Rabin signature algorithm
• Oracle machine
• Optimal asymmetric encryption padding
• Digital signature
• Schnorr signature
• Standard model
• RSA
• Cryptography
• Public-key cryptography
• Random oracle

Another Look at Provable Security Alfred Menezes (joint work with Sanjit Chatterjee, Neal Koblitz, Palash Sarkar) EUROCRYPT 2012 –1

Source URL: www.iacr.org

• Mathematics
• Mathematical proof
• Provable
• Adversary
• Science
• Cryptography
• Provable security
• Knowledge

An Introduction to Pairing-Based Cryptography Alfred Menezes Abstract. Bilinear pairings have been used to design ingenious protocols for such tasks as one-round three-party key agreement, identity-based encryption, and

Source URL: cacr.uwaterloo.ca

• Pairing
• Boneh/Franklin scheme
• Elliptic curve cryptography
• Diffie–Hellman problem
• Elliptic curve
• ID-based encryption
• Tate pairing
• BLS
• Supersingular elliptic curve
• Cryptography
• Abstract algebra
• Algebra

ANOTHER LOOK AT NON-STANDARD DISCRETE LOG AND DIFFIE-HELLMAN PROBLEMS NEAL KOBLITZ AND ALFRED MENEZES Abstract. We examine several versions of the one-more-discrete-log and one-more-Diffie-Hellman problems. In attempting

Source URL: eprint.iacr.org

• Finite fields
• Computational hardness assumptions
• Cryptographic protocols
• Group theory
• Diffie–Hellman problem
• XTR
• Index calculus algorithm
• Diffie–Hellman key exchange
• Random oracle
• Cryptography
• Abstract algebra
• Mathematics

FAULT ATTACKS ON PAIRING-BASED PROTOCOLS REVISITED SANJIT CHATTERJEE, KORAY KARABINA, AND ALFRED MENEZES Abstract. Several papers have studied fault attacks on computing a pairing value e(P, Q), where P is a public point

Source URL: cacr.uwaterloo.ca

• Mathematics
• Boneh/Franklin scheme
• Pairing
• XTR
• Supersingular elliptic curve
• Elliptic curve
• ID-based encryption
• RSA
• Weil pairing
• Abstract algebra
• Cryptography
• Algebra

COMPUTING DISCRETE LOGARITHMS IN F36·137 AND F36·163 USING MAGMA GORA ADJ, ALFRED MENEZES, THOMAZ OLIVEIRA, AND FRANCISCO RODR´IGUEZ-HENR´IQUEZ Abstract. We show that a Magma implementation of Joux’s new L[1/4] alg

Source URL: cacr.uwaterloo.ca

• Finite fields
• Logarithms
• Cryptography
• Group theory
• Polynomials
• Euclidean algorithm
• Discrete logarithm
• Factorization of polynomials over a finite field and irreducibility tests
• Cantor–Zassenhaus algorithm
• Abstract algebra
• Mathematics
• Algebra