hash加密算法有哪些_https密码学原理

一、Base64 简介

Base64 不是加密算法 , 是一种 可读性算法 , 其目的不是用于保护数据 , 其目的是为了可读性 ;

普通的二进制数据随机性很大 , 使用二进制文件打开后 , 参考下图 , 有很多奇怪的字符 , 都叫不上名称 , 可读性很差 , 也没办法表述出来 ;

使用 Base64 之后 , 其可读性增强很多 , 标准的 Base64 编码只能从下面的字符中选择字符 ;

private static final byte ENCODE[] = { 
   
    'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P',
    'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', 'a', 'b', 'c', 'd', 'e', 'f',
    'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v',
    'w', 'x', 'y', 'z', '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '+', '/',
};

Base64 由 $64$ 个字符组成 , 包括大写 A-Z , 小写 a-z , 数字 0-9 , 两个符号 + 和 / , 上面代码中的 ENCODE 字符数组中的 $64$ 个字符 ;

比特币中有一种 Base58 编码方式 , 其字符包括大写 A-Z ( 没有 I 字母 ) , 小写 a-z ( 没有 o, i 字母 ) , 数字 1-9 , 没有数字 $0$ , 这是因为数字 $0$ 与字母 o 不好区分 , 此外没有 + 和 / 符号 ;

Base58 编码比 Base64 少了 数字 $0$ , 小写字母 i, o, 大写字母 I , 两个符号 + 和 / ;

二、Base64 编码原理

Base64 编码中 , $3$ 个字节一组 , 每个字节 $8$ 位 , 总共 $24$ 位 ;

将每组的 $3$ 个字节 , 分为 $4$ 组 , 每组 $6$ 位 ;

一个字节应该是 $8$ 位 , 缺少两位 , 在高位的 $2$ 位进行补齐 , 在高位补 $0$ ;

每个字节只有后 $6$ 位有效数字 , 可以将字节的实际数据控制在 $0$ ~ $63$ 之间 ;

$6$ 位二进制数取值范围是 $0$ ~ $2^6-1$ ;

$2^6=64$

$0$ ~ $63$ 对应的字符索引表如下 :

三、最后编码组字节不足时补位 ‘=’ 符号

Base64 编码中 , 没有等号符号 ;

Base64 编码中 , 以 $3$ 位为一组 , 但是编码到最后 , 可能只剩下 $1$ 个或 $2$ 个字符组成 ;

如果只剩下 $1$ 位 , 此时需要在后面补充两个 ‘=’ 符号 , 一个实际 byte 和两个 ‘=’ 组成最后一组编码组 ;

如果最后剩下 $2$ 位 , 则在后面补充 $1$ 个 ‘=’ , $2$ 个实际 byte 和 $1$ 个 ‘=’ 组成最后一个编码组 ;

四、Base64 编码实现参考

Android 中实现的 Base64 算法 ;

/* * Copyright (C) 2010 The Android Open Source Project * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */

package android.util;

import java.io.UnsupportedEncodingException;

/** * Utilities for encoding and decoding the Base64 representation of * binary data. See RFCs <a * href="http://www.ietf.org/rfc/rfc2045.txt">2045</a> and <a * href="http://www.ietf.org/rfc/rfc3548.txt">3548</a>. */
public class Base64 { 
   
    /** * Default values for encoder/decoder flags. */
    public static final int DEFAULT = 0;

    /** * Encoder flag bit to omit the padding '=' characters at the end * of the output (if any). */
    public static final int NO_PADDING = 1;

    /** * Encoder flag bit to omit all line terminators (i.e., the output * will be on one long line). */
    public static final int NO_WRAP = 2;

    /** * Encoder flag bit to indicate lines should be terminated with a * CRLF pair instead of just an LF. Has no effect if {@code * NO_WRAP} is specified as well. */
    public static final int CRLF = 4;

