diff --git a/.rubocop_todo.yml b/.rubocop_todo.yml
index 5d7a97d6..b053b403 100644
--- a/.rubocop_todo.yml
+++ b/.rubocop_todo.yml
@@ -126,11 +126,12 @@ Style/MethodCallWithoutArgsParentheses:
   Exclude:
     - 'spec/jwt_spec.rb'
 
-# Offense count: 1
+# Offense count: 2
 # Configuration parameters: EnforcedStyle.
 # SupportedStyles: module_function, extend_self
 Style/ModuleFunction:
   Exclude:
+    - 'lib/jwt/algos.rb'
     - 'lib/jwt/signature.rb'
 
 # Offense count: 1
diff --git a/lib/jwt/algos.rb b/lib/jwt/algos.rb
new file mode 100644
index 00000000..aa46a60f
--- /dev/null
+++ b/lib/jwt/algos.rb
@@ -0,0 +1,44 @@
+# frozen_string_literal: true
+
+require 'jwt/algos/hmac'
+require 'jwt/algos/eddsa'
+require 'jwt/algos/ecdsa'
+require 'jwt/algos/rsa'
+require 'jwt/algos/ps'
+require 'jwt/algos/none'
+require 'jwt/algos/unsupported'
+
+# JWT::Signature module
+module JWT
+  # Signature logic for JWT
+  module Algos
+    extend self
+
+    ALGOS = [
+      Algos::Hmac,
+      Algos::Ecdsa,
+      Algos::Rsa,
+      Algos::Eddsa,
+      Algos::Ps,
+      Algos::None,
+      Algos::Unsupported
+    ].freeze
+
+    def find(algorithm)
+      indexed[algorithm && algorithm.downcase]
+    end
+
+    private
+
+    def indexed
+      @indexed ||= begin
+        fallback = [Algos::Unsupported, nil]
+        ALGOS.each_with_object(Hash.new(fallback)) do |alg, hash|
+          alg.const_get(:SUPPORTED).each do |code|
+            hash[code.downcase] = [alg, code]
+          end
+        end
+      end
+    end
+  end
+end
diff --git a/lib/jwt/algos/none.rb b/lib/jwt/algos/none.rb
new file mode 100644
index 00000000..17d15f14
--- /dev/null
+++ b/lib/jwt/algos/none.rb
@@ -0,0 +1,15 @@
+module JWT
+  module Algos
+    module None
+      module_function
+
+      SUPPORTED = %w[none].freeze
+
+      def sign(*); end
+
+      def verify(*)
+        true
+      end
+    end
+  end
+end
diff --git a/lib/jwt/algos/unsupported.rb b/lib/jwt/algos/unsupported.rb
index 99ddcb71..179a262e 100644
--- a/lib/jwt/algos/unsupported.rb
+++ b/lib/jwt/algos/unsupported.rb
@@ -3,14 +3,15 @@ module Algos
     module Unsupported
       module_function
 
-      SUPPORTED = Object.new.tap { |object| object.define_singleton_method(:include?) { |*| true } }
-      def verify(*)
-        raise JWT::VerificationError, 'Algorithm not supported'
-      end
+      SUPPORTED = [].freeze
 
       def sign(*)
         raise NotImplementedError, 'Unsupported signing method'
       end
+
+      def verify(*)
+        raise JWT::VerificationError, 'Algorithm not supported'
+      end
     end
   end
 end
diff --git a/lib/jwt/decode.rb b/lib/jwt/decode.rb
index 9ee144fe..29ff181e 100644
--- a/lib/jwt/decode.rb
+++ b/lib/jwt/decode.rb
@@ -43,22 +43,23 @@ def verify_signature
     end
 
     def options_includes_algo_in_header?
-      allowed_algorithms.include? header['alg']
+      allowed_algorithms.any? { |alg| alg.casecmp(header['alg']).zero? }
     end
 
     def allowed_algorithms
       # Order is very important - first check for string keys, next for symbols
-      if @options.key?('algorithm')
-        [@options['algorithm']]
+      algos = if @options.key?('algorithm')
+        @options['algorithm']
       elsif @options.key?(:algorithm)
-        [@options[:algorithm]]
+        @options[:algorithm]
       elsif @options.key?('algorithms')
-        @options['algorithms'] || []
+        @options['algorithms']
       elsif @options.key?(:algorithms)
-        @options[:algorithms] || []
+        @options[:algorithms]
       else
         []
       end
+      Array(algos)
     end
 
     def find_key(&keyfinder)
diff --git a/lib/jwt/encode.rb b/lib/jwt/encode.rb
index 35ddba79..bdeeab2f 100644
--- a/lib/jwt/encode.rb
+++ b/lib/jwt/encode.rb
@@ -1,5 +1,6 @@
 # frozen_string_literal: true
 
