The efficiency of cryptographic protocols rely on the speed of the underlying arithmetic and fini... more The efficiency of cryptographic protocols rely on the speed of the underlying arithmetic and finite field computation. In the literature , several methods on how to improve the multiplication over extensions fields Fqm , for prime q were developped. These optimisations are often related to the Karatsuba and Toom Cook methods. However, the speeding-up is only interesting when m is a product of powers of 2 and 3. In general cases, a fast multiplication over Fqm is implemented through the use of the naive schoolbook method. In this paper, we propose a new efficient multiplication over Fqm for any power m. The multiplication relies on the notion of Adapted Modular Number System (AMNS), introduced in 2004 by [3]. We improve the construction of an AMNS basis and we provide a fast implementation of the multiplication over Fqm , which is faster than GMP and NTL.
Initially, the use of pairings did not involve any secret entry. However in an Identity Based Cry... more Initially, the use of pairings did not involve any secret entry. However in an Identity Based Cryptographic protocol, one of the two entries of the pairing is secret, so fault attack can be applied to Pairing Based Cryptography to find it. In [18], the author shows that Pairing Based Cryptography in Weierstrass coordinates is vulnerable to a fault attack. The addition law in Edwards coordinates is such that the exponentiation in Edwards coordinates is naturally protected to Side Channel attacks. We study here if this property protects Pairing Based Cryptography in Edwards coordinates against fault attacks.
ABSTRACT In [Zbl 1260.11043], Lubicz and Robert generalized the Tate pairing over any abelian var... more ABSTRACT In [Zbl 1260.11043], Lubicz and Robert generalized the Tate pairing over any abelian variety and more precisely over Theta functions. The security of the new algorithms is an important issue for the use of practical cryptography. Side channel attacks are powerful attacks, using the leakage of information to reveal sensitive data. The pairings over elliptic curves were sensitive to side channel attacks. In this article, we study the weaknesses of the Tate pairing over Theta functions when submitted to side channel attacks.
The efficiency of cryptographic protocols rely on the speed of the underlying arithmetic and fini... more The efficiency of cryptographic protocols rely on the speed of the underlying arithmetic and finite field computation. In the literature , several methods on how to improve the multiplication over extensions fields Fqm , for prime q were developped. These optimisations are often related to the Karatsuba and Toom Cook methods. However, the speeding-up is only interesting when m is a product of powers of 2 and 3. In general cases, a fast multiplication over Fqm is implemented through the use of the naive schoolbook method. In this paper, we propose a new efficient multiplication over Fqm for any power m. The multiplication relies on the notion of Adapted Modular Number System (AMNS), introduced in 2004 by [3]. We improve the construction of an AMNS basis and we provide a fast implementation of the multiplication over Fqm , which is faster than GMP and NTL.
Initially, the use of pairings did not involve any secret entry. However in an Identity Based Cry... more Initially, the use of pairings did not involve any secret entry. However in an Identity Based Cryptographic protocol, one of the two entries of the pairing is secret, so fault attack can be applied to Pairing Based Cryptography to find it. In [18], the author shows that Pairing Based Cryptography in Weierstrass coordinates is vulnerable to a fault attack. The addition law in Edwards coordinates is such that the exponentiation in Edwards coordinates is naturally protected to Side Channel attacks. We study here if this property protects Pairing Based Cryptography in Edwards coordinates against fault attacks.
ABSTRACT In [Zbl 1260.11043], Lubicz and Robert generalized the Tate pairing over any abelian var... more ABSTRACT In [Zbl 1260.11043], Lubicz and Robert generalized the Tate pairing over any abelian variety and more precisely over Theta functions. The security of the new algorithms is an important issue for the use of practical cryptography. Side channel attacks are powerful attacks, using the leakage of information to reveal sensitive data. The pairings over elliptic curves were sensitive to side channel attacks. In this article, we study the weaknesses of the Tate pairing over Theta functions when submitted to side channel attacks.
Uploads
Papers by Nadia Mrabet