    /** * Encoder/decoder flag bit to indicate using the "URL and * filename safe" variant of Base64 (see RFC 3548 section 4) where * {@code -} and {@code _} are used in place of {@code +} and * {@code /}. */
    public static final int URL_SAFE = 8;

    /** * Flag to pass to {@link Base64OutputStream} to indicate that it * should not close the output stream it is wrapping when it * itself is closed. */
    public static final int NO_CLOSE = 16;

    // --------------------------------------------------------
    // shared code
    // --------------------------------------------------------

    /* package */ static abstract class Coder { 
   
        public byte[] output;
        public int op;

        /** * Encode/decode another block of input data. this.output is * provided by the caller, and must be big enough to hold all * the coded data. On exit, this.opwill be set to the length * of the coded data. * * @param finish true if this is the final call to process for * this object. Will finalize the coder state and * include any final bytes in the output. * * @return true if the input so far is good; false if some * error has been detected in the input stream.. */
        public abstract boolean process(byte[] input, int offset, int len, boolean finish);

        /** * @return the maximum number of bytes a call to process() * could produce for the given number of input bytes. This may * be an overestimate. */
        public abstract int maxOutputSize(int len);
    }

    // --------------------------------------------------------
    // decoding
    // --------------------------------------------------------

    /** * Decode the Base64-encoded data in input and return the data in * a new byte array. * * <p>The padding '=' characters at the end are considered optional, but * if any are present, there must be the correct number of them. * * @param str the input String to decode, which is converted to * bytes using the default charset * @param flags controls certain features of the decoded output. * Pass {@code DEFAULT} to decode standard Base64. * * @throws IllegalArgumentException if the input contains * incorrect padding */
    public static byte[] decode(String str, int flags) { 
   
        return decode(str.getBytes(), flags);
    }

    /** * Decode the Base64-encoded data in input and return the data in * a new byte array. * * <p>The padding '=' characters at the end are considered optional, but * if any are present, there must be the correct number of them. * * @param input the input array to decode * @param flags controls certain features of the decoded output. * Pass {@code DEFAULT} to decode standard Base64. * * @throws IllegalArgumentException if the input contains * incorrect padding */
    public static byte[] decode(byte[] input, int flags) { 
   
        return decode(input, 0, input.length, flags);
    }

    /** * Decode the Base64-encoded data in input and return the data in * a new byte array. * * <p>The padding '=' characters at the end are considered optional, but * if any are present, there must be the correct number of them. * * @param input the data to decode * @param offset the position within the input array at which to start * @param len the number of bytes of input to decode * @param flags controls certain features of the decoded output. * Pass {@code DEFAULT} to decode standard Base64. * * @throws IllegalArgumentException if the input contains * incorrect padding */
    public static byte[] decode(byte[] input, int offset, int len, int flags) { 
   
        // Allocate space for the most data the input could represent.
        // (It could contain less if it contains whitespace, etc.)
        Decoder decoder = new Decoder(flags, new byte[len*3/4]);

        if (!decoder.process(input, offset, len, true)) { 
   
            throw new IllegalArgumentException("bad base-64");
        }

        // Maybe we got lucky and allocated exactly enough output space.
        if (decoder.op == decoder.output.length) { 
   
            return decoder.output;
        }

        // Need to shorten the array, so allocate a new one of the
        // right size and copy.
        byte[] temp = new byte[decoder.op];
        System.arraycopy(decoder.output, 0, temp, 0, decoder.op);
        return temp;
    }

    /* package */ static class Decoder extends Coder { 
   
        /** * Lookup table for turning bytes into their position in the * Base64 alphabet. */
        private static final int DECODE[] = { 
   
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 62, -1, -1, -1, 63,
            52, 53, 54, 55, 56, 57, 58, 59, 60, 61, -1, -1, -1, -2, -1, -1,
            -1,  0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14,
            15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, -1, -1, -1, -1, -1,
            -1, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
            41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, -1, -1, -1, -1, -1,
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
        };

