Why was the term “discrete” used in discrete logarithm? Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern) Announcing the arrival of Valued Associate #679: Cesar Manara Unicorn Meta Zoo #1: Why another podcast?Trying to better understand the failure of the Index Calculus for ECDLPWhat is so special about elliptic curves?Why is the discrete logarithm problem assumed to be hard?What is the difference between discrete logarithm and logarithm?Calculating the discrete logarithmWhy is NON DISCRETE logarithm problem not hard as the DISCRETE logarithm problem (so computationally hard)?How to construct a hash function into a cyclic group such that its discrete log is intractable?Discrete logarithm key sizes for very short term usageDiscrete Logarithm NotationDescribing Discrete Logarithm Assumption
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Why was the term “discrete” used in discrete logarithm?
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)
Announcing the arrival of Valued Associate #679: Cesar Manara
Unicorn Meta Zoo #1: Why another podcast?Trying to better understand the failure of the Index Calculus for ECDLPWhat is so special about elliptic curves?Why is the discrete logarithm problem assumed to be hard?What is the difference between discrete logarithm and logarithm?Calculating the discrete logarithmWhy is NON DISCRETE logarithm problem not hard as the DISCRETE logarithm problem (so computationally hard)?How to construct a hash function into a cyclic group such that its discrete log is intractable?Discrete logarithm key sizes for very short term usageDiscrete Logarithm NotationDescribing Discrete Logarithm Assumption
$begingroup$
Is there anything especially "discrete" about a discrete logarithm? This is not a question of what is a discrete logarithm or why the discrete logarithm problem is an "intractable problem" given certain circumstances. I'm just trying to determine if there's some additional meaning to the term "discrete" as it's used in name discrete logarithm?
The definition of "discrete" is "individually separate and distinct". Could it be that the term "discrete" is a reference to the least non-negative residues of a modulus or the order of points for a particular cyclic group on an elliptic curve?
discrete-logarithm terminology
asked 33 mins ago
JohnGaltJohnGalt
22116
$endgroup$
add a comment |
$begingroup$
Is there anything especially "discrete" about a discrete logarithm? This is not a question of what is a discrete logarithm or why the discrete logarithm problem is an "intractable problem" given certain circumstances. I'm just trying to determine if there's some additional meaning to the term "discrete" as it's used in name discrete logarithm?
The definition of "discrete" is "individually separate and distinct". Could it be that the term "discrete" is a reference to the least non-negative residues of a modulus or the order of points for a particular cyclic group on an elliptic curve?
discrete-logarithm terminology
asked 33 mins ago
JohnGaltJohnGalt
22116
$endgroup$
1
$begingroup$
Traditional logarithm: answer is a real or complex number. Discrete logarithm: answer is an element of a finite set $mathbbZ_n$.
$endgroup$
– Mikero
24 mins ago
add a comment |
$begingroup$
Is there anything especially "discrete" about a discrete logarithm? This is not a question of what is a discrete logarithm or why the discrete logarithm problem is an "intractable problem" given certain circumstances. I'm just trying to determine if there's some additional meaning to the term "discrete" as it's used in name discrete logarithm?
The definition of "discrete" is "individually separate and distinct". Could it be that the term "discrete" is a reference to the least non-negative residues of a modulus or the order of points for a particular cyclic group on an elliptic curve?
discrete-logarithm terminology
asked 33 mins ago
JohnGaltJohnGalt
22116
$endgroup$
Is there anything especially "discrete" about a discrete logarithm? This is not a question of what is a discrete logarithm or why the discrete logarithm problem is an "intractable problem" given certain circumstances. I'm just trying to determine if there's some additional meaning to the term "discrete" as it's used in name discrete logarithm?