+require_relative './algos'
 require_relative './claims_validator'
 
 # JWT::Encode module
@@ -10,10 +11,10 @@ class Encode
     ALG_KEY  = 'alg'.freeze
 
     def initialize(options)
-      @payload   = options[:payload]
-      @key       = options[:key]
-      @algorithm = options[:algorithm]
-      @headers   = options[:headers].each_with_object({}) { |(key, value), headers| headers[key.to_s] = value }
+      @payload = options[:payload]
+      @key = options[:key]
+      _, @algorithm = Algos.find(options[:algorithm])
+      @headers = options[:headers].each_with_object({}) { |(key, value), headers| headers[key.to_s] = value }
     end
 
     def segments
diff --git a/lib/jwt/signature.rb b/lib/jwt/signature.rb
index f4a73282..e490d9eb 100644
--- a/lib/jwt/signature.rb
+++ b/lib/jwt/signature.rb
@@ -2,12 +2,7 @@
 
 require 'jwt/security_utils'
 require 'openssl'
-require 'jwt/algos/hmac'
-require 'jwt/algos/eddsa'
-require 'jwt/algos/ecdsa'
-require 'jwt/algos/rsa'
-require 'jwt/algos/ps'
-require 'jwt/algos/unsupported'
+require 'jwt/algos'
 begin
   require 'rbnacl'
 rescue LoadError
@@ -19,33 +14,21 @@ module JWT
   # Signature logic for JWT
   module Signature
     extend self
-    ALGOS = [
-      Algos::Hmac,
-      Algos::Ecdsa,
-      Algos::Rsa,
-      Algos::Eddsa,
-      Algos::Ps,
-      Algos::Unsupported
-    ].freeze
     ToSign = Struct.new(:algorithm, :msg, :key)
     ToVerify = Struct.new(:algorithm, :public_key, :signing_input, :signature)
 
     def sign(algorithm, msg, key)
-      algo = ALGOS.find do |alg|
-        alg.const_get(:SUPPORTED).include? algorithm
-      end
-      algo.sign ToSign.new(algorithm, msg, key)
+      algo, code = Algos.find(algorithm)
+      algo.sign ToSign.new(code, msg, key)
     end
 
     def verify(algorithm, key, signing_input, signature)
-      return true if algorithm == 'none'
+      return true if algorithm.casecmp('none').zero?
 
       raise JWT::DecodeError, 'No verification key available' unless key
 
-      algo = ALGOS.find do |alg|
-        alg.const_get(:SUPPORTED).include? algorithm
-      end
-      verified = algo.verify(ToVerify.new(algorithm, key, signing_input, signature))
+      algo, code = Algos.find(algorithm)
+      verified = algo.verify(ToVerify.new(code, key, signing_input, signature))
       raise(JWT::VerificationError, 'Signature verification raised') unless verified
     rescue OpenSSL::PKey::PKeyError
       raise JWT::VerificationError, 'Signature verification raised'
diff --git a/spec/jwt_spec.rb b/spec/jwt_spec.rb
index 1ffedc99..a5e5f3d6 100644
--- a/spec/jwt_spec.rb
+++ b/spec/jwt_spec.rb
@@ -510,4 +510,25 @@
       end.not_to raise_error
     end
   end
+
+  context 'algorithm case insensitivity' do
+    let(:payload) { { 'a' => 1, 'b' => 'b' } }
+
+    it 'ignores algorithm casing during encode/decode' do
+      enc = JWT.encode(payload, '', 'hs256')
+      expect(JWT.decode(enc, '')).to eq([payload, { 'alg' => 'HS256'}])
+
+      enc = JWT.encode(payload, data[:rsa_private], 'rs512')
+      expect(JWT.decode(enc, data[:rsa_public], true, algorithm: 'RS512')).to eq([payload, { 'alg' => 'RS512'}])
+
+      enc = JWT.encode(payload, data[:rsa_private], 'RS512')
+      expect(JWT.decode(enc, data[:rsa_public], true, algorithm: 'rs512')).to eq([payload, { 'alg' => 'RS512'}])
+    end
+
+    it 'raises error for invalid algorithm' do
+      expect do
+        JWT.encode(payload, '', 'xyz')
+      end.to raise_error(NotImplementedError)
+    end
+  end
 end