        /** * Decode lookup table for the "web safe" variant (RFC 3548 * sec. 4) where - and _ replace + and /. */
        private static final int DECODE_WEBSAFE[] = { 
   
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 62, -1, -1,
            52, 53, 54, 55, 56, 57, 58, 59, 60, 61, -1, -1, -1, -2, -1, -1,
            -1,  0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14,
            15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, -1, -1, -1, -1, 63,
            -1, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
            41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, -1, -1, -1, -1, -1,
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
            -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
        };

        /** Non-data values in the DECODE arrays. */
        private static final int SKIP = -1;
        private static final int EQUALS = -2;

        /** * States 0-3 are reading through the next input tuple. * State 4 is having read one '=' and expecting exactly * one more. * State 5 is expecting no more data or padding characters * in the input. * State 6 is the error state; an error has been detected * in the input and no future input can "fix" it. */
        private int state;   // state number (0 to 6)
        private int value;

        final private int[] alphabet;

        public Decoder(int flags, byte[] output) { 
   
            this.output = output;

            alphabet = ((flags & URL_SAFE) == 0) ? DECODE : DECODE_WEBSAFE;
            state = 0;
            value = 0;
        }

        /** * @return an overestimate for the number of bytes {@code * len} bytes could decode to. */
        public int maxOutputSize(int len) { 
   
            return len * 3/4 + 10;
        }

        /** * Decode another block of input data. * * @return true if the state machine is still healthy. false if * bad base-64 data has been detected in the input stream. */
        public boolean process(byte[] input, int offset, int len, boolean finish) { 
   
            if (this.state == 6) return false;

            int p = offset;
            len += offset;

            // Using local variables makes the decoder about 12%
            // faster than if we manipulate the member variables in
            // the loop. (Even alphabet makes a measurable
            // difference, which is somewhat surprising to me since
            // the member variable is final.)
            int state = this.state;
            int value = this.value;
            int op = 0;
            final byte[] output = this.output;
            final int[] alphabet = this.alphabet;

            while (p < len) { 
   
                // Try the fast path: we're starting a new tuple and the
                // next four bytes of the input stream are all data
                // bytes. This corresponds to going through states
                // 0-1-2-3-0. We expect to use this method for most of
                // the data.
                //
                // If any of the next four bytes of input are non-data
                // (whitespace, etc.), value will end up negative. (All
                // the non-data values in decode are small negative
                // numbers, so shifting any of them up and or'ing them
                // together will result in a value with its top bit set.)
                //
                // You can remove this whole block and the output should
                // be the same, just slower.
                if (state == 0) { 
   
                    while (p+4 <= len &&
                           (value = ((alphabet[input[p] & 0xff] << 18) |
                                     (alphabet[input[p+1] & 0xff] << 12) |
                                     (alphabet[input[p+2] & 0xff] << 6) |
                                     (alphabet[input[p+3] & 0xff]))) >= 0) { 
   
                        output[op+2] = (byte) value;
                        output[op+1] = (byte) (value >> 8);
                        output[op] = (byte) (value >> 16);
                        op += 3;
                        p += 4;
                    }
                    if (p >= len) break;
                }

                // The fast path isn't available -- either we've read a
                // partial tuple, or the next four input bytes aren't all
                // data, or whatever. Fall back to the slower state
                // machine implementation.

                int d = alphabet[input[p++] & 0xff];

                switch (state) { 
   
                case 0:
                    if (d >= 0) { 
   
                        value = d;
                        ++state;
                    } else if (d != SKIP) { 
   
                        this.state = 6;
                        return false;
                    }
                    break;

                case 1:
                    if (d >= 0) { 
   
                        value = (value << 6) | d;
                        ++state;
                    } else if (d != SKIP) { 
   
                        this.state = 6;
                        return false;
                    }
                    break;

                case 2:
                    if (d >= 0) { 
   
                        value = (value << 6) | d;
                        ++state;
                    } else if (d == EQUALS) { 
   