The definition of "discrete" is "individually separate and distinct". Could it be that the term "discrete" is a reference to the least non-negative residues of a modulus or the order of points for a particular cyclic group on an elliptic curve?
discrete-logarithm terminology
discrete-logarithm terminology
asked 33 mins ago
JohnGaltJohnGalt
22116
asked 33 mins ago
JohnGaltJohnGalt
22116
asked 33 mins ago
JohnGaltJohnGalt
22116
asked 33 mins ago
JohnGaltJohnGalt
22116
asked 33 mins ago
JohnGaltJohnGalt
22116
22116
1
$begingroup$
Traditional logarithm: answer is a real or complex number. Discrete logarithm: answer is an element of a finite set $mathbbZ_n$.
$endgroup$
– Mikero
24 mins ago
add a comment |
1
$begingroup$
Traditional logarithm: answer is a real or complex number. Discrete logarithm: answer is an element of a finite set $mathbbZ_n$.
$endgroup$
– Mikero
24 mins ago
1
1
$begingroup$
Traditional logarithm: answer is a real or complex number. Discrete logarithm: answer is an element of a finite set $mathbbZ_n$.
$endgroup$
– Mikero
24 mins ago
$begingroup$
Traditional logarithm: answer is a real or complex number. Discrete logarithm: answer is an element of a finite set $mathbbZ_n$.
$endgroup$
– Mikero
24 mins ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The word discrete is used as an antonym of 'continuous', that is, it is the normal logarithmic problem, just over a discrete group.
The standard logarithmic problem is over the infinite group $mathbbR^*$, this group is called 'continuous', because for any element $x$, there are other elements that are arbitrarily close to it.
The discrete logarithmic problem is over a finite group (for example, $mathbbZ_p^*$); in contrast to $mathbbR^*$, we don't have group elements arbitrarily close together; we call this type of group 'discrete'.
answered 24 mins ago
ponchoponcho
94.1k2148247
$endgroup$
$begingroup$
Would it be accurate to say that the fact that the group is discrete in a discrete logarithm, isn't what makes them useful in say DH, but instead other properties? For example, a useful property of a discrete group (in connection with DH) when the modulus and base are chosen wisely is that computing the exponent used to exponentiate a power can be made computationally infeasible (e.g. DLP)? Or is there some connection between the non-continuous nature of the discrete group that enables the intractability of DLP?
$endgroup$
– JohnGalt
2 mins ago
add a comment |
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$begingroup$
The word discrete is used as an antonym of 'continuous', that is, it is the normal logarithmic problem, just over a discrete group.
The standard logarithmic problem is over the infinite group $mathbbR^*$, this group is called 'continuous', because for any element $x$, there are other elements that are arbitrarily close to it.
The discrete logarithmic problem is over a finite group (for example, $mathbbZ_p^*$); in contrast to $mathbbR^*$, we don't have group elements arbitrarily close together; we call this type of group 'discrete'.
answered 24 mins ago
ponchoponcho
94.1k2148247
$endgroup$
$begingroup$
Would it be accurate to say that the fact that the group is discrete in a discrete logarithm, isn't what makes them useful in say DH, but instead other properties? For example, a useful property of a discrete group (in connection with DH) when the modulus and base are chosen wisely is that computing the exponent used to exponentiate a power can be made computationally infeasible (e.g. DLP)? Or is there some connection between the non-continuous nature of the discrete group that enables the intractability of DLP?
$endgroup$
– JohnGalt
2 mins ago
add a comment |
$begingroup$
The word discrete is used as an antonym of 'continuous', that is, it is the normal logarithmic problem, just over a discrete group.
The standard logarithmic problem is over the infinite group $mathbbR^*$, this group is called 'continuous', because for any element $x$, there are other elements that are arbitrarily close to it.
