A Schnorr group, proposed by Claus P. Schnorr, is a large prime-order subgroup of , the multiplicative group of integers modulo for some prime . To generate such a group, generate , , such that
with , prime. Then choose any in the range until you find one such that
.
This value
is a generator of a subgroup of of order .
Schnorr groups are useful in discrete log based cryptosystems including Schnorr signatures and DSA. In such applications, typically is chosen to be large enough to resist index calculus and related methods of solving the discrete-log problem (perhaps 1024 to 3072 bits), while is large enough to resist the birthday attack on discrete log problems, which works in any group (perhaps 160 to 256 bits). Because the Schnorr group is of prime order, it has no non-trivial proper subgroups, thwarting confinement attacks due to small subgroups. Implementations of protocols that use Schnorr groups must verify where appropriate that integers supplied by other parties are in fact members of the Schnorr group; is a member of the group if and . Any member of the group except the element is also a generator of the group.
See also: Topics in cryptography
This group theory-related article is a stub. You can help Wikipedia by expanding it.
v
t
e
This cryptography-related article is a stub. You can help Wikipedia by expanding it.
A Schnorrgroup, proposed by Claus P. Schnorr, is a large prime-order subgroup of Z p × {\displaystyle \mathbb {Z} _{p}^{\times }} , the multiplicative...
cryptography, a Schnorr signature is a digital signature produced by the Schnorr signature algorithm that was described by Claus Schnorr. It is a digital...
a finite group suitable for public-key cryptography as the alphabet—such as a Schnorrgroup or elliptic curve—and to use the associated group operator...
Ludwig Ferdinand Schnorr von Carolsfeld (11 October 1788 – 13 April 1853) was a German Romantic painter, engraver and lithographer. Schnorr von Carolsfeld...
signature (like RSA PKCS1 v1.5, EdDSA and unlike RSA PSS, DSA, ECDSA and Schnorr).[citation needed] BLS12-381 is part of a family of elliptic curves named...
discrete log problem is hard. Typically a Schnorrgroup is used. In general, J-PAKE can use any prime order group that is suitable for public key cryptography...
cryptography techniques to which they had patents, such as the RSA algorithm, the Schnorr signature algorithm and several others. Though not industry standards (because...
q} in which the discrete logarithm problem is hard. For example, a Schnorrgroup can be used. Assume there are n {\displaystyle \scriptstyle n} participants...
The Twelve Spies, as recorded in the Book of Numbers, were a group of Israelite chieftains, one from each of the Twelve Tribes, who were dispatched by...
of knowledge of a discrete logarithm, is due to Schnorr. The protocol is defined for a cyclic group G q {\displaystyle G_{q}} of order q {\displaystyle...
the discrete logarithm problem is hard. For example, a Schnorrgroup can be used. For a group of n {\displaystyle \scriptstyle n} participants, the protocol...
Signature Algorithm (EdDSA) is a digital signature scheme using a variant of Schnorr signature based on twisted Edwards curves. It is designed to be faster...
Isidoro. They were joined by Philipp Veit, Peter von Cornelius, Julius Schnorr von Carolsfeld, Friedrich Wilhelm Schadow and a loose grouping of other...
(3rd ed.), Tata McGraw-Hill, p. 441, ISBN 978-0-07-068179-8. Schnorr Handbook, Schnorr, 2016, archived from the original on 2016-10-03, retrieved 2016-10-04...
quadratic sieve. Another such algorithm is the class group relations method proposed by Schnorr, Seysen, and Lenstra, which they proved only assuming...
be part of a set liturgy or ritual, and it can be performed alone or in groups. Prayer may take the form of a hymn, incantation, formal creedal statement...
forbidden to marry Bathsheba had he been a Gentile. David's mighty men were a group of his best 37 fighters (later expanded to around 80). Although the lists...
Vienna: Art and History. Florence: Summerfield Press. ASIN B000NQLZ5K. Schnorr, Lina (2012). Imperial Vienna. Vienna: HB Medienvertrieb GesmbH. ISBN 978-3950239690...
exponentiation and the discrete logarithm problem. DSA is a variant of the Schnorr and ElGamal signature schemes.: 486 The National Institute of Standards...
prioritizing different traits when it comes to choosing a mate, with both groups favoring attractive partners in general, but men tending to prefer women...
The sons of King David are mentioned both as a group and individually several times in the biblical accounts of the reigns both of David and his successor...
God to any who did not know them. The Book of Ezra describes how he led a group of Judean exiles living in Babylon to their home city of Jerusalem where...
Global Information