                        // Emit the last (partial) output tuple;
                        // expect exactly one more padding character.
                        output[op++] = (byte) (value >> 4);
                        state = 4;
                    } else if (d != SKIP) { 
   
                        this.state = 6;
                        return false;
                    }
                    break;

                case 3:
                    if (d >= 0) { 
   
                        // Emit the output triple and return to state 0.
                        value = (value << 6) | d;
                        output[op+2] = (byte) value;
                        output[op+1] = (byte) (value >> 8);
                        output[op] = (byte) (value >> 16);
                        op += 3;
                        state = 0;
                    } else if (d == EQUALS) { 
   
                        // Emit the last (partial) output tuple;
                        // expect no further data or padding characters.
                        output[op+1] = (byte) (value >> 2);
                        output[op] = (byte) (value >> 10);
                        op += 2;
                        state = 5;
                    } else if (d != SKIP) { 
   
                        this.state = 6;
                        return false;
                    }
                    break;

                case 4:
                    if (d == EQUALS) { 
   
                        ++state;
                    } else if (d != SKIP) { 
   
                        this.state = 6;
                        return false;
                    }
                    break;

                case 5:
                    if (d != SKIP) { 
   
                        this.state = 6;
                        return false;
                    }
                    break;
                }
            }

            if (!finish) { 
   
                // We're out of input, but a future call could provide
                // more.
                this.state = state;
                this.value = value;
                this.op = op;
                return true;
            }

            // Done reading input. Now figure out where we are left in
            // the state machine and finish up.

            switch (state) { 
   
            case 0:
                // Output length is a multiple of three. Fine.
                break;
            case 1:
                // Read one extra input byte, which isn't enough to
                // make another output byte. Illegal.
                this.state = 6;
                return false;
            case 2:
                // Read two extra input bytes, enough to emit 1 more
                // output byte. Fine.
                output[op++] = (byte) (value >> 4);
                break;
            case 3:
                // Read three extra input bytes, enough to emit 2 more
                // output bytes. Fine.
                output[op++] = (byte) (value >> 10);
                output[op++] = (byte) (value >> 2);
                break;
            case 4:
                // Read one padding '=' when we expected 2. Illegal.
                this.state = 6;
                return false;
            case 5:
                // Read all the padding '='s we expected and no more.
                // Fine.
                break;
            }

            this.state = state;
            this.op = op;
            return true;
        }
    }

    // --------------------------------------------------------
    // encoding
    // --------------------------------------------------------

    /** * Base64-encode the given data and return a newly allocated * String with the result. * * @param input the data to encode * @param flags controls certain features of the encoded output. * Passing {@code DEFAULT} results in output that * adheres to RFC 2045. */
    public static String encodeToString(byte[] input, int flags) { 
   
        try { 
   
            return new String(encode(input, flags), "US-ASCII");
        } catch (UnsupportedEncodingException e) { 
   
            // US-ASCII is guaranteed to be available.
            throw new AssertionError(e);
        }
    }

    /** * Base64-encode the given data and return a newly allocated * String with the result. * * @param input the data to encode * @param offset the position within the input array at which to * start * @param len the number of bytes of input to encode * @param flags controls certain features of the encoded output. * Passing {@code DEFAULT} results in output that * adheres to RFC 2045. */
    public static String encodeToString(byte[] input, int offset, int len, int flags) { 
   
        try { 
   
            return new String(encode(input, offset, len, flags), "US-ASCII");
        } catch (UnsupportedEncodingException e) { 
   
            // US-ASCII is guaranteed to be available.
            throw new AssertionError(e);
        }
    }