The discrete logarithmic problem is over a finite group (for example, $mathbbZ_p^*$); in contrast to $mathbbR^*$, we don't have group elements arbitrarily close together; we call this type of group 'discrete'.
answered 24 mins ago
ponchoponcho
94.1k2148247
$endgroup$
$begingroup$
Would it be accurate to say that the fact that the group is discrete in a discrete logarithm, isn't what makes them useful in say DH, but instead other properties? For example, a useful property of a discrete group (in connection with DH) when the modulus and base are chosen wisely is that computing the exponent used to exponentiate a power can be made computationally infeasible (e.g. DLP)? Or is there some connection between the non-continuous nature of the discrete group that enables the intractability of DLP?
$endgroup$
– JohnGalt
2 mins ago
add a comment |
$begingroup$
The word discrete is used as an antonym of 'continuous', that is, it is the normal logarithmic problem, just over a discrete group.
The standard logarithmic problem is over the infinite group $mathbbR^*$, this group is called 'continuous', because for any element $x$, there are other elements that are arbitrarily close to it.
The discrete logarithmic problem is over a finite group (for example, $mathbbZ_p^*$); in contrast to $mathbbR^*$, we don't have group elements arbitrarily close together; we call this type of group 'discrete'.
answered 24 mins ago
ponchoponcho
94.1k2148247
$endgroup$
The word discrete is used as an antonym of 'continuous', that is, it is the normal logarithmic problem, just over a discrete group.
The standard logarithmic problem is over the infinite group $mathbbR^*$, this group is called 'continuous', because for any element $x$, there are other elements that are arbitrarily close to it.
The discrete logarithmic problem is over a finite group (for example, $mathbbZ_p^*$); in contrast to $mathbbR^*$, we don't have group elements arbitrarily close together; we call this type of group 'discrete'.
answered 24 mins ago
ponchoponcho
94.1k2148247
answered 24 mins ago
ponchoponcho
94.1k2148247
answered 24 mins ago
ponchoponcho
94.1k2148247
answered 24 mins ago
ponchoponcho
94.1k2148247
94.1k2148247
$begingroup$
Would it be accurate to say that the fact that the group is discrete in a discrete logarithm, isn't what makes them useful in say DH, but instead other properties? For example, a useful property of a discrete group (in connection with DH) when the modulus and base are chosen wisely is that computing the exponent used to exponentiate a power can be made computationally infeasible (e.g. DLP)? Or is there some connection between the non-continuous nature of the discrete group that enables the intractability of DLP?
$endgroup$
– JohnGalt
2 mins ago
add a comment |
$begingroup$
Would it be accurate to say that the fact that the group is discrete in a discrete logarithm, isn't what makes them useful in say DH, but instead other properties? For example, a useful property of a discrete group (in connection with DH) when the modulus and base are chosen wisely is that computing the exponent used to exponentiate a power can be made computationally infeasible (e.g. DLP)? Or is there some connection between the non-continuous nature of the discrete group that enables the intractability of DLP?
$endgroup$
– JohnGalt
2 mins ago
$begingroup$
Would it be accurate to say that the fact that the group is discrete in a discrete logarithm, isn't what makes them useful in say DH, but instead other properties? For example, a useful property of a discrete group (in connection with DH) when the modulus and base are chosen wisely is that computing the exponent used to exponentiate a power can be made computationally infeasible (e.g. DLP)? Or is there some connection between the non-continuous nature of the discrete group that enables the intractability of DLP?
$endgroup$
– JohnGalt
2 mins ago
$begingroup$
Would it be accurate to say that the fact that the group is discrete in a discrete logarithm, isn't what makes them useful in say DH, but instead other properties? For example, a useful property of a discrete group (in connection with DH) when the modulus and base are chosen wisely is that computing the exponent used to exponentiate a power can be made computationally infeasible (e.g. DLP)? Or is there some connection between the non-continuous nature of the discrete group that enables the intractability of DLP?
$endgroup$
– JohnGalt
2 mins ago
add a comment |
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$begingroup$
Traditional logarithm: answer is a real or complex number. Discrete logarithm: answer is an element of a finite set $mathbbZ_n$.
$endgroup$
– Mikero
24 mins ago