option "multipliers" added, how proposed from @yarikoptic;

the calculate formula is rewritten to lambda / compiled solution (up to 10 million times per seconds);
code review;

config/jail.conf

@@ -47,21 +47,38 @@ before = paths-debian.conf
 # "bantimeextra.enabled" allows to use database for searching of previously banned ip's to increase a 
 # default ban time using special formula, default it is banTime * 1, 2, 4, 8, 16, 32...
 #bantimeextra.enabled = true
+
 # "bantimeextra.findtime" is the max number of seconds that we search in the database,
 # if it is not specified - whole database will be used for ban searching
 # (please observe current "dbpurgeage" value of fail2ban.conf).
 #bantimeextra.findtime = 24*60*60
+
 # "bantimeextra.rndtime" is the max number of seconds using for mixing with random time 
 # to prevent "clever" botnets calculate exact time IP can be unbanned again:
 #bantimeextra.rndtime = 5*60
+
 # "bantimeextra.maxtime" is the max number of seconds using the ban time can reach (don't grows further)
 #bantimeextra.maxtime = 24*60*60
+
 # "bantimeextra.factor" is a coefficient to calculate exponent growing of the formula,
-# by default value of factor "2.0 / 2.885385" and default value of formula, the ban time 
+# for formula solution by default value of factor is "2.0 / 2.885385" and with default value of formula, the ban time 
 # grows by 1, 2, 4, 8, 16 ...
+# for multipliers solution by default value of factor is "1" and the ban time grows by specified multipliers 
+# corresponding ban count only
 #bantimeextra.factor = 2.0 / 2.885385
+
 # "bantimeextra.formula" used to calculate next value of ban time;
 #bantimeextra.formula = banTime * math.exp(float(banCount)*banFactor)/math.exp(1*banFactor)
+
+# "bantimeextra.multipliers" used to calculate next value of ban time instead of formula, coresponding 
+# previously ban count and given "bantimeextra.factor" (for multipliers default is 1);
+# following example grows ban time by 1, 2, 4, 8, 16 ... and if last ban count greater as multipliers count, 
+# always used last multiplier (64 in example), for factor '1' and original ban time 600 - 10.6 hours
+#bantimeextra.multipliers = 1 2 4 8 16 32 64
+# following example can be used for small initial ban time (bantime=60) - it grows more aggressive at begin,
+# for bantime=60 the multipliers are minutes and equal: 1 min, 5 min, 30 min, 1 hour, 5 hour, 12 hour, 1 day, 2 day
+#bantimeextra.multipliers = 1 5 30 60 300 720 1440 2880
+
 # "bantimeextra.overalljails" (if true) specifies the search of IP in the database will be executed 
 # cross over all jails, if false (dafault), only current jail of the ban IP will be searched
 #bantimeextra.overalljails = false

fail2ban/client/jailreader.py

@@ -97,6 +97,7 @@ class JailReader(ConfigReader):
 				["string", "bantimeextra.findtime", None],
 				["string", "bantimeextra.factor", None],
 				["string", "bantimeextra.formula", None],
+				["string", "bantimeextra.multipliers", None],
 				["string", "bantimeextra.maxtime", None],
 				["string", "bantimeextra.rndtime", None],
 				["bool",   "bantimeextra.overalljails", None],

fail2ban/server/actions.py

@@ -242,10 +242,18 @@ class Actions(JailThread, Mapping):
 		logSys.debug(self._jail.name + ": action terminated")
 		return True
 