    /** * Base64-encode the given data and return a newly allocated * byte[] with the result. * * @param input the data to encode * @param flags controls certain features of the encoded output. * Passing {@code DEFAULT} results in output that * adheres to RFC 2045. */
    public static byte[] encode(byte[] input, int flags) { 
   
        return encode(input, 0, input.length, flags);
    }

    /** * Base64-encode the given data and return a newly allocated * byte[] with the result. * * @param input the data to encode * @param offset the position within the input array at which to * start * @param len the number of bytes of input to encode * @param flags controls certain features of the encoded output. * Passing {@code DEFAULT} results in output that * adheres to RFC 2045. */
    public static byte[] encode(byte[] input, int offset, int len, int flags) { 
   
        Encoder encoder = new Encoder(flags, null);

        // Compute the exact length of the array we will produce.
        int output_len = len / 3 * 4;

        // Account for the tail of the data and the padding bytes, if any.
        if (encoder.do_padding) { 
   
            if (len % 3 > 0) { 
   
                output_len += 4;
            }
        } else { 
   
            switch (len % 3) { 
   
                case 0: break;
                case 1: output_len += 2; break;
                case 2: output_len += 3; break;
            }
        }

        // Account for the newlines, if any.
        if (encoder.do_newline && len > 0) { 
   
            output_len += (((len-1) / (3 * Encoder.LINE_GROUPS)) + 1) *
                (encoder.do_cr ? 2 : 1);
        }

        encoder.output = new byte[output_len];
        encoder.process(input, offset, len, true);

        assert encoder.op == output_len;

        return encoder.output;
    }

    /* package */ static class Encoder extends Coder { 
   
        /** * Emit a new line every this many output tuples. Corresponds to * a 76-character line length (the maximum allowable according to * <a href="http://www.ietf.org/rfc/rfc2045.txt">RFC 2045</a>). */
        public static final int LINE_GROUPS = 19;

        /** * Lookup table for turning Base64 alphabet positions (6 bits) * into output bytes. */
        private static final byte ENCODE[] = { 
   
            'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P',
            'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', 'a', 'b', 'c', 'd', 'e', 'f',
            'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v',
            'w', 'x', 'y', 'z', '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '+', '/',
        };

        /** * Lookup table for turning Base64 alphabet positions (6 bits) * into output bytes. */
        private static final byte ENCODE_WEBSAFE[] = { 
   
            'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P',
            'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', 'a', 'b', 'c', 'd', 'e', 'f',
            'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v',
            'w', 'x', 'y', 'z', '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '-', '_',
        };

        final private byte[] tail;
        /* package */ int tailLen;
        private int count;

        final public boolean do_padding;
        final public boolean do_newline;
        final public boolean do_cr;
        final private byte[] alphabet;

        public Encoder(int flags, byte[] output) { 
   
            this.output = output;

            do_padding = (flags & NO_PADDING) == 0;
            do_newline = (flags & NO_WRAP) == 0;
            do_cr = (flags & CRLF) != 0;
            alphabet = ((flags & URL_SAFE) == 0) ? ENCODE : ENCODE_WEBSAFE;

            tail = new byte[2];
            tailLen = 0;

            count = do_newline ? LINE_GROUPS : -1;
        }

        /** * @return an overestimate for the number of bytes {@code * len} bytes could encode to. */
        public int maxOutputSize(int len) { 
   
            return len * 8/5 + 10;
        }

        public boolean process(byte[] input, int offset, int len, boolean finish) { 
   
            // Using local variables makes the encoder about 9% faster.
            final byte[] alphabet = this.alphabet;
            final byte[] output = this.output;
            int op = 0;
            int count = this.count;

            int p = offset;
            len += offset;
            int v = -1;

            // First we need to concatenate the tail of the previous call
            // with any input bytes available now and see if we can empty
            // the tail.

            switch (tailLen) { 
   
                case 0:
                    // There was no tail.
                    break;

                case 1:
                    if (p+2 <= len) { 
   
                        // A 1-byte tail with at least 2 bytes of
                        // input available now.
                        v = ((tail[0] & 0xff) << 16) |
                            ((input[p++] & 0xff) << 8) |
                            (input[p++] & 0xff);
                        tailLen = 0;
                    };
                    break;

                case 2:
                    if (p+1 <= len) { 
   
                        // A 2-byte tail with at least 1 byte of input.
                        v = ((tail[0] & 0xff) << 16) |
                            ((tail[1] & 0xff) << 8) |
                            (input[p++] & 0xff);
                        tailLen = 0;
                    }
                    break;
            }

            if (v != -1) { 
   
                output[op++] = alphabet[(v >> 18) & 0x3f];
                output[op++] = alphabet[(v >> 12) & 0x3f];
                output[op++] = alphabet[(v >> 6) & 0x3f];
                output[op++] = alphabet[v & 0x3f];
                if (--count == 0) { 
   
                    if (do_cr) output[op++] = '\r';
                    output[op++] = '\n';
                    count = LINE_GROUPS;
                }
            }

            // At this point either there is no tail, or there are fewer
            // than 3 bytes of input available.

            // The main loop, turning 3 input bytes into 4 output bytes on
            // each iteration.
            while (p+3 <= len) { 
   
                v = ((input[p] & 0xff) << 16) |
                    ((input[p+1] & 0xff) << 8) |
                    (input[p+2] & 0xff);
                output[op] = alphabet[(v >> 18) & 0x3f];
                output[op+1] = alphabet[(v >> 12) & 0x3f];
                output[op+2] = alphabet[(v >> 6) & 0x3f];
                output[op+3] = alphabet[v & 0x3f];
                p += 3;
                op += 4;
                if (--count == 0) { 
   
                    if (do_cr) output[op++] = '\r';
                    output[op++] = '\n';
                    count = LINE_GROUPS;
                }
            }

            if (finish) { 
   
                // Finish up the tail of the input. Note that we need to
                // consume any bytes in tail before any bytes
                // remaining in input; there should be at most two bytes
                // total.

                if (p-tailLen == len-1) { 
   
                    int t = 0;
                    v = ((tailLen > 0 ? tail[t++] : input[p++]) & 0xff) << 4;
                    tailLen -= t;
                    output[op++] = alphabet[(v >> 6) & 0x3f];
                    output[op++] = alphabet[v & 0x3f];
                    if (do_padding) { 
   
                        output[op++] = '=';
                        output[op++] = '=';
                    }
                    if (do_newline) { 
   
                        if (do_cr) output[op++] = '\r';
                        output[op++] = '\n';
                    }
                } else if (p-tailLen == len-2) { 
   
                    int t = 0;
                    v = (((tailLen > 1 ? tail[t++] : input[p++]) & 0xff) << 10) |
                        (((tailLen > 0 ? tail[t++] : input[p++]) & 0xff) << 2);
                    tailLen -= t;
                    output[op++] = alphabet[(v >> 12) & 0x3f];
                    output[op++] = alphabet[(v >> 6) & 0x3f];
                    output[op++] = alphabet[v & 0x3f];
                    if (do_padding) { 
   
                        output[op++] = '=';
                    }
                    if (do_newline) { 
   
                        if (do_cr) output[op++] = '\r';
                        output[op++] = '\n';
                    }
                } else if (do_newline && op > 0 && count != LINE_GROUPS) { 
   
                    if (do_cr) output[op++] = '\r';
                    output[op++] = '\n';
                }

                assert tailLen == 0;
                assert p == len;
            } else { 
   
                // Save the leftovers in tail to be consumed on the next
                // call to encodeInternal.

                if (p == len-1) { 
   
                    tail[tailLen++] = input[p];
                } else if (p == len-2) { 
   
                    tail[tailLen++] = input[p];
                    tail[tailLen++] = input[p+1];
                }
            }

            this.op = op;
            this.count = count;

            return true;
        }
    }

    private Base64() { 
    }   // don't instantiate
}

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