+	class BanTimeIncr:
+		def __init__(self, banTime, banCount):
+			self.Time = banTime
+			self.Count = banCount
+
 	def setBanTimeExtra(self, opt, value):
 		# merge previous extra with new option:
 		be = self._banExtra;
-		be[opt] = value;
+		if value is not None:
+			be[opt] = value;
+		else:
+			del be[opt]
 		logSys.info('Set banTimeExtra.%s = %s', opt, value)
 		if opt == 'enabled':
 			if isinstance(value, str):
@@ -255,18 +263,31 @@ class Actions(JailThread, Mapping):
 		if opt in ['findtime', 'maxtime', 'rndtime']:
 			if not value is None:
 				be[opt] = eval(value)
-		if opt == 'factor' or be.get('factor', None) is None:
-			be['factor'] = eval(be.get('factor', "2.0 / 2.885385"));
-		# prepare formula :
-		if opt in ['formula', 'maxtime', 'rndtime'] or be.get('evformula', None) is None:
-			be['formula'] = be.get('formula', 'banTime * math.exp(float(banCount)*banFactor)/math.exp(1*banFactor)')
-			evformula = be['formula'];
-			evformula = ('max(banTime, %s)' % evformula)
+		# prepare formula lambda:
+		if opt in ['formula', 'factor', 'maxtime', 'rndtime', 'multipliers'] or be.get('evformula', None) is None:
+			# split multifiers to an array begins with 0 (or empty if not set):
+			if opt == 'multipliers':
+				be['evmultipliers'] = [int(i) for i in (value.split(' ') if value is not None and value != '' else [])]
+			# if we have multifiers - use it in lambda, otherwise compile and use formula within lambda
+			multipliers = be.get('evmultipliers', [])
+			if len(multipliers):
+				banFactor = eval(be.get('factor', "1"))
+				evformula = lambda ban, banFactor=banFactor: (
+					ban.Time * banFactor * multipliers[ban.Count if ban.Count < len(multipliers) else -1]
+				)
+			else:
+				banFactor = eval(be.get('factor', "2.0 / 2.885385"))
+				formula = be.get('formula', 'ban.Time * math.exp(float(ban.Count+1)*banFactor)/math.exp(1*banFactor)')
+				formula = compile(formula, '~inline-conf-expr~', 'eval')
+				evformula = lambda ban, banFactor=banFactor, formula=formula: max(ban.Time, eval(formula))
+			# extend lambda with max time :
 			if not be.get('maxtime', None) is None:
-				evformula = ('min(%s, %s)' % (evformula, be['maxtime']))
-			# mix with random time (to prevent botnet calc exact time IP can be unbanned):
+				maxtime = be['maxtime']
+				evformula = lambda ban, evformula=evformula: min(evformula(ban), maxtime)
+			# mix lambda with random time (to prevent bot-nets to calculate exact time IP can be unbanned):
 			if not be.get('rndtime', None) is None:
-				evformula = ('(%s + random.random() * %s)' % (evformula, be['rndtime']))
+				rndtime = be['rndtime']
+				evformula = lambda ban, evformula=evformula: (evformula(ban) + random.random() * rndtime)
 			# set to extra dict:
 			be['evformula'] = evformula
 		#logSys.info('banTimeExtra : %s' % json.dumps(be))
@@ -274,6 +295,9 @@ class Actions(JailThread, Mapping):
 	def getBanTimeExtra(self, opt):
 		return self._banExtra.get(opt, None)
 
+	def calcBanTime(self, banTime, banCount):
+		return self._banExtra['evformula'](self.BanTimeIncr(banTime, banCount))
+
 	def incrBanTime(self, bTicket, ip):
 		"""Check for IP address to increment ban time (if was already banned).
 
@@ -288,7 +312,6 @@ class Actions(JailThread, Mapping):
 		try:
 			be = self._banExtra;
 			if banTime > 0 and be.get('enabled', False):
-				banFactor = be['factor'];
 				# search IP in database and increase time if found:
 				for banCount, timeOfBan, lastBanTime in \
 				  self._jail.database.getBan(ip, self._jail, be.get('findtime', None), be.get('overalljails', False) \
@@ -296,7 +319,8 @@ class Actions(JailThread, Mapping):
 					#logSys.debug('IP %s was already banned: %s #, %s' % (ip, banCount, timeOfBan));
 					bTicket.setBanCount(banCount);
 					# calculate new ban time
-					banTime = eval(be['evformula'])
+					if banCount > 0:
+						banTime = be['evformula'](self.BanTimeIncr(banTime, banCount))
 					bTicket.setBanTime(banTime);
 					logSys.info('[%s] %s was already banned: %s # at last %s - increase time %s to %s' % (self._jail.name, ip, banCount, 
 						datetime.datetime.fromtimestamp(timeOfBan).strftime("%Y-%m-%d %H:%M:%S"),